A Variational Approach to Nonlinear Wave Theory.
ARMY ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG MISS
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A variational approach to nonlinear wave theory is explored by deriving the equations of motion for four small amplitude constant depth theories, two finite amplitude constant depth theories, and one small amplitude variable depth theory. It is determined that the rotational wave theories derived are more appealing than the irrotational theories. The characteristic relation is explored for the above theories and the effect of vertical velocity on wave reflection is investigated. Further numerical and experimental efforts are warranted to investigate the validity of the equations of motion for describing shallow water wave phenomena. Although the methodology used requires conservation of energy, the possibility exists that a variational approach might be derived for a nonconservative system thus allowing frictional energy dissipation and energy loss by breaking.
- Numerical Mathematics
- Fluid Mechanics