Abstract
When studying wavestructure interactions in the lowFroude limit, traditional asymptotic theory fails to capture vital aspects of the solution. Thus practitioners often resort to the specialised technique of exponential asymptotics. However use of this method introduced difficulties of its own, whereby oscillatory features of the solution appear to switch on and off seemingly instantaneously across manifolds known as Stokes lines (in two dimensional problems) and Stokes surfaces (in three dimensional problems). This socalled Stokes switching is often associated with sharp corners in the solid geometry.Part I of this thesis address the failure of current exponential asymptotic theory to describe the nature of Stokes switching in problems involving twodimensional smooth geometries. We demonstrate that Stokes switching does indeed occur in problems of this type and provide a visual framework to understand this switching through the method of steepest descents.
Part II of the thesis studies the problem of threedimensional flow over a submerged point source. Firstly, we study this problem in a regime where the pointsource strength is vanishingly small, and determine Stokes switching within the fluid domain. We believe our work is the first visualisation of a Stokes surface in the context of a wavestructure problem. Secondly, we study the generalised problem where the pointsource strength is of unitary magnitude. We use a specialised numerical scheme to determine Stokes switching on the freesurface and provide a unifying asymptotic methodology between the linearised and general problems.
Date of Award  12 Dec 2022 

Original language  English 
Awarding Institution 

Supervisor  Philippe Trinh (Supervisor) & Paul Milewski (Supervisor) 