Proceedings of the Conference on Behaviour of Ships in Restricted Waters, BSHC, Varna, Bulgaria, Volume II

VOLUME 2

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BULGARIAN

SHIP HYDRODYNAMICS

CENTRE

NUMEPEMINI1-TIOBEARINE

CY1013 P OrPAIIINE1111014

MAPBATEPE-CONFEDENCE ON BEI:IMOD OF

MIPS IN DESTOICTED WATERS

AOKAAL.61 ,

Tom II

PROCEEDINGS, Volume II

OguHHaguambi0 Hayt-Ho - memogoAoeuHeckuu

cemuHap 2ugpoguHannuku cyaHa

Eleventh

Scientific and Methodological

Seminar on

Shp

Hydrodynamics

BapHa 11 13 .11. 19 8 2

Varna

OPPAHH3ATOPU : BCalrapCKMM NHCTIITyT rmapognnammcn cygna

Haymno - TeXHH,LOCKMC C010361 - Bapua

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LITIEHLA PMAKIIHOHHAA KOHflErH51 MEMBERS EDITORIAL BOARD

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CT.H.C. KTH. HHZ. KOCT3AHH AOCHOOB

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CT.H.C. KTH. MHZ. KOCT3MMH nOCATOB CT.H.C. KTH. MHZ. Hemp BACHHEB H.C. MHZ. gmana KHIDEBA

ORGANIZERS: Bulgarian Ship Hydrodynamics Centre

The Scientific and Technical Unions - Varna

ORGANIZING COMMITTEE

President Dr.Reter BOGDANOV , honoured Scientist

Vice - Presidents Dr. Kostadin YOSIFOV

Dr. George LAZAROV

Org. Secretary Dr. Dimitar KOSTOV

Dobry DOBREV Eng. Diana KISHEVA

Eng. Stephan KYULEVCHELIEV Eng. Alexander LAZOV Dimitar NENKOV Svetla STOIKOVA

Dr. Peter BOGDANOV, Honoured Scientist Dr. Kostadin YOSIFOV

Dr. Peter VASSILEV Eng.Diana KISHEVA

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PREFACE

The present, second volume of the Proceedings of the 11th Scientific and Methodological Seminar on Ship

Hydrodynamics includes:

Message of greeting delivered at the opening ofthe conference, (Ill - n3)

Reports which have not been included in the first volume (Nos 26 t 49)

Recommendations of the 11th SMSSH for the future work of BSHC (P1 - P6)

Closing speech of the Director of BSHC and Chairman of the Organizing Committee (TO - ,E14)

List of the participants in the session (Cl - C5)

Contents - List of the reports published in the second volume List of authors.

We take the opportunity to thank once again most sincerely all foreign and Bulgarian organizations and

authors whose participation ensured the high scientific and technical level and positive results of the

con-ference. We express once again also our deep gratitude to a multitude of BSHC collaborators whose

enthusiasm

permitted the comparatively full and prompt preparation and printing of the Proceedings and other Conference

materials, including this, second Proceedings volume.

11PNBETCTB4E

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MESSAGE OF GREETING

on behalf of the State Committee for Scientific and

Technical Progress, the Ministry of Machinebuilding and Electronics, the Economic Corporation of

"Shipbuilding" and the Scientific and Technical Unions

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emmio npm may,mo-Texmmgecmmx com3ax mmmemepom

TeXHHKOB e Bonrapmm

000

Dear guests !

Dear participants in the conference !

Comrades !

On behalf of the State Committee for Science and Technical Progress, the Ministry of

Ma-chinebuilding and Electronics, the District Council, the Economic Corporation of Shipbuil-ding and the National Section on ShipbuilShipbuil-ding at the Scientific and Technical Unions I have

the pleasure to congratulate you with our Bulgarian " Dobre Doshli " / Welcome / to our

bea-utiful and hospitable city .

Varna is famous not only for its beautiful scenery, the sea and its tourist activities, but also as a centre of modern, constantly developing industries and marine economy.The biggest

shipyard in our country, the Bulgarian Ship Hydrodynamics Centre, the Computer Centre at

Economic Corporation of Shipbuilding, the Water Transport and Fishing Research Institutes, the Higher Technical Institutes of Shipbuilding and Water Transport, etc. are all in Varna.

During those three days the foreign guests will have the chance to get closely acquainted

with the ample possibilities of the multipurpose and extremely efficient laboratory

experi-mental complex at the Bulgarian Ship Hydrodynamics Centre, as well as with its impressive

and highly respecting achievements . It is natural to expect that a special interest will

be shown towards the impressive and respecting achievements reached, the future ambitious but real tasks, aimed at providing scientific servicing in the field of shipbuilding indus-try, water transport and other related fields in accordance with the most progressive ten

-dencies in the development of the science in the world .

The activities up to now have shown to the Naval Architects, to our customers and various

authorities and organizations that together with its scientific personnel the Institute

is an important prerequisite and a decisive factor for the design of ships with high

tech-nical performance characteristics for the Bulgarian shipbuilding industry, as well as for

its foregn customers. The Government and interested organizations, authorities and insti -tutions lend an active support to the development of the Bulgarian Ship Hydrodynamics

Cen-tre.To our satisfaction, this development continues in new and interesting fields. One of

this fields, important but scarely investigated is the behaviour of ships and other

floa-ting structures in restricted waters .

We are particularly happy at the fact that the Bulgarian Ship Hydrodynamics Centre is the

initiator of such a scientific and technical forum, directly related to the problems of

inland waterways, motion in canals, means for shelf investigation, etc. The P.R. of

Bulga-ria has one main inland waterway - the Danube.Via the system Rhine - Main - Danube we are

connected with almost all European countries . Having in mind that the water transport is

the cheapest kind of transport and the vast trade relations, the importance which this

coun-try attaches to the development of river transport and to the problems, connected with its

operation, can be estimated . It is known that the problems on which you

, the attendees

of the conference , work and which you are going to discuss, are exclusively complex

and

cannot be solved by single specialists or groups. That is why, we have supported the idea

of organizing and holding this conference and now we welcome its realization..The fact

that more than 120 specialists, including researchers from 10 foreign countries partici

-pate in the conference , speaks in favour of the interest it has attracted.This

interest

can be explained by the successful choice of a topical theme, as well as by the

vast,con-stantly expanding relations of the Centre both in Bulgaria and abroad.

We believe that the conference work, the personal'contacts, and discussions, will help you

to extend your knowledge , share thoughts and ideas. We hope that each of the partici

-pants will take back with him new facts learned and a wish for new meetings, for further maintenance of effective scientific and technical collaboration.

Dear guests and participants in the conference !

Permit me in conclusion to wish the conference successful and fruitful work. Have a plea-sant stay in our Black Sea coast city .

Thank you for your attention !

D.Panchaliev

Deputy Director General ,Economic Corporation of Shipbuilding and Chairman of the National Shipbuilding Section of the Bulgarian Scien-tific and Technical Unions.

KOHOEPEFILIVA

110BEAE1410

'C'LB

01PAI+NEHHOM (PAPBATEPE

Ho.5pt, 1982 Bapro

SHIPS MOVING IN THE TRANSCRITICAL RANGE

By

De-Bo Huang, 0. J. Sibul, W. C. Webster, J. V. Wehausen, De-Ming Wu and T. Y. Wu

The work reported here cannot properly be

called joint work, for the experiments and calculations were originally carried out

independently of each other. When preliminary

versions of each part were presented at a

meeting in Hamburg in March 1982 on the

occasion of the retirement of Karl Wieghardt,

it was evident that the calculations and

experiments complemented each other in

important ways.

In particular, the

calculations excluded certain conceivable

explanations for the experimentally observed phenomenon that is the subject of this paper. And, of course, the experimental observations

confirmed what had been predicted by the

calculations.

The original experiments (1981) were done by the first four authors, the calculations by

the last two. Everyone took part in the last set of experiments (1982) except O. J. Sibul

who died in July 1982.

The experimental part of this work was motivated by the failure in an earlier paper

[Sibul et al. 1979] to explain certain phenomena

observed in very shallow water. Let us

summarize briefly the relevant parts of this

earlier work. A ship model (length L = 4.92 ft

= 1.5 m) was attached rigidly to the towing

carriage of the Ship Model Tank of the

University of California, Berkeley. Wave gauges were also fixed to the carriage, both ahead of and to the side of the model. The carriage was

then set into motion rather abruptly and

maintained at a constant velocity u while the

resulting waves were recorded. After an initial transient disturbance, a slowly decaying almost

periodic wave was recorded. As long as the

water was sufficiently deep (depth h > 1 ft) and

the model velocity not too high, it was

possible to explain theoretically the observed

26-1

CONFERENCE on BEHAVIOUR OF SHIPS N RESTRICTED WATERS m,.mbi, 1982 vomc,

period T.

More precisely, if g

is the

acceleration of gravity, it was possible to

predict the form of gT/u as a function of Fr =

u/I5F as long as Fr was below and not too close

to 1. We refer to the cited paper for the

analysis and the explanation of discrepancies for small Fr. Figure 1 shows curves of gT/u against Fr for two cases, h = 1.2 ft and h

5.5 ft.

What concerns us here, however, was our failure to explain what was observed in some tests with h 0.5 ft. Figure 2 shows the same

theoretical curve as in Figure 1 and

experimental points obtained for various depths

near 0.5 ft. _{Although discrepancies for the}

smaller values of Fr might be explainable in the same way as were those in Figure 1, this

could not be so for the higher values. In

particular, the theoretical curve is based upon linearized theory which predicts zero for gT/u

if Fr > 1. What Figure 2 does not show,

however, is the remarkable qualitative

difference between the wave patterns for

smaller Froude numbers, say Fr < 0.7, and ones nearer to 1, say Fr > 0.8. If Fr < 0.7, there are measurable but hardly visible waves ahead

of the model,

a result of the initial

disturbance when the carriage is first set into

motion (see the paper cited above). If Fr >

0.8 the situation is dramatically different.

Waves are being continually generated, one after

the other, waves that detach themselves from the model and proceed ahead of it at a higher

velocity. Moreover, these waves become

two-dimensional, spanning the tank, almost

immediately after detachment and are very

visible as they propagate down the tank. (There

is also a wave system following the _{model, but} we are more concerned here with the _{waves that} precede it.) The boundary Fr = 0.7-0.8 is not intended to be precise, for we have measured

these preceding waves at values of Fr as low as

0.5. _{However, for values less than 0.7 they}

are much less visible. _{There is also an upper} bound. _{Somewhere in the interval 1.2 < Fr <} 1.3, the generated waves _{are no longer able to}

propagate down the tank faster than the _model.

Instead a bore is formed just ahead of the bow,

again spanning the tank, and _{accompanies the} model down the tank. _{Figure 3 shows a record}

taken from two gauges near the end of the

tank

(Gauges 2 and 3 in Figure 5b) for Fr =

1.0. The

two-dimensionality of the waves preceding the

model is evident from the near agreement of

the

records at the two gauges.we note that

the

waves preceding the model, once

generated,

appear to continue propagating

forward as free

waves, each with a supercritical

speed depending

on its own amplitude but not on each other.

The

last observation is based on the measured

data

showing that each of the preceding waves

has

profile of a solitary wave (with the

.surface displacement everywhere above

the

o

inally undisturbed water surface) and hence

benaves like one.

Wave records of this form are not

unknown. They occur, for example, in solutions

of the Korteweg-de Vries equation for an

initial hump of water.

Figure 4

shows

qualitatively what might be the time record

of

a gauge sufficiently far

from the hump [see,

e.g., Segu+ 1982].

The leading waves, moving at

supercriti,

velocity, are called "solitons".

Their numbe,

is determined by the shape of the

initial hump but is always finite.

Experiments

reported by Hammack and Segur [1974]

show good

agreement between measurements and

predictions

based upon the Korteweg-de Vries

equation.

Because of the assumptions made

in

deriving the Korteweg-de Vries equation it

cannot be used to analyze the experiments

reported here where moving boundaries occur,

and more importantly, where waves can propagate

in different directions from the moving

boundary. Recently T.

Y. Wu [1981] has

approached the problem of deriving appropriate

equations for motion in shallow water by the

classical method of averaging over depth, but

he has carried it out more consistently

and

further than is usual.

In the special case of

a fixed horizontal bottom, constant pressure

on

the free surface and two-dimensional motion,

his

equations reduce to a pair of equations

of

Boussinesq type.

With further restrictions the

Korteweg-de Vries equation can be derived.

It

is also possible to allow a moving pressure

distribution on the surface, or a moving

bump

on the bottom.

If the motion is

two-dimensional, the bottom fixed and the

imposed

pressure distribution

given by

p (x,t), then the equations may be written as

follows:

nt+

(h+n)u +n XU = 0

1

1.2

u +uu +gn +p

txxe ox

-

_{. "xxt = 0'}

where the

free

surface is

given by

n(x,t), the bottom by y = -h = const.

Y=

and the

26 - 2

depth-averaged velocity by u(x,t).

These

equations form the basis of a numerical

calculation by D.-M. Wu and T. Y. Wu for the

pressure distribution

1

P_{om 2}

- cos

(2-x + ut)

_L

!'

0

eut

L

0, elsewhere

and the initial conditions

n(x,o) = -Pc(x,o)/eg, u(x,o) = 0

.

A discussion of the numerical procedures,

including the treatment of open boundaries, i,

given in a paper by Wu and Wu [1982].

The

results of these computations will be

give-later.

Let us now turn to a more detailee2

description of our experiments.

Two types of

experiment were made.

In one, the wave gauges

were fixed in the tank, in the other they were

fixed to the carriage and moved with the model.

Figure 5 shows the positions of the gauges. In

each case they are identified as Gl, G2 or (3:

so that wave records to be shown later can

associated with particular gauges.

In

addition, for those experiments with gauges

fixed to the carriage, the resistance of the

model was measured by means of a strain gauge.

Two water depths and two models were used in

the experiments.

For the shallower depth, h

0.255 ft

0.0777 m, a double-ended model of the

forward half of Series 60, CB

0.80 with L =

3.7.5 ft = 1.143 m was used.

For the depth h =

0.349 ft = 0.1064 m a model of Series 60, CB

_:

= 0.80, L = 4.92 ft = 1.500 m was used.

The

tank bottom is not really flat, but along the

centerline is flat within 0.02 ft = 0.6 cm. The

unevenness of the bottom sets a lower

limit to

the depths at which model experiments can be

made and interpreted.

We note once again that

the model was always rigidly attached to the

carriage and could neither squat nor trim.

To

have allowed this would have added

a

complication that we wish to avoid at present.

In a series of preliminary experiments

made in 1981 with h = 0.35 ft runs of lengths

20 ft

6.10 m, 45 ft = 13.72 m and 70 ft =

21.34 m were made.

Figure 6 shows wave records

from Gauges 1 and 2 for Fr

0.9 for 20 ft and

70 ft runs. Although the two records at Gauge

I

are very similar, at least in the

beginning, it

is evident from those at Gauge 2 that solitons

were continually being generated

in the longe5

run after 20 ft had been

passed.

This behavior

was repeated in tests with 0.8

Fr ,

1.1,

was observed visually many times and has beer,

recorded on videotape.

These wave records also

P (x,t).

_'o

lisplay very clearly the effects of dispersion

on the waves trailing behind the ship model,

i.e., those behind the lowest minimum below the

mean water level.

Upon arrival at Gauge 2,

these waves have not only evolved in wave form

from that at Gauge 1, but have also become

conspicuously longer during the period of travel

between the two stations.

The same remark

applies to the records shown in Figures 3 and 8

abc.

The persistent generation of solitons is

also observed in the records from the wave

gauges fixed to the carriage.

Figure 7 shows

records for Fr = 0.95 ad Fr = 1.05 from Gauges

1 and 2 from the Series 400 of tests. From such

records one can measure directly the period of

generation of solitons and, by measuring the

displacement of maxima between Gauges 1 and 2,

one can estimate the velocity of propagation.

Figures 8 abc show records from the

gauges fixed in the tank for Fr = 0.9, 1.0 and

1.1 and h = 0.255 ft.

By measuring the elapsed

time between the start of the signal at Gauge 1

and that at Gauge

2

one can estimate the

velocity c of the soliton.

In the record at

Gauge 1, one can see solitons starting to form

that become fully developed before reaching

Gauge 2. However, as mentioned earlier, others

continue to form after the model has passed the

first gauge, and these also are visible in the

records of Gauges 2 and 3.

One should note the

gradually decreasing amplitudes for Fr = 0.9.

This occurs also for Fr = 0.8, is much less

noticeable for Fr

0.95 and does not seem to

occur for Fr

, 1.0.

For all Fr one can see

that the troughs are above the mean water level

and that a shelf of water is being formed ahead

of the model.

This is also evident from Figure

7.

What do the calculations for a moving

two-dimensional pressure distribution show?

Figures 9a and 9b show "snapshots" of the

surface at different instants ofa

dimensionless time ut/L

ut/2h for Fr = 1.0

and 1.175, the plots having been referred to a

frame fixed with respect to the pressure

distribution (bounded by the vertical broken

lines), so that the upstream uniform flow

approaches from the loft side with velocity u.

For Fr =

_{1.0, one clearly sees solitons being}

generated and proceeding ahead of the pressure

distribution. Calculations for Fr = 0.9 and 1.1

show a similar behavior [see Wu and Wu, 1982].

For Fr

_{1.175, however, no solitons are}

generated. This is also the situation for

computations for larger values of Fr, with

1.175 being

_{a numerically determined lower}

1.eund for this phenomenon.

This apparently

..,orresponds to the observed behavior in

26-3

experiments where the initially formed soliton

begins to break around Fr

1.2, although later

solitons may be smooth. As mentioned earlier,

for Fr > 1.3 no solitons are formed and

instead a bore ahead of the bow accompanies the

model down the tank. We recall that the maximum

velocity of a solitary wave (an isolated

soliton) has been calculated to be c

=

1.29,T5 [see Miles 1980, pp. 20-21 for a

discussion and references], so that for Fr >

1.3 one would not expect a soliton to be formed

that could escape from the model. This bound

may, however, be modified slightly by the shelf

of water preceding the model.

At least qualitatively, the results of

the calculations for a two-dimensional pressure

distribution moving steadily over an inviscid

fluid at small depth have agreed remarkably well

with the observed behavior of the waves formed

by a ship model moving steadily (+ 0.02 ft/sec)

down 'a towing tank.

Both show solitons being

formed that move at supercritical speed ahead of

the model or pressure distribution.

These are

followed in both cases by a longish smooth

region and then a region of waves oscillating

about the mean water level.

This consistency is

important for the light it throws upon the

physics of the phenomenon.

It tells us, for

example, that the occurrence of solitons is not

a result of three-dimensionality only (for they

also occur in the two-dimensional case), that

it is not caused by irregularity in carriage

speed (for the calculations assume constant

speed) ,

and that it is not a result of

viscosity (for the calculations assume an

inviscid fluid).

To say that the generation of solitons is

not associated v7rith three-dimensionality or the

presence of tank walls does not mean that the

walls have no effect upon the solitons

generated.

since the solitons leave the model

as essentially two-dimensional waves spanning

the tank, one naturally asks what happens as the

tank gets wider and wider.

Let us consider this

question.

It can be shown [see Miles 1980, p.

15 or Keulegan and Patterson 1940, pp. 76-771

that the energy per unit width of a soliton is

given by pgE where

r-E = I

n'clx

.

L.

It can further be shown

see Miles 1980,

p. 15] that

33'3

4

-

3 /2

a =

E

/h

or

E = [ ah

,

where a

is

the

amplitude

of the solitary

down a

tank of width b will then be

transporting pgEb energy.

If one such wave is

generated every T time units, the average rate

of work being done by the

model in generating

solitons is

pgEb

Similarly, the average work per unit

width done by the moving pressure distribution

in generating solitons is

,g

3

ah72

T

Evidently, if the tank becomes wider, and if the

depth h and model are kept the same, then if the

resistance is to remain finite, either T must

increase or a must decrease, or some combination

of the two.

If

p

the pressure

distribution is increased, it seems reasonable

to suppose that pgE/T must increase, and again

one would suppose that a

increases, or T

decreases, or some combination of both.

The

precise nature of the dependence of a and T

upon b, or upon p, can be determined by

further experiments, or calculation,

respectively.

There is one conclusion concerning a

that can be derived.

From a classical formula

for solitary waves [see Miles 1980, p. 131

c2 = gh (1 +a/h) or c/fgT1 = 1 +a/2h >1

(for always

a > 0).

Since c > u,

a

_{= 2}

[

_{_} >

2 [Fr -11

_l

_{( O.}

Hence, at least for supercritical model

velocity, there is a lower bound for a/h no

matter what the width of the tank, or what the

value of p. This seems to suggest that, as

om

P_om

becomes quite small or b quite large, T

will become large, and that T

.0 as b

i.e.

that there will no longer be solitons

generated

in an unbounded fluid, provided, of course

that

the solitons retain their two-dimensionality

as

b increases indefinitely.

A few quantitative results

have been

extracted from the wave records.

Figure 10

shows the dimensionless period uT/h plotted

against Fr. What seems most notable here

is the

linearity of the points in the region 0.8

< Fr

< 1.1.

It would be of interest to examine

the

region Fr < 0,8 to see if there is a Fr

below

4b

pg

ah

26-4

which no solitons are generated.

Figure 11

shows the dimensionless soliton velocity c//1i

plotted against Fr. Once again the results seem

to be close to linear in the region 0.8 < Fr <

1.2.

The difference between the two depths may

be a result of bottom uneveness, but needs to

be investigated further.

Plots of c/ gh

obtained from records like those shown in

Figure 7 show more scatter than Figure 11, but

are not in disagreement with it.

We have not yet discussed the

resistance. This was both measured for the ship

models and calculated for the pressure

distribution.

In both cases the resistance

fluctuated with period T, with the maximum

occurring at about the time a soliton left the

model.

An analysis of the data will be given

elsewhere.

However, from the viewpoint of the

model tester this is one of the important

results of this investigation. In tests in

shallow water at transcritical velocities, it

is to be expected that a steady state will not

be reached and that the resistance will

fluctuate periodically.

The fluctuations are a

result of natural laws, not of equipment

malfunctioning.

REFERENCES

Hammack, J. L. and Segur, H.

The Korteweg-de Vries equation and water

waves.

II.

Comparison with experiments.

J. Fluid Mech., vol. 65, pp. 298-314 (1974).

Keulegan, G. H. and Patterson, G. W.

Mathematical theory of irrotational

translation waves. J. Res. Natl. Bur.

Stand., vol. 24, pp. 47-101 (1940).

Miles, J. W.

Solitary Waves.

Ann. Rev. Fluid Mech., vol.

12, pp. 11-43 (1980)

Segur, H.

Solitons and the inverse scattering

transform. Topics in Ocean Physics, pp.

235-277. Soc. Ital. Fis., Bologna, 1982.

Sibul, 0. J.; Webster, W. C. and Wehausen, J. V.

A phenomenon observed in transient testing.

Schiffstechnik, vol. 26, pp. 179-200 (1979).

Wu, T. Y.

Long waves in ocean and coastal waters.

J. Engrg. Mech. Div. Proc. ASCE, vol. 107,

pp. 501-522 (1981).

Wu, De-Ming and Wu, T. Y.

Three-dimensional nonlinear long waves due

to moving surface pressure.

Proc. 14th Symp.

on Naval Hydrodynamics, Ann Arbor, 1982,

40r

10

0

Series 60; CE, 0.pe

Series 60, CE, 0.60

ser, es 60: Cr, 0.80. c.',urea

6 ,lehes ahead of model

1

u/ATI

02 0.3

u/s/siTI

Figure 1. _{Dimensionless wave period gT/u observed after}

an abrupt start. Top: depth = 1.2 ft, Bottom: depth 5.5 ft.

05

Figure 2. _{Dimensionless wave period gT/u observed after}

an abrupt start. Depth = 0.5 ft.

nr

0.1 Series 50

0_c

0

h 0,20.; h.,. 2, lend: Cl 0.60 6_520,Ih.. 2.0. 1.44: C. A h 0.027.: 00 P.O. 1000 0. ro o 0.500. cop. depth C. 0.40 h 0.606. et... dep., C. 0,0 60 50 40 30 20 10 10 0 CB = 0.70; LB, = 5.00'; D = 0.267' x- CB = 0.70; LB, = 5.00'; 0 = 0.134' A Ca = 0.80; LB, = 3.75; D . 0.167' double bow model, similar to Series 60, CB = 0.80

0-

As above, but 7.5 ft long

draft 0.333 ft.

0.4 0.5

30

QT,

1R,f,

1,0.

200

1. CD

am.*

Figure 3. Wave records at end of tank for Fr = 1.0,

h 0.349 ft, Gauges 1, 2 and 3.

Figure 4. Qualitative sketch of a wave gauge record taken

far from an initial hump of water in a shallow-water basin.

i 1981

t....

._>.

--EEEE>---

.0.GO --$:. t.' t ! . GI .t ...30 FT Fr. TIME, C5P,C, 1982 100 AND 200 SERIES

$7z2ES,-$

26-6

4101;k1..,.

L G3 L,fe-G3 2 FT. I FT. C354 FT. IF i2 FT

'''

Q-..

W7

i 300 SERIES AOOSERIES S 98I 982 982

Figure 5. Sketch of locations of wave gauges in

20 T. Rug

F0.9

70 Ft Aug

26-7

Figure 6. _{Records from gauges 1 and 2 for model runs of}

length 20 ft and 70 ft at Fr = 0.9 (1981 series).

N NO. 403 AND 405 1-4-0. 349 FT. g5

.al

g ..0.1 'Mg I, Z. 95 M.O0, 71,0 Fe-1. 05 111. TIME MU, Figure 7.

Records from gauges 1 and 2 fixed to carriage for Fr = 0.95 (top)

(a)

Figure 8. Typical wave records from gauges 1 and 2 for

h 0.255 ft, (a) Fr = 0.9, (b) Fr 1.0

R1_11,

1,0. 104

1

1,-40. 2,5 F

"

Figure 8. Typical wave records from gauge 3 for h = 0.255 ft,

(c) Fr = 1.1 rJr.). 114..

-

!LI I

RUN: r10. 100

F.-- 1. 0

H.-0. 055 RT.

26-'3

0.4 0 0.2r 0 1

t;l:.11I1111111

1-

111.111,11

Iltlillt

I I \LI

II /I

j 4 n LI 1 I I I I 11 I

I a";

t I

Yrk,21111/11

U.LO, p,=005, hO.5, Ax=0.2, . 1=Ax/U

I

jf=4,4

I 2 , I 48 I ja 1 I I 1 64 I I I

U.1.175, p0.I . h=0.5, ,0,x=a2, At=Ax/U

'Figure 9. Calculated free surface generated by moving pressure distribution at various instants after starting.

Dimensionless time ut/L, dimensionless length x/L, L 2h,

(a) Fr = 1.0, (b) Fr = 1.175.

26-9

t=36 -am 40 t =0.2 8 6 40 56

, no, H SIP? 92

P i2C0K 9900E 500 629its

De-Bo Huang

The Harbin Shipbuilding Engineering Institute, The University of California, Berkeley

041 0.9

(10) (11)

Figure 10. Measured values of dimensionless period of

generation of solitons, h = 0.349 ft.

Figure 11. Measured values of dimensionless speed of

propagation of solitons.

De-Ming Wu

The Harbin Shipbuilding Engineering Institute The California Institute of Technology, Pasadena

0. J. Sibul, W. C. Webster, J. V. Wehausen T. Y. Wu

The University of California, Berkeley The California Institute of Technology, Pasadena

0 80 70 60 5

0

30 20

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1.0 9 ° a 0. * 7 .111;.COT.,,OL,r0/271017 .20709 069.114 U5110E3 Or 6002; o107S7 II SC, 112 C Sac., 09084 1400 SL,E5 c

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no-CONFERENCE on

BEHAVIOUR OF SHIPS IN

RESTRICTED WATERS

November 19 82 vcrna

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