The Statistical Properties of the Slope of a Wind Driven Water Surface of a Model Tank

摘要

The communication characteristics of underwater acoustic signals are being studied in a model tank. Part of this study concerns signals which are reflected from the water surface. To obtain the characteristics of these signals, the statistical description of this random moving surface is very important. The most important factors determining the state of this surface are the waveheight and the surface slope. The waveheight statistics have been studied before and this study is concerned with the slope statistics of the water surface. The slope statistics are obtained with a device which utilizes a lightbeam refracted at the surface and a photocell. From an analysis of the output voltage of this photocell, the statistics of the components of the slop of the surface are derived. The probability density function of the crosswind slope compares well with a Gaussian, but the probability density function of the down-wind slope is skewed towards the slopes in the tails of the waves. The variation of the variances of the cross-wind slope and of the down-wind slope with windspeed is then investigated. The sum of the variances of the cross-wind slope and the down-wind slope increases linearly with windspeed and their ratio is constant. (Author)