Some aspects of the Coriolis-Stokes forcing in the oceanic momentum and energy budgets

The Coriolis‐Stokes (CS) force is a wave‐induced forcing of the Eulerian mean motion in a rotating ocean. For idealized conditions, it is demonstrated by comparison with Lagrangian results that the appropriate surface boundary condition for the Eulerian mean wave‐induced flow is that of vanishing vertical shear. The Eulerian mean current derived by applying this condition plus the inviscid Stokes drift yield the Lagrangian wave‐induced drift velocity, apart from a small boundary‐layer correction. Appreciation of the importance of the CS force in the momentum balance has led to investigations of the role of the CS force in the energy budget. The present study shows that the CS force is not a source for the rate of change of the total average energy density in the fluid, when the vertical integration is performed to the moving material surface. However, results to fourth order in wave steepness confirm earlier findings that the CS force acts to change the vertically integrated Eulerian kinetic energy of the mean flow. A new interpretation relates this effect to the fact that the mean Eulerian Coriolis force performs work in acting along the motion of the Lagrangian wave‐induced mass (caused by the divergence effect) at the surface. Key Points: The shear of the CS‐driven Eulerian mean current vanishes at the surface The CS force does not act to change the total mean energy density