Understanding Stokes forces in the wave‐averaged equations

The wave‐averaged, or Craik‐ Leibovich , equations describe the dynamics of upper ocean flow interacting with nonbreaking, not steep, surface gravity waves. This paper formulates the wave effects in these equations in terms of three contributions to momentum: Stokes advection, Stokes Coriolis force, and Stokes shear force. Each contribution scales with a distinctive parameter. Moreover, these contributions affect the turbulence energetics differently from each other such that the classification of instabilities is possible accordingly. Stokes advection transfers energy between turbulence and Eulerian mean‐flow kinetic energy, and its form also parallels the advection of tracers such as salinity, buoyancy, and potential vorticity. Stokes shear force transfers energy between turbulence and surface waves. The Stokes Coriolis force can also transfer energy between turbulence and waves, but this occurs only if the Stokes drift fluctuates. Furthermore, this formulation elucidates the unique nature of Stokes shear force and also allows direct comparison of Stokes shear force with buoyancy. As a result, the classic Langmuir instabilities of Craik and Leibovich , wave‐balanced fronts and filaments, Stokes perturbations of symmetric and geostrophic instabilities, the wavy Ekman layer, and the wavy hydrostatic balance are framed in terms of intuitive physical balances.