Abstract
Until recently, measurements below the ocean surface have tended to confirm “law of the wall” behavior, in which the velocity profile is logarithmic, and energy dissipation decays inversely with depth. Recent measurements, however, show a sublayer, within meters of the surface, in which turbulence is enhanced by the action of surface waves. In this layer, dissipation appears to decay with inverse depth raised to a power estimated between 3 and 4.6. The present study shows that a conventional model, employing a “level 2½” turbulence closure scheme predicts near-surface dissipation decaying as inverse depth to the power 3.4. The model shows agreement in detail with measured profiles of dissipation. This is despite the fact that empirical constants in the model are determined for situations very different from this near-surface application. The action of breaking waves is modeled by a turbulent kinetic energy input at the surface. In the wave-enhanced layer, the downward flux of turbulent kinetic energy balances its dissipation. The model produces analytic descriptions for the depth of the layer, and for profiles of velocity, turbulent kinetic energy, and dissipation. The surface roughness length (in the water) is a critical parameter in the solutions. There are indications of a relationship between the roughness length and surface wave parameter such as the amplitude or inverse wavenumber. Roughness lengths at least up to 1 m appear to be feasible.
