Short-Wave Behavior of Long-Wave Equations
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 124, Issue 5
Abstract
The stability of nonlinear dispersive-wave equations near the short wave limit is examined analytically and computationally. Equations of first and second order are analyzed based on their linear dispersion relations. Computational tests are performed on the nonlinear version of the equations, which confirm the theoretical estimates. Equations are derived based on approximations of the water-wave Hamiltonian, and are shown to possess different stability properties depending on the order of the Hamiltonian expansion in terms of a small parameter. It is shown that the smoothest solution is achieved by the regularized form of the equations, which, however, lead to excessively dissipative computational results. Consistent results are obtained by the second-order, Hamiltonian-based equations. All equations are solved by a Fourier pseudo-spectral method, which permits direct comparison of the various equation forms based on identical initial conditions that asymptotically reach the short wave limit.
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Copyright © 1998 American Society of Civil Engineers.
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Published online: Sep 1, 1998
Published in print: Sep 1998
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