Statistics of Random Wave Field

The effects of free surface fluctuations on the probability density function and spectrum of fluid particle velocities and pressure of a random gravity wave field are examined. The waves are assumed to be unidirectional, stationary, Gaussian, and in deep water. These are the usual assumptions of incompressible inviscid fluid and irrotational motion and wave. Expressions of the probability density function and spectrum of velocities and pressure are derived, and numerical results are obtained and presented graphically. Comparisons are made with the case in which the free surface fluctuations phenomenon is ignored. Results indicate that the quantities are all non-Gaussian. Pressure and horizontal velocity is unskewed and zero-mean. With and without the free surface fluctuations phenomenon considered, the spectra of the velocities and pressure differ appreciably; the difference being most pronounced at points above and around the mean water level.