Applied Mathematics and Mechanics - English Edition Vol. 25, No. 6, pp. 647-655, Shanghai University Press, Jun. 2004 (ISSN: 0253-4827)


Interaction of viscous wakes with a free surface


D.Q. Lu

  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.

Author Keywords
  free-surface wave; viscous wake; viscosity; submergence depth; Oseenlet; Lighthill's two-stage scheme; asymptotic solution


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Applied Mathematics and Mechanics - English Edition, Vol. 20, No. 4, pp. 343-349, Shanghai University Press, Apr. 1999 (ISSN: 0253-4827).

Hamiltonian formulation of nonlinear water waves in a two-fluid system

D.Q. Lu, S.Q. Dai, B.S. Zhang

Abstract  In this paper, it is dealt with that the Hamilton formulation of nonlinear water waves in a two-fluid system, which consists of two layers of constant-density incompressible inviscid fluid with a horizontal bottom, an interface and a free surface.  The velocity potentials are expanded in power series of the vertical coordinate.  By taking the kinetic thickness of lower fluid-layer and the reduced kinetic thickness of upper fluid-layer as the generalized displacements, choosing the velocity potentials at the interface and free surface as the generalized momenta and using Hamilton's principle, the Hamiltonian canonical equations for the system are derived with the Legendre transformation under the shallow water assumption.  Hence the results for single-layer fluid are extended to the case of stratified fluid.

Keywords  two-fluid system, Hamilton's principle, nonlinear water waves, shallow water assumption, Hamiltonian cononical equations



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