Note on Coriolis-Stokes force and energy

In this study, we consider the origin of the Coriolis-Stokes (CS) force in the wave-averaged momentum and energy equations and make a short analysis of possible energy input to the ocean circulation (i.e., Eulerian mean velocity) from the CS force. Essentially, we find that the CS force appears naturally when considering vertically integrated quantities and that the CS force will not provide any energy input into the system for this case. However, by including the "Hasselmann force", we show some inconsistencies regarding the vertical structure of the CS force in the Eulerian framework and find that there is a distinct vertical structure of the energy input and that the net input strongly depends on whether the wave zone is included in the analysis or not. We therefore question the introduction of the "Hasselmann force" into the system of equations, as the CS force appears naturally in the vertically integrated equations or when Lagrangian vertical coordinates are used.