The distribution of wave heights and periods in ocean waves

Abstract

SUMMARY ~N T R O D U C T I O NA number of investigators have analysed wave records to determine statistical relations between the various parameters describing a particular record. For example Putz (1952) analysed 15 records from underwater pressure recorders in various depths of water between 45 and 90 ft off the California coast, and Seiwell (1948) carried out a series of analyses of similar records from the North Atlantic; more recently Watters (1953) has analysed pressure records made by an Admiralty wave recorder at Greymouth in New Zealand. From a theoretical approach Longuet-Higgins (1952) deduced relations between the root-mean-square wave height, the mean height of the highest one-third of the waves and the most probable height of the largest wave in a given interval of time. His results are in good agreement with those published by the investigators mentioned above.The National Institute of Oceanography has recently developed an instrument (Tucker 1952) which may be fitted to the hull of a ship below the water-line and which continuously records the water-level. A feature of the instrument is the elimination, by an ingenious device, of the ship's own vertical motion. When the ship is stopped the record may be expected to provide wave measurements more detailed and accurate than any obtained by eye estimation, no matter how experienced the observer. Such an automatic record can be made anywhere at sea. The instrument responds to waves with periods between 5 and 25 sec and within this range there is practically no attenuation of short-period waves such as is inherent in bottom pressure recorders. One of the instruments has been installed in a British Ocean Weather Ship, and through the kindness of the Director of the Meteorological Office and the Director of the National Institute of Oceanography a series of records, made three-hourly in February and March 1953, have been made available for analysis. This paper summarizes the results. As far as the writer is aware these are the first instrumental records of deep ocean waves to be analysed. METHOD OF ANALYSISThis was quite straightforward. The height H of each wave from crest to trough was measured to the nearest foot and the period T of each wave taken off the time scale on the record to the nearest second. The records include a few taken while the ship was moving slowly to regain station; parameters for these have been calculated but none of them has been plotted on the diagrams, nor have they been used when calculating ' best-fit' straight lines or correlation coefficients. They are included in the table of results for the sake of completeness. THE RESULTSThe analysed results are shown in Table 1, and plots showing the relation between various 138 records were made while the ship was stopped. The pairs of quantities have been drawn. parameters are defined as follows : G1Y

Wind waves in the Black Sea: results of a hindcast study

“…The theoretical background is developed in e.g. Putz (1952), Darlington (1954), Munk (1955), Goodknight and Russel (1963), Pierson and Moskowitz (1964), Glukhovskij (1966) and Davidan et al (1978). The results of applied studies are summarized in several monographs and handbooks, such as Rzheplinskiy (1969) and Simonov and Altman (1991).…”

Wind Waves and Swell

“…In order for the concept of significant wave height and period to be of more value studies were made of the distribution of wave heights and periods about their mean values (Ehring, 1940;Seiwell, 1948;Wiegel, 1949, Rudnick, 1951Munk and Arthur, 1951;Darbyshire, 1952 Putz, 1952;Pierson and Marks, 1952;Watters, 1953;Yoshida, Kajuira, andHidaka, 1953;and Darlington, 1954). These papers advanced the concept of the "statistical nature" of ocean waves.…”

“…Of more importance in the consideration of waves in the generating area is the work of Darbyshire (1959), the data on wave frequency distribution being given in Fig. 14. Darlington (1954) has made a similar study of wave records obtained with the NIO shipborne wave recorder (Tucker, 1956) in the North Atlantic. Most of the recordings reported were made with the ship stopped.…”

“…These two parameters were chosen as they were the most generally available ones. The data shown are for wind waves rather than swell, although there may be some swell present in the records of Bret-Schneider (1954) and Darlington (1954). A line was drawn through the wind-wave tunnel data of Sibul (1955), neglecting the smallest waves as these probably were affected considerably by surface tension.…”

Wave measurements along the California coast

“…An 1 average' wave period of some type is used to derive the multi plication factor by which the bottom pressures are transformed into surface wave heights. The sig nificant period is longer than the mean period (tie significant period being associated with the groups of large waves in the record [Darlington, 1954]),…”