Abstract

Shaun Belward*, Wayne Read and Patrick Higgins

Fluid flowing over topography occurs in many physical situations. As a typical example, consider air flowing over a mountain range. In this case, the topography of the mountain range can have a considerable effect on the motion of the air. This movement can have catastrophic results for aviators, if it is not predicted. As a consequence, study of flow over topography has been a research topic of prime interest for many decades. Formally, the problem can be modelled as a nonlinear free boundary problem. Although methods such as Boundary Integrals have been used, analytic series methods have also been developed to solve some of these problems. Arguably the hardest problem to solve is the lee wave problem: when the flow conditions are suitable, lee waves form downstream of the obstacle. Wave solutions pose several problems for the analytic series methods. The solution method is iterative, and at each step the existing solution must be updated. For the iterative scheme to converge, very accurate series solutions must be obtained at each step. The convergence rate of the series solution itself is critical in this process, and depends to a large extent on the free boundary representation. In this paper, we compare and discuss the convergence rates for a variety of free surface representations.

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