**
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**

**
**

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.

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

KeyWords Plus SHIP-WAVE PATTERN; VISCOSITY; FLOW

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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
**

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

**
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