Two Dimensional Hydrodynamics Model with Evaporation for Coastal Systems
Authors: Sukhinov A. I. , Kolgunova O. V. , Ghirmay M. Z. , Nahom O. S. 
Published: January 2024

Introduction. The use of two-dimensional (2D) hydrodynamic models is relevant, despite the development of numerical methods of marine hydrodynamics focused on the use of three-dimensional spatial models. This is due to the modelling of hydrodynamic processes in shallow and coastal systems in solving practically important problems of predicting the transport of pollutants in suspended and dissolved forms. Evaporation for the Southern of Russia marine coastal systems (the Azov Sea, the Northern Caspian, etc.), and even more so in the coastal areas of the Red Sea, is a signiﬁcant factor that aﬀects not only the balance of water masses, but also makes changes in the momentum of the system and the distribution of the velocity vector of the aquatic environment. This eﬀect is signiﬁcant for coastal currents and shallow-water systems.

Materials and Methods. The traditional method of converting the terms of the Navier-Stokes equations containing diﬀerentiation by horizontal spatial variables was used, involving the rearrangement of diﬀerentiation operations by horizontal spatial coordinates and integration by vertical coordinate when constructing a spatially two-dimensional model of hydrodynamics of marine coastal systems when integrated by vertical coordinate. This made it possible to avoid the appearance of non-physical sources of energy and momentum in the spatially two-dimensional model, which can be essential in traditional 2D models with signiﬁcant depth diﬀerences characteristic of coastal systems. The implementation of the analogue of the law of conservation of the total mechanical energy of the system for the constructed 2D model is investigated.

Results. Using the correct transformation of the 3D model (integration of the Navier-Stokes equations and continuity along a vertical coordinate, taking into account evaporation from a free surface), spatially two-dimensional models of hydrodynamics are constructed, for which the basic conservation laws, including mass and total mechanical energy of the system, are fulﬁlled. The implementation of an analogue of the law of conservation of total mechanical energy for various types of boundary conditions, including at the bottom, is investigated. The evaporation from the free surface is correctly accounted for not only in the continuity equation, but also in the equations of motion taking into account wind and waves.

Discussion and Conclusion. 2D model of hydrodynamics has been constructed and studied, taking into account evaporation not only in the mass balance equation (continuity), but also in the Navier-Stokes equations of motion. The proposed model can be used for predictive modelling of hydrophysical processes, including the spread of pollutants in the aquatic environment of coastal systems and shallow reservoirs in relation to marine systems such as the Sea of Azov, the Northern Caspian Sea, coastal areas of the Red Sea, etc. Spatially two-dimensional models of marine hydrodynamics, without replacing three-dimensional models, can serve as a model basis for operational forecasting of situations in coastal systems and shallow-water objects using computing systems with relatively low performance and a moderate amount of RAM (5–10 Tﬂops, 2–4 TB, respectively).