Mathematical modeling of turbulent layer penetration in a stratified fluid

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

“…A more intensive expansion of the turbulent layer in comparison with the experiment was obtained by the classical e − ε-model. The calculations for the advanced model [2] are in good agreement with the experiment. The second series of numerical calculations relates to variant 3.…”

“…The calculations were performed on uniform grids with the number of nodes from 120 to 250, time steps from 0.01 to 0.03 s. Fig. 1 illustrates the vertical distributions of the main flow parameters U/U max , K uz , ρ(z) at the time of 240 s. The calculation results of ρ(z) according to model 1 are in good agreement with the calculations using second-order turbulence models [2]. The calculation results of U/U max , K uz according to model 1 are in qualitative agreement with the calculations according to the second-order turbulence models from [2].…”

“…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.…”