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Internal cnoidal waves in continuously stratified fluids
Abstract
The analytic and numerical aspects of periodic internal gravity waves of finite amplitude in stratified fluids are studied. The governing dynamical equations for two-dimensional incompressible inviscid flows confined between two rigid horizontal planes are the Euler equations for a heterogeneous (stratified) fluid. The traveling wave ansatz and the introduction of the "height function" reduce the system into a nonlinear elliptic eigenvalue problem where the eigenvalue is recognized as the propagation speed of traveling waves. This eigenvalue problem is then solved by a constrained variational principle and the solutions of the problem represent the periodic internal waves of the original system. In order to compute these solutions, a globally convergent computational algorithm is presented. Using this numerical scheme, a series of computer experiments are carried out and numerical results concerning cnoidal waves and solitary waves in a stratified shear flow are obtained.
Subject Area
Mathematics
Recommended Citation
Wang, Sheng, "Internal cnoidal waves in continuously stratified fluids" (1991). Doctoral Dissertations Available from Proquest. AAI9132931.
https://scholarworks.umass.edu/dissertations/AAI9132931