Theory of the Turbulent Drift Friction Layer of the Ocean

Abstract

The paper proposes a theory of the stationary turbulent drift friction layer that, under the conditions of stable stratification, can appear as the upper mixed layer (UML) of the ocean or as one mixed to the bottom in shallow water. An analytical solution of the drift current equations is obtained as an infinite power series valid for the vertical turbulence exchange coefficient of arbitrary form. General properties of the solution are derived in the form of asymptotic theorems. These state that two types of dynamic processes can form, depending on the free-slip or no-slip conditions at the lower boundary of the drift friction layer at small dimensionless depth. With the free-slip condition, the currents are transverse to the wind direction and the stress distribution is linear in the whole layer. With the no-slip condition, the currents are along the wind direction and the stress distribution is constant in the whole layer as well. Based on this model of vertical turbulent exchange, including equations of turbulent kinetic energy and dissipation of turbulent kinetic energy, the first type is shown to be inherent in the UML when a dimensioned stratification parameter increases, while the second type applies to shallow water where drift currents penetrate to the bottom. The possible formation of a layer with a linear velocity profile and constant turbulence values in the second type is discussed. Analytical models describing both types of these processes are suggested.