Large‐amplitude periodic lee waves in stratified fluids Pt. (1) – Non‐linear solution

Abstract

SUMMARYThis paper deals with a two-dimensional train of free, internal gravity standing waves in an inviscid, incompressible, stably-stratified fluid bounded by a rigid base and free surface. The waves are similar to those studied by R. R. Long, and are assumed to be periodic in the horizontal direction, and independent of time. The classical linearized theory has been extended by examining the wave equation with a variable Lo2 parameter. The equation has been solved numerically, and the method of approach has been to regard the non-linear terms as ' perturbations ' on the main wave term which is treated in the classical linearized theory.Deviations from the linearized theory are shown to become more pronounced the larger the amplitude of the wave, as the streamlines become displaced by presence of the non-linear terms, and the relative magnitudes of non-linear coefficients are compared with the main terms for the cases computed. The undisturbed fluid stream is the same for all the computed wave profiles, and the amplitude has been varied from small to large to show the development of rotor regions.

Internal waves in the sea : a summary of published information with notes on applications to naval operations / O.S. Lee.

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