Exponential asymptotics and Stokes surfaces in nonlinear three-dimensional flows

John A. Fitzgerald; Philippe H. Trinh

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arXiv · 2403.05420

Exponential asymptotics and Stokes surfaces in nonlinear three-dimensional flows

John A. Fitzgerald·Philippe H. Trinh

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Abstract

In this dissertation, we seek to expand the scope of work done by Lustri and Chapman (2013) in modelling 3D flow past a point source, in order to account for more general flows, where the strength of such a source, $\delta$, is now $O(1)$. We find that in order to solve for the Stokes surfaces of this nonlinear system, we must develop a numerical scheme to shoot from the analytically continued free surface into real space. The principal contribution of this work is a demonstration of the disparity between the line of intersection found by Lustri and Chapman (2013) and that found by our own nonlinear numerical method, along with proposed extensions for further avenues of research e.g. including surface tension.

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John A. Fitzgerald, Philippe H. Trinh. 2024-03-08. Exponential asymptotics and Stokes surfaces in nonlinear three-dimensional flows. https://arxiv.org/abs/2403.05420

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