{'fraction_non_alphanumeric': 0.020608439646712464, 'fraction_numerical': 0.0, 'mean_word_length': 5.7105263157894735, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
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.