  Ocean surface gravity waves play an important role for the air-sea momentum
fluxes and the upper ocean mixing, and knowledge of the sea state leads in
general circulation models to improved estimates of the ocean energy budget and
allows to incorporate surface wave impacts, such as Langmuir turbulence.
However, including the Stokes drift, in phase-averaged equations for the
Eulerian mean motion leads to an Eulerian energy budget which is physically
difficult to interpret. In this note, we show that a Lagrangian energy budget
allows for a closed energy budget, in which all terms connecting the different
energy compartments correspond to well known energy transfer terms. We show
that the so-called Coriolis-Stokes force does not lead to an energy transfer
between surface gravity waves and oceanic mean motions as previously suggested.
In an energy budget for the Lagrangian mean kinetic energy, the work done by
the Coriolis-Stokes force does not contribute, and should be used to estimate
the kinetic energy balance in the wave affected surface mixed layer. The
Lagrangian energy budget is used to discuss an energetically consistent
framework, which can be used to couple a general circulation ocean model to a
surface wave model.
