Asymptotics beyond-all-orders in wave-structure interactions

  • Yyanis Johnson-Llambias

Student thesis: Doctoral ThesisPhD


When studying wave-structure interactions in the low-Froude 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 so-called 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 two-dimensional 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 three-dimensional flow over a submerged point source. Firstly, we study this problem in a regime where the point-source 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 wave-structure problem. Secondly, we study the generalised problem where the point-source strength is of unitary magnitude. We use a specialised numerical scheme to determine Stokes switching on the free-surface and provide a unifying asymptotic methodology between the linearised and general problems.
Date of Award12 Dec 2022
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorPhil Trinh (Supervisor) & Paul Milewski (Supervisor)

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