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Title: Wave variability and wave spectra for wind-generated gravity waves
Authors: United States. Army. Office of the Chief of Engineers
Bretschneider, Charles L., 1920-
Keywords: Wave distribution functions
Wave spectra
Gravity waves
Issue Date: Aug-1959
Publisher: United States, Beach Erosion Board
Engineer Research and Development Center (U.S.)
Series/Report no.: Technical memorandum (United States. Beach Erosion Board) ; no. 118.
Description: Technical Memorandum
Abstract: Wave records from a wide variety of locations have been utilized in a statistical analysis of the probability distributions of wave heights and wave periods; and a family of wave spectra which allows for arbitrary linear correlation between wave height and wave period is suggested. It is found that the marginal probability distribution of wave heights follows Rayleigh's distribution closely. This conclusion is based upon 90 records of 100 waves each plus several extra long records taken in deep and shallow water. About half of these records represent time sequences of water levels at particular locations and the other half are time sequences of pressure at subsurface depths (from which the wave heights were estimated using the linear wave theory). The Rayleigh distribution for wave height variability has been suggested previously by Longuet-Higgins and Watters. An apparently new result of the present work is that the marginal distribution of the square of the wave period also follows Rayleigh's distribution remarkably well. From the Rayleigh distribution for wave height variability it is possible to derive the marginal distribution of wave period variability, also verified with the available data. An analytical expression which allows for non-zero linear correlation between wave height and period squared is suggested for the joint distribution of wave heights and periods. The joint distribution is employed in the determination of the mean wave period for the highest waves. Also an analytical expression for the family of wave spectra is derived from the suggested joint probability distribution of heights and periods. The basic assumption underlying the suggested spectra is the condition of the linear correlation between wave height and period squared. These spectra are compared with those proposed by Darbyshire and Neumann and with the numerically evaluated spectrum obtained recently from Project SWOP and are found to be in good agreement with the latter. The spectrum for a fully developed sea, a special case of the proposed family of spectra, is also consistent with the measurements of Burling and the theoretical work of Phillips, which indicate that for high frequencies the spectral energy is inversely proportional to the fifth power of the frequency. It is also found that the present family of spectra predicts a mean square slope of the sea surface which is in closer accord with the data of Cox and Munk than that inferred from the spectra of Darbyshire or Neumann. It is proposed that in the early stage of wave generation the correlation coefficient between wave height and period squared is nearly unity because of the maximum possible steepness of the waves. As the generation proceeds it is proposed that this correlation decreases, ultimately approaching zero for a fully developed sea. Corresponding to the suggested behavior of the correlation coefficient betweem wave heights and periods, the intial spectrum is narrow and becomes wider as the generation continues. It is found that so-called "siginificant" wave period is closely related to optimum or modal value of the period spectra and hence the energy of the waves as a group should have a propagational speed approximately equal to the group velocity of the significant waves. A revision of the earlier wave forecasting relationships proposed in an earlier work by Bretschneider are revised to take into account the variation in spectral width.
Appears in Collections:Technical Memorandum

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