Analytical solutions for a non-stationary model of wind currents
UDC
51.7DOI:
https://doi.org/10.31429/vestnik-19-3-17-24Abstract
In this paper, we consider a simplified three-dimensional mathematical model of wind currents in a reservoir obtained by analyzing a model based on a system of complete nonlinear equations of hydrothermodynamics written in traditional approximations. The analysis is carried out on the basis of the procedure for resizing the model with the subsequent exclusion from the system of equations of terms describing advection and horizontal diffusion. The problem is considered in a rectangular area with the assignment of the components of the tangential friction stress of the wind in a special way that allows you to describe complex wind situations. Within the framework of the above limitations, an analytical solution was found for the integral components of the horizontal velocity components of the wind flow model. The accepted restrictions are quite soft and allow you to preserve the most important properties of the simulated processes in the model. This makes it possible, when choosing the main parameters in the model that reflect the specifics of the reservoir, to obtain some properties of the currents in this reservoir "in the first approximation". In this paper, the components of the shear stress of wind friction are set in accordance with a special law that allows describing complex wind situations, and an analytical solution of the non-stationary problem is obtained.
Keywords:
dimensionless problem, wind currents, test problem, analytical solution, current function, integral velocityAcknowledgement
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