Submitting Campus

Daytona Beach

Department

Mathematics

Document Type

Article

Publication/Presentation Date

4-4-2016

Abstract/Description

Three major unresolved problems that remain in oceanography are studied in depth, namely (a) unsteady waves, where waves are allowed to grow or decay in time and space; (b) sharp-crested waves (also known as fully nonlinear Stoke waves), which are note characteristic in oceans; and (c) group of waves, which can often become sharp crested as they propagate downstream, as demonstrated here experimentally in a wave tank. The ultimate aim of such investigation is to improve the parameterization of the energy input from wind to waves. In this paper, we (i) present results on the simplest approximation to wave groups which result to a fully nonlinear Stokes waves (those having a sharp-crest); (ii) impose the boundary condition at the surface wave, rather than at the mean surface; (iii) assume the wave phase velocity is complex which consequently allows the wave amplitude to vary according to ( ) , 0 kc ti a t = a e where a0 is the initial constant amplitude, k is the wave number, and i c is the wave complex phase speed; and, (iv) include the dominant viscous term in the perturbation equations. It is shown that: (i) yields an energy-transfer coefficient that is larger than that previously calculated for monochromatic waves and agree well with experimental data; (ii) has no major effect on the end-results; (iii) shows the variation of dimensionless energy-transfer parameter β with the wave age for unsteady waves; (iv) the vertical component of perturbation velocity is not singular at the critical point.

Publication Title

Advances and Applications in Fluid Mechanics

DOI

https://doi.org/10.17654/FM020010021

Publisher

Pushpa Publishing House

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