A practical three dimensional formalism for the ocean , coupling random waves , mean flow , and turbulence

Wave-mean flow equations for mass and momentum conservation in three dimensions, previously obtained with a vertical coordinate transform, are generalized here to random waves, and re-derived from the Generalized Lagrangian Mean equations. Combining the momentum equation with a three-dimensional equation for wave pseudo-momentum yields a set of equations describing the interactions of waves, mean flow and turbulence. Consistent boundary conditions and parameterizations are described. These include a Generalized Lagrangian Mean equation for the turbulent kinetic energy that describes the stretching of turbulence by the shear of the wave-induced Stokes drift. The equations derived here are readily integrated by coupling a spectral wave model to an ocean circulation model, with practical applications to the forecasting of surface drift, upper ocean mixing, coastal ocean circulation, and wave forecasting.