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Influence of the Directions of Vibrations and Gravity on the Formation of Vortex Structures of a Nonuniformly Heated Fluid in a Square Cavity


The interaction of two mechanisms of thermal convection—gravitational and vibrational in the Boussinesq fluid convection in an inclined square cavity is investigated. The cavity is subjected to a constant gravity field, vibrations and constant temperature gradient determined by the temperatures at two opposite isothermal walls. The thermal buoyancy convection arising in a fluid is determined by the Grashof number and average vibrational-convective flows are characterized by the vibrational Grashof number. First, the equation for average flow vorticity is obtained from the equations of thermal vibrational convection written in the creeping-flow approximation by the reduction to the Sturm–Liouville problem. Then, the obtained set of equations for average flow is solved numerically by the finite difference method. The analysis shows that by varying the parameters of the problem it is possible to control the structure of the average flow, changing it from nearly single-vortex through three-vortex to four-vortex and vice versa. For any value of the vibrational Grashof number and angle of cavity inclination, the angle of the vibration direction and the gravitational Grashof number can be chosen in such a way that a symmetric four-vortex flow of vanishingly low intensity (dynamic equilibrium) is established in the cavity.

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The study was funded by Perm National Research Polytechnic University in the framework of the federal academic leadership program Priority 2030. The authors also would like to thank anonymous referees for their helpful suggestions on this paper.

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Correspondence to Albert N. Sharifulin.

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This article belongs to the Topical Collection: The effect of gravity on non-equilibrium processes in fluids

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Sharifulin, A.N., Plotnikov, S.A. & Lyubimova, T.P. Influence of the Directions of Vibrations and Gravity on the Formation of Vortex Structures of a Nonuniformly Heated Fluid in a Square Cavity. Microgravity Sci. Technol. 34, 97 (2022).

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  • Thermal vibrational convection
  • High frequency vibrations
  • Vortex structures
  • Square cavity