TY - JOUR

T1 - Theory of weakly damped free-surface flows

T2 - A new formulation based on potential flow solutions

AU - Dias, F.

AU - Dyachenko, A. I.

AU - Zakharov, V. E.

PY - 2008/2/18

Y1 - 2008/2/18

N2 - Several theories for weakly damped free-surface flows have been formulated. In this Letter we use the linear approximation to the Navier-Stokes equations to derive a new set of equations for potential flow which include dissipation due to viscosity. A viscous correction is added not only to the irrotational pressure (Bernoulli's equation), but also to the kinematic boundary condition. The nonlinear Schrödinger (NLS) equation that one can derive from the new set of equations to describe the modulations of weakly nonlinear, weakly damped deep-water gravity waves turns out to be the classical damped version of the NLS equation that has been used by many authors without rigorous justification.

AB - Several theories for weakly damped free-surface flows have been formulated. In this Letter we use the linear approximation to the Navier-Stokes equations to derive a new set of equations for potential flow which include dissipation due to viscosity. A viscous correction is added not only to the irrotational pressure (Bernoulli's equation), but also to the kinematic boundary condition. The nonlinear Schrödinger (NLS) equation that one can derive from the new set of equations to describe the modulations of weakly nonlinear, weakly damped deep-water gravity waves turns out to be the classical damped version of the NLS equation that has been used by many authors without rigorous justification.

KW - Free surface

KW - Navier-Stokes equations

KW - Potential flow

KW - Viscosity

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U2 - 10.1016/j.physleta.2007.09.027

DO - 10.1016/j.physleta.2007.09.027

M3 - Article

AN - SCOPUS:38849134959

VL - 372

SP - 1297

EP - 1302

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 8

ER -