Coupled sea surface-atmospheric model 1. Wind over waves coupling

A wind over waves coupling scheme to be used in a coupled
wind waves-atmosphere model is described. The approach is
based on the conservation of momentum in the marine
atmospheric surface boundary layer and allows to relate the
sea drag to the properties of the sea surface and the
properties of the momentum exchange at the sea surface.
Assumptions concerning the local balance of the turbulent
kinetic energy production due to the mean and the wave-induced
motions, and its dissipation, as well as the local balance
between production and dissipation of the mean wave-induced
energy allow to reduce the problem to two integral equations:
the resistance law above waves and the coupling parameter,
which are effectively solved by iterations.
To calculate the wave-induced flux, the relation of
\markcite{{\it Plant} [1982]} for the growth rate parameter is
used. However, it is shown by numerical simulations that the
local friction velocity rather than the total friction
velocity has to be used in this relation, which makes the
growth rate parameter dependent on the coupling parameter.
It is shown that for light to moderate wind a significant part
of the surface stress is supported by viscous drag. This is in
good agreement with direct measurements under laboratory
conditions. The short gravity and capillary-gravity waves play
a significant role in extracting momentum and are strongly
coupled with the atmosphere. This fact dictates the use of the
coupled short waves-atmosphere model in the description of the
energy balance of those waves.