On the interaction of small-scale turbulence and internal waves in the framework of the semi-empirical turbulence model in a stratified fluid

The interaction of small-scale turbulence with internal and surface waves is an urgent problem of hydrology and oceanology. In particular, this issue is especially important for the properties of the upper layer of the ocean and the inland waters.

Small-scale processes that exist against the background of average profiles of various hydrophysical quantities (temperature, velocity, density, and large-scale currents caused, in particular, by wind forcing) are usually nonlinear and therefore effectively interact with each other. We consider some aspects of the interaction of internal waves and turbulence in the upper layer of the ocean and inland waters within the framework of the semi-empirical theory of turbulence in a stratified fluid. The model used in this study takes into account  mutual transformation of the kinetic and potential energies of turbulent fluctuations [Ostrovsky&Troitskaya, 1987; Zilitinkevich et al., 2013]. The effects of amplification and maintenance of turbulence by low-frequency and high-frequency internal waves, quasi-stationary distributions of turbulent energy in the presence of a shear caused by a low-frequency internal wave are investigated; the role of the transformation of energies on the indicated processes is analyzed.

A modification of the k-epsilon mixing scheme is also proposed, which removes the limitation on the existence of turbulence at large values of the gradient Richardson number. Within the framework of the modification, the parameterization of the Prandtl number is used, which makes it possible to take into account the influence of density stratification and velocity shear on mixing processes.

A numerical study of the influence of vertical mixing schemes on the transfer processes of biochemical fields in an internal reservoir was also carried out. The modified scheme was implemented into a three-dimensional model of thermo-hydrodynamics and biochemistry of an inland water body [Gladskikh et al., 2021], and a series of numerical experiments was conducted.

The work was supported by the RFBR (20-05-00776; 20-05-00322; 21-05-52005), and by Moscow Center of Fundamental and Applied Mathematics (agreement with the Ministry of Science and Higher Education 075-15-2019-1621).

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