Department of Civil Engineering, Akdeniz University, Dumlupınar Bulvarı, Kampus/Antalya 07058, Turkey.
Present address: Department of Engineering Sciences, Middle East Technical University, İnönü Bulvarı, Ankara 06531, Turkey.
Department of Engineering Sciences, Middle East Technical University, Inönü Bulvarı, Ankara 06531, Turkey.
We developed analytical solutions to the wind set-down and the wind set-down relaxation problems. The response of the ocean to the wind blowing over a long-narrow and linearly sloping shallow basin is referred to as wind set-down. The shoreline exhibits oscillatory behavior when the wind calms down and the resulting problem is referred to as wind set-down relaxation. We use an existing hodograph-type transformation that was introduced to solve the nonlinear shallow-water wave equations analytically for long wave propagation and obtain an explicit-transform analytical solution for wind set-down. For the wind set-down relaxation, the nonlinear shallow-water wave equations are solved analytically as an initial-boundary value problem, with forced initial data derived from our wind set-down solution.
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