INTERACTION OF VISCOUS WAKES WITH A FREE SURFACE

注意：本论文已在Applied Mathematics and Mechanics(English Edition, Vol 25, No 6, Jun 2004，pp647－655)上发表
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LU Dong-qiang (卢东强)1,2
(1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University,Shanghai 200072, P.R. China;
2. Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, P.R. China)

Abstract: The interaction of laminar wakes with free-surface waves generated by a moving body beneath the surface of an incompressibleviscous fluid of infinite depth was investigated analytically. The analysis was based on the steady Oseen equations for disturbed flows. The kinematic and dynamic boundary conditions were linearized for the small-amplitude free-surface waves. The effect of the moving body was mathematically modeled as an Oseenlet. The disturbed flow was regarded as the sum of an unbounded singular Oseen flow which represents the effect of the viscous wake and a bounded regular Oseen flow which represents the influence of the free surface. The exact solution for the free-surface waves was obtained by the method of integral transforms. The asymptotic representation with additive corrections for the free-surface waves was derived by means of Lighthill's two-stage scheme. The symmetric solution obtained shows that the amplitudes of the free-surface waves are exponentially damped by the presences of viscosity and submergence depth.
Key words: free-surface wave; viscous wake; viscosity; submergence depth; Oseenlet;Lighthill' s two-stage scheme; asymptotic solution

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Received date: 2002-11-01; Revised date: 2003-11-11
Foundation items: the Hong Kong Research Grants Council (HKU 7076/02E); the Municipal Key Subject Program of Shanghai

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