Numerical simulation of three-dimensional turbulent flows based on the mathematical model of wave processes

Turbulence and subsequent mixing are important mechanisms that determine the dynamics of the coastal zone, the transfer of momentum, mass and heat. The article describes a spatially inhomogeneous three-dimensional model of wave hydrodynamics with improved parametrization of the vertical turbulent exchange coefficient. A small-scale motion is excluded from the Navier-Stokes equations by applying a filtering operation and subsequent averaging the filtered data. To this end, in the two-dimensional and three-dimensional cases, different types of filters are used, namely a box filter, a Gaussian filter and a Fourier filter with a gradual decrease in the filter width, which makes it possible to reproduce a wider frequency range of the solution fluctuations. The filtration and averaging procedure were applied to natural data, which were obtained during the expedition to the Central-Eastern part of the Sea of Azov and the Taganrog Bay on board the research vessel "Deneb" of the Southern Scientific Center of the Russian Academy of Sciences. The three-dimensional vector of the water medium velocity was measured using the Workhorse Sentinel 600 hydrophysical ADCP probe, which allowed taking more than 3,000,000 initial measurements at more than 150,000 points (at each point in each of the 17 stations). The obtained data are expected to be used for numerical simulation of three-dimensional turbulent flows in the framework of the spatially inhomogeneous three-dimensional model of wave hydrodynamics, using the LES approach and making comparison with the results of averaging according to RANS. The article considers the possibilities of applying different types of approximations for parametrization of the vertical turbulent exchange. The algebraic models for calculating the coefficient of vertical turbulent exchange and semi-empirical turbulence models are compared.