|M.Sc Thesis||Department of Civil and Environmental Engineering|
|Supervisors:||Prof. Stiassnie Michael|
|Prof. Agnon Yehuda|
|Full Thesis text|
This study deals with the problem of wind waves generation. Scientific interest in momentum and energy transfer between the ocean and atmosphere and wave forecasting are examples of directly related research topics of the wind waves generation problem. The problem deals with the instability of water waves in the presence of a shear flow. The study contains a full formulation of the linear stability problem in 2D for the viscous and inviscid models. The formulation leads to an ODE which controls the problem. The governing equation for the inviscid model is Rayleigh's equation, whereas the governing equation for the viscous model is the Orr-Sommerfeld equation. After applying the boundary conditions the resulting problem is an eigenvalue problem for the wavenumber or for the wave frequency. These eigenvalue problems were solved using numerical methods chosen especially for each model. The mean flow of the air and water plays a main role in the problem because the solution is sensitive to this choice. We use three versions of the mean flow profile; two of them are profiles which have been used in previous studies and one of them is a new profile which we suggest as a more physical profile. The results were calculated for both models and many different scenarios. In the viscous model, we expand the range of wavelengths and wind intensities with respect to previous studies to 0.001m<λ<0.2m,0.1m/sec<u*<1m/sec. The results are presented in a comprehensive set of figures. In the viscous model we discovered the presence of a new unstable mode at high wind intensities for the case in which we used a profile with a shear current. This second unstable mode is characterized by a slower phase velocity. A comparison between the results of the inviscid model and the viscous model is of major important. We compare these two models not only by comparing the eigenvalues and the eigenfunctions, but also by comparing the pattern of the dynamic boundary condition. The comparison at low wind intensities shows that the inviscid model and the viscous model have similar patterns, although the growth rates in the viscous model are twice as large or more than those of the inviscid model. At high wind intensities the results of these two models are far from similar. The results of the comparison emphasize the question, in what sense is Rayleigh’s equation is an approximation for a large Reynolds number to the Orr-Sommefeld equation.