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Complex dynamics in a stratified lid-driven square cavity flow. (English) Zbl 1415.76216
Summary: The dynamic response to shear of a fluid-filled square cavity with stable temperature stratification is investigated numerically. The shear is imposed by the constant translation of the top lid, and is quantified by the associated Reynolds number. The stratification, quantified by a Richardson number, is imposed by maintaining the temperature of the top lid at a higher constant temperature than that of the bottom, and the side walls are insulating. The Navier-Stokes equations under the Boussinesq approximation are solved, using a pseudospectral approximation, over a wide range of Reynolds and Richardson numbers. Particular attention is paid to the dynamical mechanisms associated with the onset of instability of steady state solutions, and to the complex and rich dynamics occurring beyond.

MSC:
76D50 Stratification effects in viscous fluids
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
76D33 Waves for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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