Calculation Formulas for the Wave-Induced Steady Horizontal Force and Yaw Moment on a Ship with Forward Speed

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Mekejweg 2,_{2628 co DeIft}

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Reports of Research Institute

_for

Applied Mechanics

Volume XXXVII, Number 107

Februay

1991

Published by

Research Institute for Applied Mechanics KYIJSHU UNIVERSITY, FUKUOKA, JAPAN

Reports of Research Institute for Applied

Mechanics are the continuation of Reports of Research Institute for Fluid Engineering and of

Reports of Research Institute for Elasticity

Engineering, Kyushu University.

The Research Institute should not be

responsi-ble for statements or opinions advanced in the

following papers.

All communications should be addressed to the

director or to the librp.rian of the Institute.

Research Institute for applied Mechanics Kyushu University, Kasiga, 816 Japan

p7ifltedby

SHUKOSHA PRINTING CO. FUKUOKA

Reports of Research Institute for Applied Mechanics

Vol. XXXVII No. 107, 1991

Calculation Formulas for the Wave-Induced

Steady Horizontal Force and Yaw Moment

on a Ship with Forward Speed

By Masashi KAsIirwAGI*

A new analysis method based on the theory of Fourier transform is provided for the added resistance, stèady sway force, and yaw moment acting on an advancing ship in oblique waves. The principle of linear and angular momentwri conservation is used to relate the steady force

and moment to far-field disturbance waves generated by the ship.

Maruo's added-resistance formula is derived easily with the present method in which Parseval's theorem is effectively used in place of the stationary-phase method. The new method is extended to the analysis of the steady sway force and yaw moment. Calculation formulas for these force and moment are obtained in a form analogous to that for the added resistance, involving only the Kochin function as unknown. In the limit of vanishing forward speed, the obtained formulas reduce to Maruo's for the drift force and Newman's for the drift moment.

Key words: Added resistance, Steady sway force, Steady yaw

moment, Momentum principle, Kochin function,

Forward-speed effects

1. Introduction

When a ship is floating on the surface of waves, the mean drifting force and yawing moment will be exerted on the ship as a result of wave actions. These

drift force and moment are of second order in the wave amplitude, but of

engineering importance in designing the control system to maintain the position or heading of ships in waves. A rational theoretical analysis of this subject, based on the priñciple of momentum conservation, was provided first by Maruo'

2 Masashi KASHIWAGI

for the drift force in the horizontal plane and later by Newman2 for the steady yawing moment. It has beén common since these two papers to perform

"exact" numerical computations of the arift force and moment when the ship's forward speed is zero.

When a ship -is' advani ngàt cbn'stañt föfWai-dséèd;'thë ame kind of second-order steady force ändmornent *ill..be. alsò exerted. on the ship.

Maruo34 applied the-momentum-principle analysis to:the case of forward speed present, and provided a formula for the ship's longitudinal component of the steady horizontal force. This component is known as the added resistance in waves and has interested many researchers in the field of naval architecture, because the prediction of wave resistence is crucial in considering economical operations of ships in actual seaways. With this engineering reason, many studies ón the added resistance have been made so far; references of these are includéd in the proceeding of symposium5 held by the Society of Naväl Archi tects of Japan:

In oblique waves, due to the steady sway force and yaw moment, the ship

will advance with the drift angle and check helm to maintain a designated

course and thus experience the increase of resistanëe arising from thèse secon-dary causes. Therefore in discussing the overall propulsive performance of a

ship in wáves, we nèed to focus more áttention on the sway force and yaw

moment besides the added resistance. However no calculation formulas exist for these steady force and moment, involving only the Kochin functioñ as does the added-resistance formula. It may be true that Maruo's addédresistance

analysis can be directly applied to the lateral force component, but it seems difficult to derive a compact formula for the yaw moment, as long as we follow Maruo's procedure of analyzing the momentum relation. His procedure is

complicated, because the statiönary-phase methddis skillfully used to lead to a final experssion. Thus, to succèed in obtaining a compact formula for the

steady yaw moment, we must first develop a new analysis method with which Maruo's added-resistance formula can be easily derived, and next apply it to the principle of angular momentum conservation which relatès the moment on a ship to the far-field ship-generated waves.

The present paper reports the work performed along the above lines. In

the new analysis -method, Parseval's theorem in the Fourier-transfòrm theory is effectively utilized, and thereby complicated calculi seen in Maruo's analysis are avoided. The obtained formulas permit the prediction of the steady sway force

and yaw moment in terms only with the Kochin function equivalent to the far-field disturbance waves. Of course Newman's zero-speed results are

recovered from the present formulas in the limit of vanishing forward speed.

2. Far-fiéld asymptotic form of the velocity potential

For the sake of subsequent analyses on the principle of momentum and enetgy conservation, we need to obtain the asymptotic form of the disturbance

Calculation Formulas for the Wave-Induced Steady Horizontal Force

and Yaw Momeñt on a Ship with Forward Speed 3 velocity potential at large distances from a ship. Let us consider a ship advancing at constant forward velocity U into a plane progressive wave of

amplitude a, circular frequency Wo, and wavenumbér 'k0. The water depth is

assumed infinite and thus k0 = w'/g, with g the acceleration of gravity. The angle of wave incidence, is denoted by and measured as in 'ig. 1, With x _{. 9} corresponding to the following wave. Dueto the effect of :th incident wave,

the ship performs sinusoidal oscillations about its mean position with the

circular frequency of encounter w, which is related to.Woby w = .wokoU cos x.

Fig. i Coordinate ystem and notations

As shown in Fig. 1, we take a right-hand Cartesian coordinate system

O-xyz, translating with the same velocity as that of the ship.

The x-axis is

positive in the direction of ship's forward motion, the y-axis positive starboard, and the z-axis positive downward, with the origin placed on the undisturbed free surface.

To justify the linearity, we assume the amplitudes, of incident wave and

ship's oscillations to be small. Further we assume the flow inviscid with

irrotational motion. Then the velocity potential can be introduced and written by linear assumption as

y, z,

t) = Ux+(x, y, z, t)

' (1)

y, z, t) = Re[Ø(x, y, z)eitvh] (2)

4 Masashi KASHIWAGI

çao

-

_&L

In the above, o is the potential of the incident wave and ça the disturbane

potential due tò the presence of a ship. The latter is divided into the scattered pòtential Ç07 and the radiâtion potential 'Pi (i

1, 2, «, 6) due to forced

ñotion of the ship in each mode of six degrees of freedom; is the amplitude in the jth mode of motion. The sythbol 'Re' in (2) means the real part to be taken.

The velocity potentials, çao and ça, are governed by Laplace's equation and subject to the linearized free-surface bundary condition

(6)

on z O and the condition of vanishing velocity as z - - In addition, the

disturbance potential ça satisfies a suitable radiation ondition.

From Green's theorem, the disturbancepotential ça- at any point P = (r, y, z) in the fluid is given by

(P)=ff(9,

(Q)-)G(P;Q)dS(Q)

(7)

where Q = (, ij,

) denotes the integration point on the wetted portion of ship hull S, ; a/an is the normal differentiation with respect to the integration point, with the normal defined positive into the ship hull; and G(P; Q) denotés the Green function or source potential which satisfies the same free-surface and radiation conditions as those to be satisfied by ça. With the Fourier-transform technique, this Green function can be written in the form6

G(P;Q)

(-;--7)

i

t°

-- I e''d/c Re I

e _ndn. 2rj-00 .10 _{(n+zv)Jn2±k2}

i [

fk4 _v LLJk1 .1k3

j/k2_v2

r

r

pk3 ° V

+II +I-+

_2iTL J-00 1k2 /o4

/v2k2

where

X e_v )_iY_ol.JvZ_k2_i.r_)d/c

=

K+2kr+-Ç-Calculation Formulas for the Wave-Induced Steady Horizontal Force

and Yaw Moment on a Ship with Forward Speed 5

K=j-, r--,

K0=-k1

= ---[1+2r±1+4r]

k2 2 k3

[12r'14r]

-k4 2

Í1for<k<ki

= sgn(w+kU) = 1 1 for k2 < k <

In the case of r >1/4, wavenumbers k3 ànd k4 given by (13) is not real, and thus the limits of integration in (8) should be interpreted such that k3 = k4 for r >1/

4. (Hereafter this convention will be understood.)

To obtain a far-field approximation to the disturbance potential ça when the transverse distance gil is large let us first consider the asymptotic approxima tion of the Green function itself. It is obvious that all the terms except the last

one in (8) vanish for large values of gil. (Thèse terms represent the local

disturbance in the vicinity of the x-axis.) Therefore, substituting only the last

term of (8) into (7), we obtain the desired approximation of the. velocity

potential valid at large distances from the x-axis:

y, x V _{_VZiEYS_ikXdk}

I2_ k2

e where

H(k) = r r

(--- ----\ _v±iek1,/v2_kLfikdS

j ìs,\dn

(Pan/e

is the Kochin function equivalent to the complex amplitude of the . far-field

disturbance wave. The upper or lower of the complex signs in (15). and (16) is

to be taken according as the sign of y is positive or negative, respectively.

With the convention that the Kochin function is zero outside of the integration range explicitly shown ii (15), we shall write (15) in the form

y, z)

_J:kkH

V/21' _k2

e1v2_k2e2dfc

(17)

Here the notation (14) has been used.

From this equation, we can readily obtain the Fourier transform of the

:Mahi

SHIWAI

F(ço(x, y,

4) fx;

y,

z)edx

(18)

= iEkH(k)

/V2 k2 (19)

Note that neglected in (17) or (19) are only the local disturbances near the x-axis and that the momentum or the energy associatedÌth these terms become infinitely small as the coordinate x tends to plus or minus infinity

The Fourier transform of the incident-wave potential Ço will be derived by substituting (4) into the definition (18), with the reult

F{çoo(x, y, z)} = 2,rô(k_kocosx)e_k0z_0! (20)

where 5(k - k0 cosx) isDirac's delta function, thus contributing only for k = k0

cosx.

For convenience in subseqúent derivations, we decompose the Kochin

func-tión inthe form'

H(k) = C(k)±ikS(k)

(21)

-where

=

f

L(---S(k) ₌

fLH(afl-)(

We note that C(k) and S(k) represent the symmetric and antisymmetric com-ponents, respectively, with respect to the center plane of a ship symmetrical about y = 0.

3. The added resistance

The principle of linear momentum conservation

In this sectiòn, we shall consider by use of the Fourier-transform technique the same problem as that analyzed by Martio4 and show that Maruò's added-resistance formula can be derived with considerable easé. Following Maruo, we begm by considering the rate of change of linear momentum within the fluid domain bounded by the ship's wetted surface SH, thé free surface SF, and a

control surface Sc at a large distance from the ship. Using Gauss' theorem and taking account of that there is no flux acrossSH and SF and that the pressure

is zero on SF, we get:

a'

=

-ff

ndSff[n+pVø(n

Vø)]dS (23)

where is the fluid pressure, p the fluid density, and n the normal vector.

ffns

R = f

_j

f[

flx+ 4-

Linz) ]ds (26)

In the present analysis, instead of the usual control surface of a circular cylinder of large radius about the z-axis, we take two flat plates as the control surface, which are, as shown in Fig. 1, located at y =.± Y and extend fíom x

=

to x = +co and from the instantaneous free surfacè dowñ t z±dx.

(The value of Y is assumed large such that the local waves near the x-axis can be neglected.) Careful readers might be anxious about the nwméntùm flux frori

the vertical planes parallel to the y-axis at x = ± .

H6ever the control

surfäce considered here is of infinite length in the x-diréction and áll thé disturbance waves radiating away from the x-axis are precisely taken into

account. Thus, neglected are only the contributions from thè local waves which

exist only near the x-axis; these will become zero at x = ± in the three-dimensional case.

Note that the x-component of the normal vector is zero on' the present

control surface.

Then, neglecting terms higher than O()-as in-the usual

procedure, we readily obtain from (26)

---=

pfaf:[-

--]'dx

(27)

Here [ ]!y means the difference between the values of the quantity in brackets

at y = Y and at y = - Y.

Substituting (2) into (27) and performing the

time-average calculation, it follows that

Calculation Formulas for the Wave-Induced Steady Horizontal Force

and Yaw Moment.on a Ship with Forward Speed 7 As usual, we take time average of the abofe. Because òf the. periodicity of fluid motion, there can be no net increase of momentum in-the control volume from one cycle to another. Therefore the steady force in the horizontal plane can be related to the far-field velOcity potential, in the ofm

=

-f f

[n+pV(--_

Unz) ]ds (2

where, from Bernoulli's equation,

p{--- U-+vv_gz}

(25)

and n1 is the i-component of the normal vector. In (24) and (25), eq. (1) has been substituted and the overbar in (24) means taking time average.

Since a resistance is defined as the force in the negative x-direction, we obtain from (24) an expression for the added resistance

8 Masashi KASHIWAGI

(34)

Here we have used the convention concerning the integration range noted in

1

-+ I

_{+fi{IH+cI2+'H-I2}

[

fk,

k, - jk k4J kdk 8x I1)2 k2

k

=4pRef

_{dzj [}

_I1ydX

(28)

where the asterisk denotes the complex conjugate.

Next we substitute the velocity potential (3) for Ø into the above. The result will involve terms which are quadratic in the disturbance potential ç and the incident-wave potential ço separately, plus the cross terms of and o. The contributiOn from o alone is zero, because there can be rioforce associated with the undisturbed incident wave system. Taking these into consideration, (28)

can be written in the form

k =

(T+)

(29)

4Refdzf[

]dx

(30)

=

4Ref dzf [

₊ (31)

We notice that the integrations with respect to z are of the fornì to which the fóllowing Fourier-transform theorem (Parseval's theorem) can be applied:

f:f(x)g*(x)

=

f:F(k)G*(k)dk

(32) where F(k) and G(k) are Fourier transforms of 1(x) and g(x), respectively,

which may be calculated from the definition (18).

Letusconsider first eq. (30). Since the potential has exponential.

depen-dence on the coordinate z as seen in (17), the z-integration in (30) can be

carried out with the formula:

fe_20zdz

= -th- (33)

The x-integration in (30), on the other hand, can be performed by applying the Parseval s theorem (32) in terms of the Fourier transform of given by (19)

After perfOrming the z- and z-integrations in this manner, we get the following

result with relative ease. .

Calculation Formulas for the Wave-Induced Steady Horizontal Force

and Yaw Moment on a Ship with Forward Speed 9

deriving (17). In (34), it is understood that k3 = k4 in the case of r>1/4. We proceed to the second term R2 defined by (31). In the calculation of (31), it is sufficient to retain only terms which are independent of the coordinate y, because according to the theory of hyperfúnction7, sinusoidal terms will vanish when taking the limit of Y - after performing the x- and z-integra tions.

Therefore only two cases should be considered here: k0 sin z =

EkIV2_k2 and k0 sin

x = Ek./V2k2.

We begin with the first case, k0 sin x = E01v2_k2. Since we are going to apply the Parseval s theorem (32) to the x-integration in (31) we must consider

the product of the Fourier transforms of and o, given by (19) and (20), respectively. Thus due to Dirac's delta function appearing in (20), we can put k = k0 cos X; from thisand k0 sin x = EkIVO_k2, we have y ko. Therefore

the s-integration in (31) takes the form

jo

(v+ko) - 2v

1 1

(35)

Applying this result and Parseval's theorem, eq. (31) can be reduced to

=

4icocosx Im[H(ko, x)1 (36)

where 'Im' denotes the imaginary part, and H(k0, z) is the function obtained after substituting k k0 cos and EkIy2_ k2 = k0 sin z into the Kochin

func-tion H(k) and thus can be written as

H(ko x)=ff('

a

SH \ an (37)

In the second case of k0 sin z = - Eki v2k2, we can easily confirm that the reductions analogous to the first case lead to the same final result as (36) and

(37). Therefore we have completed all of the necessary integrations.

Substituting (34) and (36)

into (29) gives the formula fôr the added

resistance in waves:

= 8,rko[

t:'

r3x:

}uH+k)12+ H-(k)!2}

X

/2 k2

kdk - 4cosx Im[H(ko, z)] (38)

Principle of energy conservation

In Maruo's analysis, the last term of (38) is transformed further using the energy-conservation principle. Since no external force exists except the con-stant towing force and the gravitational force keeping the equilibrium position of the ship in space, there is no work done or no dissipation of energy. Thus,

.10 - . Masahi KASHIWAGI

owing to the periodic nature of.the flüid motion, we have the reIation

i:

ff

(--

enx)ci.s O (39)

Notihg thát flr

= O oñ the control sutfäce shown in Fig. 1 and neglecting

higher-órder tèrms resulting from the free-surface elevation, the above equation can be transformed as

ff:[* -

]dx

=

4Ref°°dzf[

iwØ

]dx

= 0 (40)

'SÜbstitutiñg '(3) ad decomposihg the result into two parts like (29), we can

write (4Ø) in the form .

4!m f°dzf°[

=

4imf°izf°°[

(41)

The procedure of performing these integrations with respect to x and z is the'same as that for (30) and (31); that is, we apply Parseval's theorem (32) with the Fourier transforms of and o. After straightforward reductions, we

get the following result:

[

f2

C3L: ] {IH(k)I2+ H(k)12}

Iv2-k

dk

= 41m[H(ko, z)] (42)

Here H(ko, z) is the Kochin function defined by (37)

With ths enetgy relation, the added-resistance formula (38) can be recast

in the foim ...

.:

[ k, k3

pga2 = 8rko[ f00

j

f

]IH(k)I2+IH-(k

.X kocosx)dlc (43)

If the relation (21) is substituted for H(k), the above equation can be expressed as

paT

4,rko[ f:'L:'r

].[Ic(x)2+I$k)J2}

Calculation Formulas for the Wave-Induced Steady Horizontal Force

and Yaw Moment on a Ship with Forward Speed 11 Introducing Hanaoka's variable transformation8

K0

{1 2rcosO±I1-4rcosO},

2cosO

we can confirm that (43) or (44) is identical to that derived by Maruo4.

However, a point to be emphasized here is that the derivation in this paper ia quite simple in comparison to Maruo's, because the Fourie-transform technique is used in place of the stationary-phase method which was essential in Maruo's analysis. We can see from (44) that symmetric waves C(k) and antisymmetric waves S(k) contribute independently to the added resistance and no contribution exists from the interaction between them.

4. The steady sway force

The y-component of (24) gives the formula for the steady sway force:

7;;=ff[fl+

Sc

(un)]dS

Evaluating this on the control surface shown in Fig. 1, (46) can be reduced to

1y

I dx

/ _JY

=

(32 (2

\ax/

\3zj

Y

+pg[E

-

_-

-jI

_J-vdx

+O()

-= --'-rdr[

2

a2

4 io

i-L ax

3z

+Ref°[{KIç2I2+ i

-K0 ax

(47)

Here eq. (25) for the pressure p has been substituted and , is the unsteady

elevation of the free surface, which is given by

=

--

(

-

O(q2) (48)

Calculating time average in (47) and substituting (3) for the velocity

potential, we can write (47) in the following decomposed form

jç=

(49) where 2 Y ay j-y (50)

(3

\/

SlY

j

i dx

12 Masashi KASHIWAGI =

+Ref dzf '

[*

₊

*

* ±4Ref[{Kçoçoo*+ q,3O*)}

_]dr

(51)

Note that Y1 represents the contributions from ship-generated disturbance

waves and Y2 the contributions from the interactions of incident wave and

ship-generated waves.

Let us first consider . Yi. In order to apply the Parseval's theorem (32) to

the x-integrations in (50), we need to obtain the Fourier transform of the

derivatives with respect to x y z of the disturbance potential which can be done easily using (19). The z-integration, which is necessary in the first term in (50), can be performed by use of (33). Summarizing these, we obtain the result

:(IH1(k)2_ IH_(k)12){

2(v2-k2) ± 2(v2_k2)

v2k2

(K+-Ç-±2rk)}a'k

=

_{f:(IHJ2_JH:kI2vdk}

(52)

Froth (21), the following relation holds:

IH(k)I2IH(k)I2

= 2ekIm{2C(k)S*(k)} (53)

Thus, recalling the convention about the range of integration with respect to k, eq (52) can be written in the foim

=

-

[f:'r3--L:]

Im{2C(k)S*(k)}1Jdk (54)

Next we consider the second term, Y2, defined by (51). Also here, we apply the Parseval's theorem with the Fourier transforms of and ; these

are given by (19) and (20), respectively. With thereasons stated in transform-ing the iñteraction terms between and o in the added-resistance formula,. we can concentrate on the case of k = k0 cos x, ±Ek./v2 k2 =k0 sin , and thus

y k0. Using these relations, eq. (51) can be transformed as

1

Yz =

---Re[--HIko

[ i /

j

1kocos2x k0

sinx +

--

kosinx

(kox)2 +2rkocosx)}]

(K+

Calculation Fórmulas for the Wave-Induced Steady Horizontal Force

and Yaw Moment oñ a Ship with Forward Speed -13

=

4ko5inx[H(ko, z)]

where H(ko, z) is given by (37).

As in the added-resistance formula, the above result can be put in a different form by applying the principle of energy conservation. Substituting the rela-tion (42) in (55) and expressing the resulting equation in terms of C(k) and

S(k) defined by (21), we get :

=

kosin[ -f:'r3--L:1

-{Ic(k)12+Isç )I2}

1V2_k2¿1k (56)

Therefore, substitution of (54) and (56) into (49) gives the formula for the

second-order steady svay force:

pg2 =

_4r/[

f'+f"+f]Im{2c(k)s*(k)}vdk

+[ f:' +f-f ]ici+ IS(k)12}

k2dk (57)

From this result, we can see that the first-term comes from the interaction between symmetric and antisymmetric waves, whereas thé second term comes from the independent contributions of symmetric and antisymmetric waves Since the second term is multiplied by sin x both terms in (57) become zero in

head and following waves for a ship with transverse symmetry. -

-5. The steady yaw moment

In order to relate the wave-induced steady yaw moment to the far-field

velocity potential, we consider the principle of angular momentum about the z -axis. Newman2 gave an expression for the rate of change of the verticäl

component of angular momentum, which is of general and thus applicable to the

present problem. This can be expressed as

-c9= ff(rxn)zdS..

Vø)]dS (58)

Here r is the position vector and the subscript z denotes the z-còrnponent of vector quantities. Note that the first term on the right-hand side of (58) is the

minus yaw moment, because the unit normal is defined positive when pointing out of thefluid domain.

14 Masashi KASHIWAGÌ

exists no net increase of angular momentum in the control volume. Therefore we get

=

ffp(rxn)zdS

=

_ff[p(rxn)z+p(rxVø)z(n vøYldS

(59)

Here the pressure of fluid is given by (25), and it follows from (1) that

(rxn)z=xnynz

=

x--_y(4-_ u)

₍₆₀₎

n

=

Evaluating the above equations on the control sùrface shown in Fig. i and

discarding terms higher than O(3),eq. (59) canbe reduced to

M;

Çdf[ x{(I)2+()_()2}

]y

4P9f:[]dx

.+pff:[y

]Y+f.o[

_-1Y

dy J- (61)

whre

, is given by (48).

As before calculating time average and substituting (3) gives the following expression: M; = (62) where N ₌ 2)

.]' dx

4 o - dx dz dy dx dy - y

_+Re.L:[

x{KI2+ i

KoIdxI dxJ=o

2y{(ii*+_.

}]Y

₍₆₃₎

L_

.2 o ,

dx. dx

dz dz dy dy dx dx dy dx dy -v

_4Ref°[

_x{K+é

₎

Calculation Formulas for the Wave-Induced Steady Horizontal Force

and Yaw Moment on a Ship with Forward Speed 15

+

{ ir(ç*_

° '\+-J-- + a0*

i '

dx (64)

a ay J K0 \, a 3y ax ay Iiz=oj-y

In order to apply Parseval's theorem (32) to the x-integration in (63) and (64), the Fourier transform of the derivatives of times the coordinate x must be obtained. Consideringx(aço/ax) as an example, it follows from (17) that

= -k-f :EkH(k) vVífk2 exe'dk

=

i-zfc

_k2

e'°2"

]e1rd/c(65)

Therefore the Fourier transform of the above can be readily found:

F{x-}

=

kH(k)

-

_4H±(k'l

EkVk _vz;ie,y,f.,2_k2

-

Zdkl

\ 1J/zk2e

-

_iHi1/c d - EkVk

v.

k 'dkt./2_k2

je

H(k) vk(viík)

where dv

/

k (67)

Regarding the Fourier transform of a*/ax, we have from (17.)

F{ a}

= [H±(k)]*

Ekvk_VZ±Ilk2

₍₆₈₎ Similarly, we can obtain Fourier transforms which are necessary in carrying out the x-integration in (63). According to Parseval's theorem, we must consider

the integration of the product of (66) and (68) with respect to k and similar

integrations appearing in (63). In carrying out these integrations, we note that the integrand originating from the second term on the right-hand side of (66) is pure, imaginary and. thus does notcontribute to the final result. Furthermore we can confirm that ,tIe _{atiori. .f all the.terms 1iner1y proportional to. y,} includmg the contribution from the last term in (66) is precisely zero Con

cerning the integration with respect to z in (63) eq (33) can be used Summarizing these reductions, we shall get:

N1

_.imf°[ fH(k)(H(k) )*

VZiC,y./1)2k2

16 Masashi KASHIWAGI

--f{H-(k)}(H-(k) )* ]vdk

(69)

Using (21), this equation can be rewritten in the form

=

_:Re{C

)S*(k) - C*(k)S '(k)}vdk

=

[ -t:' + i+ t:

]Re{C '(k)S*(k)_ C*(k)S '(k)}vdk

(70)

Hère from (22), C'(k) and S'(k) are explicitly given as

C'(k)l

-

_{r r}

_{__\}

S'(k)J - J

JsH\dn

caJe

>< [ (

v'+

Ícos(Iv2_k2)

}

-- vv'k

Jsïn(r/1v2_k2) dS

± Iv2_k2cos(2_k2)

71

It is-clear from (70) that only the interactions between symmetric andantisym metric waves contribute to the N1 term, which is the same as the steady sway force.

Next, we consider the, second term, N2, defined by (64), which originates from the interaction of the incident wave and ship-generated waves. Following the foregoing procedure, the Parseval's theorem (32) will be used in conjunction with the Fourier transfòrms (20) and (66). Then we can put k ko cos z due to the property of Dirac's delta function in (20) and ko sin z =Ek,/v2_ k2 or k0

sin z = - Ek.! y2 k2 depending on the value of z due to the reasons stated in transforming (31); thus the relation y = ko holds.

Aftér the x-integration using Parseval's theorem and the z-integration

using

fze_2dz

(1)2

(72)

and (33), the interim result will consist of three parts, just like (66): the first (denoted by Ni) includes the derivative of theKochiri function, the second(N) iñcudes the terms linearly proportional to y, and the third (N23) ié the remain der. After somewhat lengthy cälcülations, these three parts can be found to be:

N21 (73)

(74) N22 = O

Calculation Formulas for the Wave-Induced Steady Horizontal Force

and Yaw Moment on a Ship with Forward Speed 17

Ñ= 4sinxRe{(r+

kocosx

)H(ko, x)}

K0

Here the quantity in braces in (73) should be evaluated at k = k0 cos x and

±ekIv2_k2 _{= kosinx, with the complex sign taken according to H(k) or}

H(k), respectively. Therefore, using the relation k0 = y = (w+kU)2/g and notation (21), the final result can be written as

N2=N21+N22+N

= --sinxRe[ (w+kU){(w+kU)Hk(k)} 1k=kocosX (76)

± EkVk k osin t

=

4sinxRe[ ko{C'(k0, x)+iS'(ko, z))

+(r+

kocosxK0

where C'(k0, )+iS'(ko, z) isto be interpreted as

[ {c(k)+ j S(k)} j../V2_k2=koSIflXlkkocOSx

Substituting (70) and (77) into (62), we obtain the formula for the steady

yawing moment in waves:

M i [

fki

rk3 O .Jkz

L. I

pga2 - 4.'rk + + Re{C'(k)S)(k)_C*(k)S'(k)}vdk

+sinxR:[ C(ko, x)+

S'(ko, z)

+----(r+ kocos _{)H(kO, z)] (78)}

ko\ K0

This is the result obtained for the first time by the present analysis. In the limit of vanishing forward speed, r and 1/Ko are zero from (li), and k1 = co, fr2 =

K, k3 = K, and k4 = 00 from

(12) and (13). Thus we can confirm that

Newman's result21 at zero forward speed is recovered from the present result.

6. Concluding remarks

The formulas obtained in this paper permit us to calculate the second-order sway force and yaw moment, provided that the Kochin function is determined from the velocity potential on the ship hull. Although there are still a number of problems to be resolved for a reliable solution by the three-dimensional panel method, some progress have been made recently in developing a fast algorithm

of the Green function with forward speed and sinusoidal oscillation; for

instance, Iwashita & Ohkusu91. Therefore it will be possible in the near future to obtain the Kochin function from the "exact" solution of the entire boundary-value problem. However, from the viewpoint of economical computations with

(75)

18 MasashiKASHIWAGI

relatively good accuracy, the unified slender-ship, theory developed by

Newman10> and Sciavounos'" may be the first to be tested for the determination of the Kochin function The computational work along this line is now in

prógress, and the results will be presented in the fòreseeable future together with experiments to verify a' part of them.

Acknowledgment

The author wishes to thank Prof. M. Ohkusu of Research Institute for Applied Mechanics, Kyushu University, and Dr. M. Takagi of Technical

Research Institute of Hitachi Shipbuilding & Engineering Co., Ltd., for their invaluable discussions and encouragement.

References

Maruo, H.: The Drift of a Body Floating on Waves, J. Ship Res., Vol. 4, No.

401, (1960) pp. 1-10

Newman, J. N.: The Drift Force and Moment on Ships in Waves, J. Ship Res.,

Vol. 11, No. 1, (1967) pp. 51-60

Mamo, H.: Wave Resistance of a Ship in Regular Head Seas, Bulletin of the

Faculty of Engineering, Yokohama National Univ., Vol. 9, (1960) pp. 73-91

Mamo, H.: Resistance in Waves; Chap. 5 in Researches on Seakeeping.

Qual-ities of Ships in Japan, Soc. Náv. Arch. Japan 60th.Anniv. Ser., Vol. 8, (1963) pp. 67

-102

Proceeding of the ist Marine Dynamics Symposium; Ship Motions, Wave Load and Propulsive Performance in a Seaway, Soc. Nay. Arch. Japan, (1984) pp. 1-189 (in Japanese)

Ogilvie, T. F. and Tuck. E. O.: A Rational Strip Theory for Ship Motions, Dep. Nay. Arch. Mar. Eng., Univ. Michigan, Rep.. No. 13, (1969) pp. 1-92

1mai, I.: The Theory of Hypeifunction and Its Applications, Science Inc., Japan, (1981) Vol. 1, pp. 61 (in Japanese)

Hanaoka, T.: Hydrodynamical Investigation Concerning Ship Motions in Regu-lar Waves, Doctoral Thesis, Kyushu Univ., (1957) (ir> Japanese)

Iwashita, H. and Ohkusu, M. : Hydrodynamic Forces on a Ship Moving with

Forward Speed in Waves, J. Soc. Nay. Arch. Japan, Vol., 166, (1989) pp. 187-205 (in

Japanese)

Newman, J. N.: The Theory of Ship Motions, Adv. AppI. Mech., Vol. 18, (1978)

pp. 221-283

Sclavounos, P. D..: The Diffraction of Free Surface Waves, J.. Ship Res., Vol. 28,

Summaries of Papers Published in Buiiétiñ öf 'Research

Institute for Applied Mechanics

(Japanese) No 68, 1989

A laboratory study of the Antarctic. CircumpolarCirculation

By Masaki TAKEMATSU and Tsugio KITA

This paper describes a series of laboratory experiments designed to study the effects of thermal forcing and geometry (ice cover, partial

meridional barrier and subsurface ridge) on the circulation of the

Antarctic region. The working fluid occupies a brod 'ánnúlár basin of constant depth (an fp1ane) with vertical, coaxial, cylindrical sidewalls. The whole apparatus is mounted on a turntable rotating. in the clock-wise direction. A uniform cooling is applied at the inner sidewall. of the basin which has been in thermal equilibrium with the working fluid The transient responce of the fluid is observed over a diffusion tigne (typically, 90 mm) by means of the Thymol blue dye, technique.. The

effects of the external marameters and geometry on the thermally

induced circulation are examined in some detail Similar experiments are carried out also for the wind-driven circulation.whichis generated

by applying a circular air stream at the free surface of the working

fluid.

The thermally induced circulation is crudely described by the

thermal wind relation except in the vertical boundary layer adjacent t,o the inner sidewall: It is eastward moviñg and it decreases in strength with depth. In the bottom layer, the flow is almost stagnant, and

satisfies the non slip boundary condition directly (i e without forming an Ekman layer). Accordingly, the thermally induced circulation has non-zero net horizontal transport. In passing we note that this is also true of the thermal motion on a sloping bottom (see, Takematsu and Kita, 1989, Dyn. Atmos. Oceans, Vol. 13). In the vertical boundary layer along the inner sidewall, there appears a weak westward counter-current near the bottom. This westward bottom counter-current is signiticantly iñtènsified by the presence of an ice cover (an annular rigid plate) and it is deflected northward by a subsurface ridge. The eastward current in the upper layer is rather insensitive to changes in geometry, although it increases in breadth due to a subserface ridge or an ice cover. It is thus demonstrated that the thermal motion on the f-plane resembles the

20

Antarctic circulation in varioùs essential respects.

An important finding in the wind driven circulation experiments is

that the presence of an ice cover induces an intense upwelling and

downwelling motion along the offshore edge of the ice cover.

In conclusion, this study suggests that the presence of an ice cover as well as thermal forcing and associated baroclinicity are essential -to the dynamics of the Antarctic circulation.

Simulation of the Eastern Tropical Pacific Ocean:

Seasonal Variation

By Shin-Ichiro UMATANI and Toshio YAMAGATA

A regional ocean circulation model with fine horizontal resolution

of O.25 X O.25 'is developed in order to obtain a cohereñt seasonal

picture of the eastern tropical Pacific off Central America in a normal year. Several 'important conclusions useful to judge past conflicting hypotheses about the Costa Rica Dome and to organize past abserva-tions off Central America are obtined.

-The model Costa Rica Dorne evolves in spring off the Gulf of

Papagayo and matures in summer and early fall in accord with strength-eniñg of the NECC due to the northward migration of the ITCZ.

The cyclonic turn of the NECC off the coast of Central America is found to be mainly responsible for the existence of the model Costa Rica Dome in summer and fall. In winter strong northers converging the southernmost ITCZ from three passes in Central America excite three' noticeable wárni anticyclonic gyres confined in the upper layer, each of which s accompanied by comparatively weak cyclonic circula-tions with strong upwelling generated by the local wind stress curl.

The present model results are remarkably similar to the data

available at present except that the values of sea water temperature in the Dome are lower than those observed by a few degrees.

Locally-Induced Nonlinear Modes and Multiple Equilibria

in Planetary Fluids

By Kei SAKAMOTO and Toshio YAMAGATA

The nonlinear response of the barotropic quasi-geostrophic

equa-tion to a steady vorticity source with a form of Stern's modon is

discussed in the present paper. The main results are summarized in the following:

The system with equal forcing and dissipation possesses both high amplitude steady state and low amplitude steady staté when the forcing is weak.

When weak dissipation cannot be balanced against strong forc-ing, modons are generated successively in spite of the steady forcing.

On the basis of the present analysis and the OGCM simulations (cf. Yamagata and Umatani, 1990), it is suggested that the nonlinear eddies off the coast of Costa Rica are generated in wintertime via the above process.

The effect of basic easterlies on an evolution of ENSO

By Yukio MASUMOTO and Toshio YAMAGATA

The effect of the atmospheric and oceanic basic fields on an

evolution of ENSO is investigated by use of a simple air-sea coupled model. In the first numerical experiment, the observed basic winds, SST fields and their seasonal cycles are taken into account by use of a "flux correction method". As in the anomaly model (cf. Yamagata and Masumoto, 1989), an air-sea coupled disturbance emerges in the model

basically at a right time and a right place of the equatorial Pacific.

However, it does not penetrate far into the eastern Pacific.

In the second experiment, in order to clarify the role played by the basic easterlies, zonally averaged climatological winds are adopted to realize basic conditions in a simple manner. It is demonstrated that the easterlies with strength above a certain critical magnitude prevent the coupled disturbance from propagating eastward through active equato-rial upwelling which cools the SST.

On the basis of the present parameter study, the tropospheric

biennial oscillation associated with the strong and weak Asian summer

22

a çandidate :which;modulates thè .basic atmospheric and oceaniç conditions. r.

Air-sea interaction henoinena'uitder the existence of swell

propagating against the wind

By Hisáshi MITSUYASU and Yoshikazu YOSHIDA

A laboratory experiment has been made to clarify the dynamical processes at air-sea boundary where, swell is propagating against the

wind. The following interesting results have been obtained; (i) the

magnitude of the decay rate' of swell. by adverse wind is almost the same to that of the growth rate of Waves by favorable wind, and the

both are proportional to (u/c)2, (ii) the growth of wind waves is

intensifiedby the co-existing swell of the opposite direëtion, Which is in clear contrast with the 'attenuation of wind waves by the co-existing swell of the same direction, (iii) the high frequency spectrum of wind

waves are not affected by the co-existing swell, and (iv) the drag

coefficient of sea surface increases when the wind blows over the swell of the opposite direction; The phenomena seernsto be clósely related

to the intensification of Wind waves by the swell of the opposite

Direct Current Measurements of Kuroshio

i

in the East China Sea (II)

A Study of Systems for Measuring Wide Oceanic Areas (6th Report)

By Shinjiro MIZUNO, Kazuo KAWATATE, Tomoki NAGAHAMA, Takasige SHINOZAKI, Akimasa TASHIRO, Michiyoshi ISHIBASHI,

Tetsuji ABE and Arata KNEKO'

-As part of Kuroshio Observation Project of Research Instiute for Applied Mechanics, Kyushü University, an array of tWo subsurface

moorings was deployed on the shelf-slope 1000 m deep and on the

Okinawa Trough 1500 m deep for 13 months from 29 October 1987 to. 2 December 1988. The primary results are: (1) An intercomparison of an ADCP and Aanderaa current meters at the time of:deploymentshowed a good agreement of the Kuroshio currents at the two mooring stations. (2) A simple model of Kuroshio meandering was devised to interprete time series of the Kuroshio strong currents (3) The dominant periods of Kuroshio meander consist of two periods: 10-15 dáys and about a month periods. (4) In April 1988, an instability of Kuroshio currents occurred, causing great effècts on the water temperature at the edge of the shelf in the East China Sea and on the sea level difference across the

Tokara strait south of Kyushu Island. .

-Kuroshio Traverse Survey Using a ADCP

Motion-Controllable Towed Vehicle

A Study of Systems for Measuring Wide Oceanic Areas (7th Report)

By Hiroyuki HONJI, Wataru KOTERAYAMA, Arata KANEKO, Masahiko NAKAMURA, Masafumi KAMACHI, Masarù INADA

and Michiyoshi ISHIBASHI

During Dec. 7-8, 1988, we towed an ADCP vehicle (DRAKE), across the Kuroshio Current, along a 166-km-long transect between SE of Tanegashima. and NE of Amami Ôshima. We tested capabilities of the newly developed vehicle and obtained short-time veloéity profiles

24

cessfully. The data show that thè main current flowed .to east to

south-east with a maximum velocity of about 90 cm s' ,though it was

disturbed partly by the upstream bottom topography. We measured the

current to the depth of about 340 m although the flow velocity

de-creased with the depth no conspicuous flow variability in the vertical direction was observèd within the range of this depth.

Visualization of the Kuroshio Current Fields by

a Fish-Mounted Type ADCP

- A Study of Systems for Measuring Wide Oceanic Areas

(8th Report)

By Arata KANEKO, Wataru KOTERAYAMA, Hiroyuki HoNfl, Kazuo KAWATATE, Hisashi MITSUYASÛ, Shinjiro MIzuNo,

Yoshio HASHIMOTO, Masafumi KAMACHI,

Masahiko NAKAMURA, Tsutomu H0RI, Akimasa TASHIRO, Michiyoshi ISHIBASHI

and Tokuzo HOSOYAMADA

The sectional velocity fields of the Kuroshio west of Okinawa, south of Shikoku and south of Enshu-Nada have been visualized by means of an Acoustic Doppler Current Profiler (ADCP) on a towed fish with fixed fins (EIKO). The dynamic characteristics of the Kuroshio such as velocity structures and volume transport were found to show large variability, depending on the surrounding geographic conditions and the latitude of the observation sites.

A Three - Dimensional Calculation Method

for Side-Wall Effects of a Towing Tank

on Hydrodynamic Forces Acting on a Ship Model

By Masashi KASHIWAGI, Masaru INADA and Makoto YASUNAGA

When experiments of a ship model are carried out in a towing tank with limited width, the waves reflected on the side walls of a tank may

exert a great influence on the measured hydrodynamic forces acting on

and resulting motions of a ship model. In order to estimate these

side-wall effects with quantitatively good accuracy, a three-dimensional integral-equation method is developed. The proposed calculation

method is restricted to the zero-speed problem, but provides in principle an exact solution for a body of arbitrary geometry.

Validity of the calculation method is discussed by comparing the numerical results with corresponding experimental values. Expeti-ments are also conducted for a hemisphere and a ship model with two planes of symmetry, to get the added mass, damping coefficient, and wave-exciting force and moment, with tank-wall effects included. It is found that there exists quite favarable agreement between experimen tal and numerical results. Based on these reliable numerical computa-tions, the tank-wall effects on the characteristics of ship motions are discussed.

On-site Experiments of Depth and Roll Controlable

Towed Vehicle "DRAKE"

A Study of Systems for Measuring Wide Ocean Areas

(9th Report)

-By Wataru KOTERAYAMA, Makoto OHKUSU, Hiroyuki H0ÑJI,

Yusaku KYOZUKA, Masashi KASHIWAGI, Masahiko NAKAMURA

and Masaru INADA

The towed vehicle system is suitable for ocean measurements

because of its high speed mobility and reliability in mechanism. We developed a towed vehicle system which can carry an acoustic doppler

current profiler and CTD sensor (Conductibity-, temperature- and

depthsensor).

The current profiler demands a high level of stability in pitch, roll and heave of the towed vehicle, so that the main wing and the tail wing

are controlled automatically to maintain the operation submerged

depth and roll stability.

In this paper the structure of the towed vehicle and the

perfor-mance confìrmed by experiments on the observation line across the Kuroshio are described. The perförmance obtained in experiments will be compared with the theoretical estimate.

26

Second-order Waves generated by a Wavemaker

By Yusaku KYOZUKA

A singularity of second-order velocity potential at intersections between a body and free-surface is studied in the wave generation of a piston wave maker, relating to the calculation of second-order forces

acting on a floating body among waves. First- and second-order solutions are obtained by the series of eigen functions, which enable us easy to control the accuracy of the numerical calculations.

It is confirmed numerically that second-order free-surface condi-tion shows logarithmic singularity at the interseccondi-tions and therefore, the second-order potential would be obtained by the integration of it on

free-surface.

As an application of this theory, second-order oscillation of a piston wave maker not to generate second-order free-waves is calculated and the wave form at infinity is compared with that of an usual sinusoidal

oscillation.

A cross-spectral analysis of small voltage variation in the

submarine telecommunication cable between Hamada

and Pusan with speed variation of the Tsushima warm current

By Kazuo KAWATATE, Akimasa TASHIRO, Michiyoshi ISHIBASHI, Takashige SHINOZAKI, Tomoki NAGAHAMA, Arata KANEKO,

Shinjiro MIZUNO, Jun-ichi K0JIMA, Toshimi A0KI, Tatsuji IsHIMoTo, Byung Ho CH0I, Kuh KIM,

Tsunehiro MnTA and Yasunori OucHI

We obtained a time series of electric voltage records in the

subma-rine telecommunication cable buried between Hamada and Pusan together with a set of speed records of the Tsushima warm current

measured southeast of the island. A cross-spectral analysis was made between small voltage variation and speed variation. We showed that a strong correlation exists between the two variations.

Two-dimensional Interaction between Short

and Long Waves

By Masayuki OIKAWA, Makoto OKAMURA and Mitsuaki FUNAKOSHI

Two-dimensional resonant interaction between a internal gravity wave and a surface gravity wave packet in a two-layer fluid is inves-tigated. The equations describing this interaction are derived.

Modulational instability of a plane wave solution of the equations is discussed. Two kinds of soliton solutions to the equations are given.

On the Density-Stratified Wind Tunnel System

By Yuji OHYA, Kenichiro SUGITANI and Yasuharu NAKAMURA

The present paper reports on a new density-stratified wind tunnel of a closed-circuit type, recently installed in our laboratory. The tunnel has a 60 cm high by 40 cm wide by 170 cm long rectangular working section, which has glass panels around two sides with flow visualization in mind. The tunnel, which was designed to produce layers or continu-ous stratification, is horizontally divided into six parts by thin alumin-ium plates except the working and converging sections. Each part is

filled with gas of different density, which is a mixture of air and a

heavy gas. Thus, we can obtain a density-stratified flow with an

expected density profile in the working section. It is possible to make

a strong stratification so that we can make experiments with low

Froude numbers and relatively high Reynolds numbers without using a very low air speed. The specific density ratio of a gas mixture is easily determined with an oxygen meter.

28

Near Wakes of a Circulár Cylinder in Stratified Flows

By Yuji OHYA, kenichiro SUGITANI and Yasuharu NAKAMURA

The present paper reports on the first piece of research carried out in a new density-stratified wind tunnel of a closed-circuit type, recently

installed in our laboratory. The flow around a circular cylinder in

linearly stratified flows is experimentally investigated, by means of

flow visualization, at Reynolds numbers of 5-9 X 1O and

non-dimensional buoyancy frequencies K smaller than 1.5. Measurements of wake yelocity fluctuations are also made using hot-wire anemome-ter. The results are summarized as follows:

As K increases, the vortex shedding from a circular cylinder is gradùally strengthened and the Strouhal number becomes lower than that of a homogeneous flow.

At a critical value of K, the enhanced vortex shedding is suddenly suppressed by the stable stratification and the Strouhal number shows a jump to a high value.

At large values of K, the formation of internal lee waves domi-nates the cylinder wakes.

Comparison of Fiñite Differencing Schemes on the

Flow around a Cirëular Cylinder

By Ryuzo NAKAYAMA,YUji OHYA and Yasuharu NAKAMURA

Comparison of finite differencing schemes are carried out using the flow around 2D-circular cylinder at Reynolds numbers of 100 and 1000. The schemes considered here are those of central difference, Kawa-mura & Kuwahara (K-K), Agarwal (UTOPIA),. Leonard (QUICK).

Evaluation is made with respect to accuracy, stability and the CPU

time required. At a Reynolds munber of 100, the difference in the

results of the 3rd order upwind schemes are not found, however, central differenciñg scheme causes a spacial oscillation in the solution. At a Reynolds number of 1000, KK and QUICK schemes show good stability and accuracy.

Strength of Kevlar Braid Epóxied into

Metal Socket Termination

By Hiromi HJYAMA, YOji KOGA and Yoshihiro TAKAO

A specimen with less than i m long tested in a laboratory is

necessary to investigate the fatigue strength of synthetic fiber rope

terminations, especially in deep sea environment with both corrosion and high pressure effects. Rope terminations are supposed to fail

frequently under practical loading.

First, a Kevlar rope termination method with metal socket is

discussed in detail. Static and fatigue experiments of this termination are performed, together with the numerical analysis based on the finite element technique, which will show the capability of the present termi-nation.

Local distribution of deformation around PMMA

methanol crazes and related shadow patterns

By Kiyoshi TAKAHASHI, Hiroshi MIYAGI and Aly Abo-El-Ezz

Out-of-plane deformation distribution (W(x» was measured for a crack-craze system in PMMA plates in methanol uniaxially loaded with a constant load apparatus. The measurement was performed particu-larly in a collapse of time after crazes were arrested in methanol (stage

III). The results were compared with corresponding caustic pattern change. The change of W(x) qualitatively agreed with caustic pattern growth behavior in the stage III. A peak existed in W(x) at the craze tip. Dried methanol craze exhibited a drastic shift of stress concentration

from a craze tip to a crack tip.

30

Dynamic perforation, characteristics of higi-strength

polyethyiene fabrics I.

Dependence of impact velocity on dynamic energy absorption By Kiyoshi TAKAHASHI, Haruo KOMATSU and Hiroshi Yasuda

Abasic impact test was performed on fabrics made of ultra-high strength polyethylene fibers by using a gas gun facility. Perforation of .a steel ball with a' diameter of 10 mm was stûdied from a view point of

the kinetic energy of the ball absorbed in the course of the impact.

Positron Annihilation Measurements of Defects in YBa2Cu3O7_

By Eiichi KURAMOTO and Minoru TAKENAKA

Positron aniiihilation rneàsurements have been - performed for a high temperature suberconductor YBa2Cu3O7

in order to obtain

informations of defects. In the angular correlation measurement no narrow domponent .corresponding to positronium (Ps) formation was observed. After 2.7 MeV He irradiation (2.5 X l0'6/cm2) the increase of the second lifetime component was observed in positron annihilation lifetime measurement. This second lifetime Was about 230 psec.

Accordiñg to Jensen's calculation this lifetime component corresponds to vacancies of metallic ions, such as Cu, Ba, Y and Cu-O divacancies.

It was also found that keeping at room temperature for a long time

Positron Annihilation Measurements of Defects in Graphites

By Eiichi KURAMOTO, Minoru TAKENAKA

and Masayuki HASEGAWA

Positron annihilation measurements have been performed in order

to obtain informations of structures and defects in various kinds of

graphites. In the angular correlation measurements of HOPG in the orientation of P2 ¡I c-axis prominent side ,peaks at about, ± 3 mrad was, observed. This i's considered to be due to contribution of r electron orbitals. Positron annihilation lifetime measurements, showed that shortest lifetime of about 220 psec was, observed in HOPG type graph-ites, lifetime of about 360 psec for isotropic graphites and that of about 400 psec (longest one) for glassy carbons For carbon fibers about 375 psec was obtained. 'Radiation-induced vacancies in HOPG.increased' the

lifetime by about 20 psec and decreased the side peaks because of

destroying r electron orbitais at vacancy sites.

A New Double-crystal X-ray Diffraction System

for Variable Xray Wavelength Experiments

-By Noboru TSUKUDA and Tetsuhiro YAMASHITA

Usually, precise x-ray diffraction experiments iequire

double-crystal arrangements. If one attempts a new set-up for the adequate

x-ray wavelength, it sometimes takes several hours to maintain the

reliability.. A new double-crystal system has been developed, in which, the sample goniometer position is fixed and only the monochromator is movable aiond direct beam line. A reliable set-up, is completed with a short work. The system is effective for successive experiments with various x-ray wavelengths. By the use of the system, rocking curves of AlGa1_ As multilayer films have been demonstrated.,

32

Interaction of solutes with electron-irradiation-induced defects

in iron-molybdenum dilute alloys

By Hironobu ABE, Yoichi UEDA Yasuhisa AoNo and Eiichi KURAMOTO

Dilute Fe-Mo alloys (solute content: 650-4300 at. ppm) have been

electron-irradiated (E28 MeV, T. =77 K) together wijh pure Fe.

Their recovery characteristics of the radiation-induced defects have been investigated by electrical resistivity measurements. The definite recovery stages found in the alloys at around 160K and 260K have been attributed to the detrapping of a self-interstitial and a vacancy from a solute, respectively. By a combination of isochronal and isothermal annealing, the activation energiés and the reaction orders of respective main recovery stages have been determined in the one of Fe-Mo alloys (650 at. ppm). From these results, the corresponding binding energies of an interstitial-solute pair and a vacancy-solute pair have been

esti-mated to be - 0.1 eV and - 0.2 eV, respectively.

Effects of low-temperature electron irradiation on plastic

deformation of Fe-C dIlute alloy single crystals

By Köichi MAKI!, Yasuhisa AUNO and Eiichi KURAMOTO

Plasticity of electron irradiated Fe-C dilute alloy single crystals at low temperature was investigated by means of both yield stress (flow stress) and activation parameters determined by means of stress relaxa-tion technique.

In as-irradiated alloys carbon doping caused the rapid suppression effects on irradiation softening. In post-irradiation annealed alloys the isochronal annealing process of yield stress was strongly influenced by the small amount of carbon. the new recovery stage of yield stress was observed at the decompositiòn or formation stages of I-C, I,,-C, V-C,

VC, VnCm, complex and the C-migration stage, which have been

already reported by measurement of electric resistivity. Especially, the softening stage characteristic in Fe-C alloys was observed between stages II and III.

yield stress-temperature curves of post-ifradiation annealed alloys were devided into two regions in the low and high temperature regions as well as irradiated high purity iron. The critical temperature i.e., the

boundary between these temperature regions, which varies to high

temperature with increasing annealing temperature, was independent of carbon concentration. However,the clear gap of yield stress at the critical temperature was observed at a high carbon concentration.

Radiation Damage of Ni Irradiated by keY Energy Deuterium Ions

By Masahiro YASUKAWA, Naoaki YOSHIDA and Takeo MUROGA

Nature of microstructure in Ni irradiated with deuterium iOns of keV energy and its role on deuterium trapping were studied by means of transmission electron microscopy.

Because of strong interaction of injected deuterium atoms and radiation induced point defects, pronounced secondary defects are

formed depending on irradiation temperatures and ion energy. In the case of low energy less than 0.5 keV, where displacement damages are scarcely expected, platelet-like deuterium clusters are formed at room temperature. They are formed preferentially at pre-existing disloca-tion lines. Thermal stability of the clusters is comparatively low,

namely they start to dissociate above 100CC and disappear completely by the annealing up to 500CC. Similar clusters have been observed in stainless steel, Fe, W and Mo irradiated with hydrogen isotope ions of keV energy. This means that the platelet-like clusters are general

trapping site under irradiàtion of highflux lowenergy hydrogen isotope

ions.

When the ion energy exceeds i keV, where displacement damage occurs, small dislocation loops of interstitial type are formed at room temperature, and their density and size increase with increasing irradia-tion dose. They become unstable and form dislocairradia-tion networks above 400CC by annealing. Depth distribution of the dislocation loops corre-sponds well to theoretical projected range of injected deuterium ions, and the density of the loops at the peak is 2 to 3 order higher than that of electron irradiation with similar damage rate These results indicate that deuterium atoms have very strong influence on interstitial loop formation. According, to computer simulation of defect cluster forma-tion taking account of diffusion and interacforma-tion of the point defects and deuterium atoms, interstitial-deuterium binding energy should be about

34

0.4 eV to exlain the observed dëhsity Of: ihterstitial:loöpsi

-Dislocation loops re:aldfortred ir the deeper-region beyd th theoretically estimated deuterium and damage distributions This

suggest that intersitials'aiid: deutthurn .tons diffusiig inside :thé

sariiples form intetstitial:'1oop thee

-

,

With incieasing irradiation tètnperatuie, density of'the disldcatin

loops decreases but it is still very high ven at :3006 :. Deûteriurn bubbles are also formed by strong irradiation above 3 X lO21ions/m2 at the same temperature These results suggest that deuterium atoms which have been often ignored at elevated temperatures, also play very important rolês on the formation of microstructure at elevated temper-atures.

The present study indicates the possibilit that hydrogen isötoes

penetrating into plasma facing materials due to PWI, cause not only subsurface damage but also modify damage structure formed inside the materIals by D-T neutrons.

Mlcrostrtìcture and strength of fusion candidate austenitic

steels joined with insulating ceramics

By Yasuo MURATA, Tákeo MUROGA, Yasuhisa AoNo, Naoaki YOSHIDA and Yasushi FUKUZAWA

Joining of ceramics with metals is anticipated to improve their

thermal shock resistance which is the key isue for the application of ceramics to fusion first walls. The improved properties of ceramics by joining are expected to be beneficial also for the use in insulators or

windows. In this study, fabrication and charactrization of ceramic/ metal joints were carried out using fusion candidate ceramics and

alloys.

Insulating ceramics (Al203, Zr02) were joined with austenitic stain-less steels (JPCA -- fusion candidate modified austenitic steel, SUS3O4) by diffusion bonding at 620 C 9 MPa and 1 hour using a Al-lMn-2Si foil as a filler material. This filler material was chosen by its good adhesion with À1203 and Zr02 after &ffusion bondin. The strength were estimated using 4 pOint bending tést and, after the tests, fracture surfaces were examined by a Scanning Electron Microscope (SEM) The interfaces were examined by a Transmission Electron Microscope (TEM) including microchemical analyses using an Energy Dispersive Xray Spectrometer (EDS).

SEM observation of the joined materials showed that a reactiöú layer about 001mm thick was formed between JPCA and Al-1Mn-2Si

filler. The:fracture:during the bendintestsodcure&at thereaction layèr especially in theviinity ofJPCAYreactibn1ayeriht&rfaceAsä result, strengthöf thè Al203/JPCAandZr02/JPCAare .closeto each

other at around 170 MPa although the strength of Zr02 is much higher thanthat of Äl203.

High density of dislocations and strong strain fieldwreobserved by TEM at the JPCA/reaction layer interface. The reaction layer was composed mainly of Al, Fe, Ni, Cr and Si. The EDS analyses showed that Ni concentration in the reaction layer was depleted in the vicinity

of the interface, where fine grain structures were observed. These

decomposition and structural changes are expected to result in the

preferential fracture at this area.

The strength of SUS3O4/Al203 joined material was lower and

around 80 MPa. The TEM observation and EDS analyses showed fine phase-separation with drastic positional dependence of compositioñ in the reactiòn layer. Especially the nickel concentration was quite low in most positions analysed. Thus, the depletion of nickel is thought to result in the decrease in strength of the reaction layer.

This study showed that further improvement of strength of the

present joined materials is possible by improving reaction products

between the filler material and the stainless steel. Preventing the

nickel depletion at the reaction layer by use òf new filler, second

Ni.based filler or higher nickel stainless steel may be possible waysof the improvement.

Modification of a Limiter under Ultra Long Pulse Operation

in Superconducting High-Field Tokamak TRIAM-1M

By Kazutoshi T0KuNAGA,Tadashi FUJIWARA, Naoaki YOSHIDA, Takeo MUROGA, Satoshi ITOH and TRIAM-Group

Surface morphology and composition have been investigated for a limiter after hydrogen plasma discharges in Superconducting High. Field Tokamak TRIAM-1M by means of an optical microscope and SEM-EDS system. In this Tokamak, the limiter and vacuum vessel were made of 304 stainless steel. This limiter was used in about 9000

times at ohmic discharges and aboût 2500 times at current drive

discharges. The maximum duration of the current drive discharges was

36

1-92 sec.

On the plasma side, heavy melting damage due to heat load from

plasma was observed especially in the inner part of torus of upper

limiter. The depth of this molten and resolidified layer was about ito 2 mm. where Cr was depleted by about 6 % (wt%). This modification is considered to-be caused by Iong.time heat load due to contact with bulk plasma in long duration discharges. The preferential depletion of Cr is considered to be due to its high vapor pressure. This corresponds to the result of the theasürement of visible spectrum from the plasma which showéd intense -peak at Cr.

On the ion side and the electron side, an impurity deposition layer

which was composed of Fe, Cr, Ni, C and O was- obserbed. The maximum thickness of layer was about 12 m. In the inside of torus or the edge of the limiter, the impurity deposition layer was molten and 'resolidified and thus, attached. with the substrate adhesively. On the other hand, in the outer part of limiter, deposit layer was not molten and thus, loosely attached with base material. As a result, the impurity layer was partially exfoliated.

The erosion due to sputtering by ion bombardment was observed in addition to the impurity deposition and the exfoliation on the ion side.

On the-other hand, microholes was obserbed in outer part on the

electron side. They are considered to be caused by embritilethent due to hydrogen implantation because the microhardness of this area -was about 3 timés that Of the- area where plasma did not interact with the limiter material.

The present observation showed a new heat flux effect which occured during long time heat load during long discharges. This implied a new requirement of, the limiter and wall materials for the Tokamak under-long pùlse operatiôn.

-High Heat Flux Experunent on Graphite Material

-

wIth Focúsed Pulse Laser Beams

-By Hiroshi KAMEZAKI, Kazutoshi TOKUNAGA, Shigehisa FUKUDA,

- Noaki Y0sÑIDA -and T-akeo MUROGA

- The surface morphologiëal changes and emission of gases and

particles were investigated for isotropic graphites by the focused pulse laser beams. Especially gas analyses by a quadrupole mass analyzer (QMA) made it possible to elucidate dynamic processes of gas/particle

émission under pulse high heat load. This.is new information because it is difficult to obtain these pulse characters from the conventional thermal desorption spectroscopy (TDS).

The graphite samples used in the present work were isotropic

graphite (1G-hOU) and 0.009 mm pyrolytic carbon coated graphite (1G

-hOU + PyC). A ruby laser with the output power of 6.4 J and the

pulse length of i ms was used as a heat source. Laser irradiation was carried out at room tempreture in a high vacuum chamber, and heat flux was controlled by moving a lens with focal length of 50 mm located in front of the specimen. Gas analysis was carried out at focal Ïength of 75 mm (640 MW/rn2 ). Surface morphology was investigated by a Scanning Electron Microscope (SEM).

In the 1G-hOU, a variety of gas emission, (H2, CO2 and hydrocar-bon compounds) were detected by the laser shots. The emission of carbon clusters (C1-C6) was also detected. This indicate atomistic process of sublimation under pulse high heat.load. This type of emis-sion were not detected by TDS. The QMA output for C1, C3 and C5 decayed very quickly after the laser shotscompared with those of other carbon clusters and compounds showing odd-even alternation of the properties of carbon clusters.

In the pyrolytic carbon coated graphite, although initial gas desorp-tion was lower than isotropic graphite, exhousdesorp-tion of the gas release came late under repeated shot on the same place.

Soliton and chaos associated with the Buneman instability

By Mitsuo KONO, Masahiro KAWAKITA and Nobuyuki HAMAMATSU

A nonlinear equation describing the development of the Buneman instability has been derived and solved with the aid of Hirota's bilinear transform [J. Math. Phys. 14, 810(1973)] to give a variety of stationary solutions, such as pulsating solitons, temporálly localized and spatially periodic solutions, as well as ordinary solitons.

38

Reflection and Transmission of Two-Dimensional Solitons

By Chihiro MATSUOKA and Nobuo YAJIMA

The propagation' of two-dimensional solitons in inhomogeneous media has been investigated A nonlinear counterpart of Snell's law has been obtained associated with reflection and refraction of shallow water solitary waves and planar ion-acoustic solitons. The propatga-tion of solitons in these media is described by the KdV equapropatga-tion. As for

the case of shallow water solitons, the reflection and transmission coefficients as well as the number of solitons emerged have been

estimated with the aid of the inverse scattering method.

Data Processing System on High -Field Superconducting

Tokamak TRIAM-1M

By Eriko JOTAKI, Shoji KAWASAKI, Shin-ichi MORIYAMA,

Akihiro NAGAO, Kazuo NAKAMURA, Naoji HIRAKI, Yukio NAKAMURA and Satoshi ITOH

The data processing system on the high-field superconducting tokamak TRIAM-1M is described.

This system is consisted of

CAMAC modules and process control computer. Many and various

electric signals, which are transmitted from diagnostic systems for tokamak plasma, are acquired, analyzed and displayed in this data

processing system with the developed software within the discharge interval of 3 -- 5 minutes.