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Two-dimensional convection of an incompressible viscous fluid with the heat exchange on the free border. (English) Zbl 1413.76027
Summary: The exact stationary solution of the boundary-value problem that describes the convective motion of an incompressible viscous fluid in a two-dimensional layer with square heating of a free surface in Stokes’s approach is found. The linearization of the Oberbeck-Boussinesq equations allows one to describe the flow of fluid in extreme points of pressure and temperature. The condition under which the counter-current flows (two counter flows) in the fluid can be observed, is introduced. If the stagnant point in the fluid exists, six non-closed whirlwinds can be observed.

76F02 Fundamentals of turbulence
76F45 Stratification effects in turbulence
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
76R05 Forced convection
76U05 General theory of rotating fluids
Full Text: DOI MNR
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