Stokes drift and its discontents

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.