DIMENSIONS OF SEA WAVES O N THE N O R T H - A T L A N T I C
byIR J. G E R R I T S M A
Technological University Delft, Sfiipbuilding Department
Introduction
The study of ship motions at sea requires, among other things, some knowledge of the dimensions of the prevailing waves. This knowledge should guide us i n selecting the size and type of the artificial waves in which ship models are run.
A t the request of the Laboratory for Shipbuilding Research i n Delft, the K.N.M.L (Royal Netherlands Meteorological Institute) in De Bilt, supplied data concerning wave dimensions on the North-Atlantic sea route. These data were collected during the years 1 9 4 9 - 1 9 5 2 , partly by Dutch merchant ships (ap-proximately 9 0 % of the data) and partly by a weathership (about 1 0 % of the data).
The observations were made in the area:
• 6 0 ° - 3 0 ° West , 3 0 ° - 1 0 ° West , , , 4 0 ° - 5 0 ° N o r t h ^ ' ^ ' i 4 5 ° - 5 0 ° North ^'^^
and the following data were collected: a. wave period in seconds
These data are classified as follows: 1. According to three months' periods:
a. December, January, February b. March, April, May
c. June, July, August
d. September, October, November
2. According to the wave directions:
Each direction sector is 3 0 ° wide.
The total number of observations amounted to . 3 5 , 6 5 9 .
The observed wave height is the mean of the maximum heights of clearly distinguishable wave groups.
Wave heights are given i n intervals of 0.5 m, whereais the wave-period intervals are. 2 seconds each.
Frorh the formula:
T ^ 0.8 N/X in which:
163
it is possible to determine the wave length.
In table 1 the wave length according to this formula are given.
TABLE 1
T sec . . . . J ' 7 9 11 13 15 17
A m 39 76 126 189 264 352 452
From this table it is clear that the wave-period intervals of 2 sec are fairly large in comparison with the wave-height intervals of 0.5 m.
htterpretation of the observations
The data supplied by the K . N . M . I . were re-arranged to suit our purpose: the study of ship motions.
We want to obtain an impression of: a. wave height
b. wave length c. wave direction
d. steepness of waves (as given by the ratio wave height
wave length
It is clear that the observations give only a rough
picture of the reality: they are based on fairly rough estimates.
Owing to the complex nature of the seaway i t is probably not possible to get much better estimates of the wave dimensions without the aid of expensive apparatus.
However, the large number of data is a guarantee that the derived mean values are not too erratic.
I n broad outline the analysis of the data is the same as that in Dr H . U . Roll's "Höhe, Lange und Steilheit der Meereswellen" (Deutscher Wetter-dienst, Seewetteramt, Einzelveröffentlichungen, No. 1).
I n the first place two dimens'ional frequency tables are set up, in which the connection between wave length (wave period) and wave height is shown (see pp. 5, 6). The widths of the columns are proportional to the wave-length intervals. Con-sequently, the width of the columns increases f r o m left to right. For instance, a period interval of 5 to / •seconds corresponds .with a wave-length interval of 39 to 76 metres, and a period interval of 15 to 17 seconds gives a wave-length interval of 3 52 to 452 metres (see table 1). The wave-height intervals
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DECEMBER -JAtlUAm - FESRUARV
NO DIRECTION: S.2 •
S 7 S f f fJ /7>/7 X WAVE PERIOD SEC. J9 76 IS& 703 set 3sa 45a mvE LENani m.
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MARCH - APRIL - MA7
a i ^ L ^ ^ . e s.o SOUTH NO DIRECTIOfl: S:0 % h 70
1
JUHE-JUU- AUCUST NO DIRECTION: 4.3 %5 7 9 H 73 7S 77 >77 X WAVE PE/tlOD SEC 3V 76 72S 73.9 261 JS2 452 WAVE LENTTTJ, m
SEPTEMBER - OCTOBER - f70VE/^BER
NORTH 74^ .3/ \
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/^^ ]£ SOUTH NO DIRECTION: 5.3 %165
have a constant value of 0.5 m, the lines are equi-distant.
I t is now possible to draw straight lines of wave height
""""^^"^ wave length frequency tables, which give an indication of the wave steepness.
Wave lengths > 4 5 2 m (with a corresponding period > 17 sec) are taken together: the frequency of these large waves is small. Also the wave heights
> 9 m are taken together.
The frequencies of the cases:
X, impossible to estimate the wave period;
Rx, impossible to estimate the wave height, but < 5 m;
R x - f 50, impossible to estimate the wave height,
but > 5 m; •
are shown in the frequency tables.
The frequencies are expressed in "/„o of the total _ observations for each quarter of the year. The sum totals of the columns give the frequency distribution of the wave length, whereas the surn totals of the lines give the frequency distribution of the wave heights.
Analysis of these frequency distributions for the
12 wave-direction sectors showed that the shape of
these distributions is more or less independent of the wave direction, at least the differences in .shape are irrelevant for our purpose.
Thus i t is possible to give frequency distributions for each quarter of the year for:
a) the wave length 1 independent of the wave b) the wave height / direction; see pp. 5 to 6. c) the direction of waves.
Figures 2 to 9 give these distributions in graphical drawings. I n the figures of the wave-direction distribution, the' direction of the heavy lines gives the wave direction. Their length is proportional to the frequency of that direction (this frequency is also given in fo in the figures).
Connection bet^ueen wave height and wave length I t is not possible to calculate the wave steepness by using only the frequency distributions of wave length and wave height as given in figs 2 to 9.
For instance:
the maximum frequency of wave height does not necessarily coincide with the maximum frequency of wave length. A first impression of the connection between wave height and wave length is given by the lines , of constant steepness in the frequency tables.
Generally speaking, we may assume that the frequencies are concentrated in the centre of gravity of the rectangle in which the frequency is written. I n some cases the theoretical maximum steepness
1 : 7 is exceeded; but only when a rectangle lies
entirely below a hne of constant steepness, is i t certain that the steepness which corresponds to that line, is exceeded. The frequency of the cases in
which the steepness 1 : 7 is exceeded appears to be very small; probably, errors i n the estimated wave dimensions account for these too high values of wave steepness.
For getting a surveyable representation of the , connection between wave height and wave length the following procedure was followed.
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For each quarter of the year the wave height (at constant wave length) was calculated which was not exceeded in 2 5 %, 5 0 % and 7 5 % of the cases respectively.
The wave lengths which correspond with these wave heights are given in table 2 .
TABLE 2 . , . , m e a n w a v e l e n g t h p e r i o d s e c m e a n p e r i o d s e c ^ rm/^ ^ 7 -A = 1*'1).D4 < 5 ~ 4 ~ 2 5 7 G 56 7 — 9 8 1 0 0 9 — 11 10 1 5 6 11 — 13 12 2 2 5 13 — 15 14 3 0 6 15 — 1 7 1 6 4 0 0 I . S . P . - Vol. 1, No. 3 - 1954
The dotted parts of the lines indicate that only a small number of observations are available i n the region.
Probably, the longer waves with their smaller steepness have a "swell" character, whereas the shorter ones may be described as "sea".
