Semi-Empirical Parameterization of Vertically Inhomogeneous Turbulent Exchange in Stratified Shallow Water Bodies Based on In Situ Data

   Introduction. Turbulent mixing in stratified shallow water bodies plays a key role in the formation of hydrophysical structure, governing the transport of momentum, heat, and dissolved substances. Despite advances in turbulence modelling, existing parameterizations often fail to accurately reproduce the vertically inhomogeneous structure of turbulent exchange, especially under complex thermohaline stratification and unsteady flow conditions.

   Materials and Methods. The study is based on in situ data obtained during field campaigns in the Sea of Azov and the Taganrog Bay. Temperature, salinity, and density were measured using a CTD probe (Sea-Bird Electronics SBE 19plus), while three-dimensional velocity components were recorded using an Acoustic Doppler Current Profiler (ADCP Workhorse Sentinel 600). Based on the collected data, vertical gradients of density and velocity, turbulence fluctuations, and stratification stability parameters were calculated. A semi-empirical parameterization of turbulent viscosity and diffusivity coefficients was developed, taking into account flow shear characteristics, the Richardson number, and vertical velocity fluctuations.

  Results. A new parameterization of vertically inhomogeneous turbulent exchange based on synchronous in situ data is proposed. It is shown that incorporating velocity fluctuations and thermohaline gradients allows for an adequate representation of local mechanisms of turbulence generation and suppression. A comparison with classical turbulence models (k–ε, k–ω, and the Smagorinsky model) demonstrates improved accuracy in reproducing vertical profiles of velocity and density. The root mean square error is reduced by up to 30–40%, while the Nash–Sutcliffe efficiency exceeds 0.8.

   Discussion. The proposed parameterization provides a more accurate description of the vertical structure of turbulent exchange due to the direct use of measurable environmental characteristics. Unlike traditional models, it ensures pronounced vertical inhomogeneity of exchange coefficients and correctly reproduces stratification zones. The limitations of the approach are related to its dependence on the quality of in situ data and the lack of explicit consideration of unsteady and wave-induced processes.

   Conclusion. A semi-empirical parameterization of turbulent exchange based on high-resolution in situ data has been developed and implemented. Its superiority over classical models in simulating stratified flows is demonstrated. The obtained results can be applied in hydrodynamic models to improve the accuracy of predicting turbulent mixing and transport processes in shallow marine basins.

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