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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.

MSC:
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
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