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Stokes drift and its discontents.

Jacques Vanneste1, William R Young2

  • 1School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3FD, UK.

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|April 25, 2022
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Summary
This summary is machine-generated.

We show that the divergent Stokes velocity can be decomposed into a solenoidal part and a small remainder for surface gravity waves. Redefining the Lagrangian mean flow yields an incompressible mean, resulting in a purely solenoidal Stokes velocity.

Keywords:
Stokes driftsurface gravity waveswave–mean flow interaction

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Area of Science:

  • Fluid dynamics
  • Wave theory
  • Mathematical physics

Background:

  • The Stokes velocity, fundamental in fluid dynamics, is known to be divergent even in incompressible fluids.
  • Existing definitions, while useful, present challenges in fully describing fluid motion under wave influence.

Purpose of the Study:

  • To decompose the divergent Stokes velocity into physically meaningful components.
  • To develop an incompressible Lagrangian mean flow for accurate wave dynamics.
  • To explore the implications for momentum equations and Stokes pumping.

Main Methods:

  • Application of Generalized Lagrangian Mean (GLM) theory specialized for surface gravity waves.
  • Utilizing Lie series expansion for effective implementation.
  • Decomposition of Stokes velocity into solenoidal and remainder components.

Main Results:

  • The Stokes velocity is shown to be decomposable into a solenoidal component and a remainder term.
  • A redefined, exactly incompressible Lagrangian mean flow leads to a purely solenoidal Stokes velocity.
  • The derived Lagrangian-mean momentum equation is analogous to the Craik-Leibovich equation.

Conclusions:

  • The decomposition offers a more refined understanding of wave-induced fluid transport.
  • The construction provides a novel approach to handling wave dynamics in fluid mechanics.
  • This work contributes to the mathematical understanding of physical fluid dynamics.