Theory of weakly damped freesurface flows: A new formulation based on potential flow solutions
Abstract
Several theories for weakly damped freesurface flows have been formulated. In this Letter we use the linear approximation to the NavierStokes 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 deepwater gravity waves turns out to be the classical damped version of the NLS equation that has been used by many authors without rigorous justification.
 Publication:

Physics Letters A
 Pub Date:
 February 2008
 DOI:
 10.1016/j.physleta.2007.09.027
 arXiv:
 arXiv:0704.3352
 Bibcode:
 2008PhLA..372.1297D
 Keywords:

 47.10.ad;
 47.15.km;
 47.35.Bb;
 NavierStokes equations;
 Potential flows;
 Gravity waves;
 Physics  Atmospheric and Oceanic Physics;
 Physics  Fluid Dynamics
 EPrint:
 doi:10.1016/j.physleta.2007.09.027