On the numerical modelling of the turbulent layer penetration into a stably stratified fluid

On Application of Prandtl-Obukhov Formula in the Numerical Model of the Turbulent Layer Depth Dynamics

“…In the study of the process of the turbulent layer deepening simplifications are made, as a result the averaged horizontal homogeneous motion is described by a system of differential equations [2][3][4]:…”

“…The system (1) is not closed. For its closure, semi-empirical models of turbulence are used [2][3][4]. In this paper, it is proposed to parameterize the ratios of vertical turbulent exchange to use the Prandtl-Obukhov formula derived from stationary equations of balance of turbulence energy and its dissipation rate [10].…”

“…An example of a flow where vertical turbulent exchange plays a decisive role is the flow occurs when a turbulent liquid layer deepens in a stably stratified reservoir at the action of wind. Many works are devoted to its study (see, for example, references in [1][2][3][4][5][6][7][8]). The classical e − ε -model of turbulence and its modifications are used to describe the process of the mixed layer deepening in the stratified fluid.…”