Refraction of waves near the Dogger Bank

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•.i,nie~iral'repert RI 197313/L

L•.à, Holthuijsen ,

Vloeistofmechanica

Afd. Weg- en Waterbouwkunde Technische Hogeschool Delft

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Refraction of waves near the Dogger Bank.

internal report 'R/1973/3/L

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page

I Introduction. 1

11 Refraction in the North Sea. 2

111 Interpretationof the refraction diagrams. 5

IV Practical experiences. 7 V Conclusion. 8 References. Diagrams. 8 9

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-1

-1 Introduction.

The geometry of the seabottom may cause waves to refract such

that a concentration of wave-energy occurs. In view of the particular

shape and dimensions of the Dogger Bank, it was interesting to find

;

out whether such a phenomenon'may occur in this area. It is expected

that only langer waves will show the effect mentioned (periods of about 12 s). These waves occur quite frequently in the North Sea and are usually travel

-ling.in sautherly directions.

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,

11 Refraction in the North Sea, particularly near the Dogger Bank.

During an investigation on ·theeaustic phenomenon in wave

refraction, a test was carried out in a model where the conventional

refraction theory breaks down (crossing orthogonals): waves propagating

over a circular shoal (see ref. 1).

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The related refraction diagram is shown in diagram 1. A similar situation

has been investigated by Pierson (ref. 2).

Although the conventional'refraction theory does not hold in this case, it was found in the laboratory that astrong energy concentration occurs near the convergence area. The directions of the waves agreed fairly well with the direction given by the conventional refraction computation.

By applying model laws we see that a situation similar to the one in the model can exist at sea. For instance enlarging the horizontal and

vertical scale x 1000 and taking the period of the waves x VIOOO would

result in,a minimum depth of the shoal of 20 mand a wave period of about

15 s. The minimum depth over the Dogger Bank is about 20 mand, although

the slope of the seabottom near the Dogger Bank is far less than in the

model, strong convergence may occur for waves with a period of about 15 s.

In order to find out whether such a situation may exist near the

IX>ggerBank, a computer program of the Delft University of Technology

has been used (conventional refraction computation), A map of contourlines

was digitized on a grid of 50x50 km2• The approximat~d seabottom is

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-3-12 and IS s. The results of.:'thecomputations are given in diagrams 3, 4

and S.

The approximation of the'seabottomis very rough and the computations

only hint at the possibility of energy concentration south of the Dogger

Bank.

area investigated

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The period of 15 s is close to the resonance period of giant tankers. These tankers manoeuvre in this part of the North Sea. Pierson (ref. 3)

showed that it is not unlikely that the loss of two British trawlers was.

due to the rough character of waves in such convergence areas. One of these trawlers was lost just south of the Dogger Bank.

To investigate the situation more thoroughly, a second set of

computations has been carried out based on a more detailed approximation of the seabottom. The area chosen is smaller than for the first set of computations and was located so as to LncLude the areas of expected ray-convergence. The bottom approximation is presented in diagram 6 (gridsize 25x25 km2).

area investigated

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'--I • I • I • • • I L_..J

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20E,540N (orientation for diagram 6). --...Euro-channe1

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Computations have been carri.ed out for periods 10, 12, and 15 s and

directions 338°, 0° and 22° ;èlative to North. The results are presented

in diagrams 7-15. The phenomenon of energy concentration mayalso occur

when waves approach a gully from a certain sector of directions. In order

to find out whether waves from the Channel may provoke this phenomenon

in the southern part of the North Sea, one computation has been carried

out for period 12 s and direction 203°. The result of this computation

is shown in diagram 16.

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-

5-111 Interpretation of the refraction diagrams.

Tc compile the results of thc rcfraction diagrams, tbe concentration

areas are shown in diagram 17. In the areas indicated the distance betwcen

initially neighbouring rays is less than 1/10 of their initial distance. In order to know how close the computations approach the physical

reality, we must look at the restrietions of the model used.

The program used to calculate the rays is based upon thc conventional refraction theory. This in many cases results in a fairly good estimate of the refraction picture. As soon however, as diffractlon is not negligible tbe metbod used is incorrect. This is especially tbe case when energy

concentration occurs. Diffraction effects will then cause the increase

of the amplitude to be less pronounced than indicated by the refraction computations.x This implies for instance that the long, narrow concentration areas will be shorter and broader than indicated. Although the theory used does not hold here, the computed .directions of tbe rays (based upon the approximated bottom) may give the direction of the waves to a fair degree of precision as was found during the test in the physical model (page 2).

The inaccuracy of the bottom approximation though will cause the direction

\

of the waves to deviate from the real direction at sea. Another restrietion on the numerical model is the fact that we cannot possibly imitate the large variety of wave frequencies and directions present at sea. \veshould think of

the seasurface as being composed of an infinite number of wavecomponents: at sea a continuous two-dimensional wave spectrum is present. From this concept of the two-dimensional spectrum it follows that the concentration areas will only contain high energy when the initial spectrum (tbat is: in the northern part of the North Sea) contains substantial energy near

the components investigated. It also follows tbat the components investigated may be present all at the same time and tbat neighbouring components (in the

spectral plane) may bave concentratlon areas near the ones found in this study. Together witb the diffraction effects, this will result in an

in-creasing of the size of the concentration areas and a more diffuse character of the concentration areas. The periods investigated are rather long and wil1 in most cases represent swell in the North Sea (spectrum has small frequency and direction range) but they mayalso be part of a spectrum

generated by a "local" storm.

*

Ref.! has investigated a theory of SchonfeLd, which combines refraction

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The area of most pronounced concentration 1S area "Ncrth" (see diagram 17).

Here convergénce occurs for all cases. Moreover the directions of the waves

in this area may differ up to 900 at th~ same time. The conclusion is then

that here, during northern storms, very high and confused seas may occur.

Also swell from the north can be high and have a confused character.

The interpretation of area IIMiddlellis difficult because here the rays

interseet at small angles. The intersecting of rays though occurs for all

cases'investigated (except for 10 s, 200). Therefore a somewhat higher sea may be expected in this area (as compared to a situation not including

refraction by the Dogger Bank). The direction varibility due t'othe

refrac-tion by the Dogger .Bankis not great and confusion will.be much less than

in area "North",

For a northern swelI a convergence area is found in area "Soucb", Here

again the rays interseet at very small angles. The -lccation of'this area

seems to be very dependent upon the geometry of the seabottom just east

of area IIMiddle".It must be noted that giant tankers traveling for

Rotter-da~ have to'go through this arei as they must pass the Euro-channel near

Hook of Holland. High energy values of'swell in this area may cause

ser10US trouble to these tankers as they cannot deal with these waves while

traveling in this channel (direction of the tankers is obligatory). A more detailed study should be carried out to clarify this problem.

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-7-IV Practical experiences.

In order to find out whether the convergence arcas are known to fisher--:

men, the author had some discussions \olith skippers from Scheveningen harbour.x The question posed to each skipper was: "Are there any areas

of high and confused seas in the southern part of the North Sea during a

northern wavefield?". The results of the discussions are presented in

diagram 18. The skippers described the Dogger Bank as "unsafe". In particular

area of the South West Patch was described as "dangerous" during any wèather

condition. One skipper a150 indicated the area near the Silver Pit and tha

two areas naar Hook of Holland as being dangerous during any weather cond

i-tion. The same description was given to the "Rug van Tèrschelling" by two skippers. It should be noted that tha fisharmen àssumed that the waves ara reflected from "dry grounds" (shoals). The'areas indicated by them were pointed out on the map by "knowing" and by looking at these "dry

grounds". The concept of refraction was introduced only later in each

discussion. To what extent the experiences of the skippers relate to waves

of periods 10 - 15 s is not known.

Comparing this map with the compiled results of the computations

(diagram 17), we see that area "North" lies between the South \VestPatch

\

and the Silver Pit. The Silver Pit is situated between areas "North" and

"Middle". The two areas near Hook of Holland coincide partly with area

"So~th". The "Rug van Terschelling" is not found in the refraction co

mputa-tions.

Af ter tha skippers had indicated tha areas, their comment was asked

concerrnng diagram 17. Theyall confirmed the existence of area "North" but

none of them acknowledged area "Middlè". Only one skipper confirmed his

bad experiences near area "South".

Apart from the areas of diagram 18, the skippers usually avoid the banks (Lehman Bank area, coastal areas etc.) and the area west of the Bruine Bank during wes te.rnor south-western winds.

The site of the loss of the British trawl.er"Boston Pianeer" is marked with t

in the relevant diagrams (10,11,12,17). This ship was lost in a wavefield

coming from the north. From the diagrams for a

=

00 (diagrams 10,11,12)

it is deduced that the "Boston Pioneer" may have encountered a very high and confused sea. This is in accordance with Pierson's conclusion (ref. 3).

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'v Conclusion.

Refraction comput ations- have shown rather conv incingIy that waves

with periods 10-15 s, coming from northerly directions will concentrate energy just south of t.he Dogger Bank. This result was confirmed by fishermen. The loss of a ship in this 'areatoo confirms the picture.

The computations hinted,at the existence of another concentration area some'50 km south-east of'the forementioned area. The existence of

this area was not confirmed by fishermen.

W11ether energy concentration occurs near Hook of Holland (as':may

be inferred from the,refraction computations) or not, is an open question. A more thorough calculation, based on a more accurate appoximation of the

seabottom may invalidate or back up the present computational result.

References.

(I) Hol~huijsen,L.H.,"Aninvestigation of two-dimensional wave propagation", Delft University of Technology, Dept. of Civil Engng.,vloeistofmechanica,

internal report R/1971/IO/H,1971.

(2) Pierson,W.J.,"The interpretation of crossed orthogonals in wave-refraction phenomena",Techn.Memo., no,21,U,S .Army,B.E.B., 1951•

(3) Pierson,l.J.J.,"Theloss of two British trawlers - A study in wave-refraction", The Journalof Navigation, vol.25,July 1972)no.3.

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