Date of Award

9-2021

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Mathematics and Statistics

First Advisor

Benjamin F. Akers, PhD

Abstract

The instabilities of overturned traveling waves are determined by the use of spectral methods. Two separate numerical methods, Spectral Stability Analysis and Dynamic Stability Analysis, are used to assess the instabilities of branches of waves solved from conformally-mapped Euler equations. The branches of waves with Bond number less than two were found to be spectrally stable to super-harmonic perturbations. The branches of waves with Bond number in [2,3) had some waves that were stable and some that were unstable. All overturned waves with Bond number greater than or equal to two were unstable.

AFIT Designator

AFIT-ENC-DS-21-S-002

DTIC Accession Number

AD1151636

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