Generation of Interfacial Coherent Structures by Internal Waves in Stratified Fluids

Date of Award

Fall 2024

Project Type

Dissertation

Program or Major

Mathematics

Degree Name

Doctor of Philosophy

First Advisor

John P McHugh

Second Advisor

Greg P Chini

Third Advisor

Mark Lyon

Abstract

Large amplitude internal waves in a density stratified fluid are treated numerically. The flow is modeled using the Navier-Stokes system of equations under the Boussinesq approx- imation. The background density profile is two layers of constant density with a smooth transition region, created with the hyperbolic tangent function. The numerical method evaluates derivatives in the vertical and the longitudinal horizontal direction with finite dif- ferences, and in the transverse horizontal with Fourier transforms. Temporal integration is performed using a splitting algorithm. Waves are forced at one boundary to create a self- focusing wave packet so that a large amplitude wave will form away from the wavemaker. The results show that if the amplitude is large, a coherent structure forms at the front of the packet. This structure moves relatively slowly, often slower than the group velocity of all individual waves in the self-focusing packet that created the structure. A second method of wavemaking using a chamber of heavy fluid confirms that large amplitude waves form this coherent structure. Three dimensional simulations suggest that the structure will become three dimensional for long times.

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