MECHANICS OF FLUIDS, GAS AND PLASMA

Numerical solution of a boundary value problem describing convective current of viscous incompressible fluid in a horizontal layer

N. V. Burmasheva^ab, E. Yu. Prosviryakov^ab, A. V. Iankovskaia<sup>ab

a</sup> Institute of Engineering Science, Urals Branch, Russian Academy of Sciences, Ekaterinburg
^b Ural Federal University named after the first President of Russia B. N. Yeltsin

Abstract: The article examines the effect of wind on convective flow in a viscous, incompressible fluid with vertical turbulence. A mathematical model is used to describe this process. The main focus is to analyse how wind parameters affect key characteristics of convective flow, including velocity and degree of turbulence.Unlike the analytical approach, this work presents a numerical solution to the boundary value problem describing stationary convective fluid flow in a horizontal layer. The velocity field, which is linear in terms of variables, is examined.These conclusions have potential for application in future research into hydrodynamic phenomena and flow stability issues.

Keywords: Oberbeck-Boussinesq system, overdetermined system, numerical solution, shear flow, backflow, stratification.

Received: 19.08.2025
Revised: 24.10.2025
Accepted: 20.08.2025

DOI: 10.60797/IRJ.2025.160s.32