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INTERACTION OF VISCOUS WAKES WITH A FREE SURFACE
作者姓名:卢东强
作者单位:ShanghaiInstituteofAppliedMathematicsandMechanics,ShanghaiUniversity,Shanghai200072,P.R.China
基金项目:theHongKongResearchGrantsCouncil (HKU 70 76/0 2E),theMunicipalKeySubjectProgramofShanghai
摘    要:The interaction of laminar wakes with.free-surface waves generated by a moving body beneath the surface of an incompressible viscous 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.

关 键 词:自由表面波  尾流伴流  粘滞性  渐近解  流体力学
收稿时间:1 November 2002

Interaction of viscous wakes with a free surface
Lu?Dong-qiang.INTERACTION OF VISCOUS WAKES WITH A FREE SURFACE[J].Applied Mathematics and Mechanics(English Edition),2004,25(6):647-655.
Authors:Lu Dong-qiang
Institution:Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200072,P.R.China;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 incompressible viscous 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.
Keywords:free-surface wave  viscous wake  viscosity  submergence depth  Oseenlet  Lighthill's two-stage scheme  asymptotic solution
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