Viscous potential free-surface flows in a fluid layer of finite depth

Abstract

It is shown how to model weakly dissipative free-surface flows using the classical potential flow approach. The Helmholtz-Leray decomposition is applied to the linearized 3D Navier-Stokes equations. The governing equations are treated using Fourier—Laplace transforms. We show how to express the vortical component of the velocity only in terms of the potential and free-surface elevation. A new predominant nonlocal viscous term is derived in the bottom kinematic boundary condition. The resulting formulation is simple and does not involve any correction procedure as in previous viscous potential flow theories [Joseph2004]. Corresponding long wave model equations are derived.

Keywords

Bibliographic record

BibTeX Citation

@article{Dutykh2007viscouspotential,
  author = {Dutykh, D. and Dias, F.},
  title = {Viscous potential free-surface flows in a fluid layer of finite depth},
  journal = {C. R. Acad. Sci. Paris, Ser. I},
  year = {2007},
  volume = {345},
  pages = {113--118},
  doi = {10.1016/j.crma.2007.06.007},
  abstract = {It is shown how to model weakly dissipative free-surface flows using the classical potential flow approach. The Helmholtz-Leray decomposition is applied to the linearized 3D Navier-Stokes equations. The governing equations are treated using Fourier—Laplace transforms. We show how to express the vortical component of the velocity only in terms of the potential and free-surface elevation. A new predominant nonlocal viscous term is derived in the bottom kinematic boundary condition. The resulting formulation is simple and does not involve any correction procedure as in previous viscous potential flow theories [Joseph2004]. Corresponding long wave model equations are derived.},
  keywords = {physics.class-ph, physics.gen-ph, physics.ao-ph, nlin.SI, Mathematics, Physics, math.MP, physics.flu-dyn, math-ph}
}