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Fluid Dynamics

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01-12-2022

Stability of an Advective Flow in a Horizontal Fluid Layer Heat-Insulated from Below with Rigid Boundaries

Authors: K. G. Shvarts, Yu. A. Shvarts

Published in: Fluid Dynamics | Issue 8/2022

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Abstract—

In this paper, we study the stability of an advective flow in a flat horizontal layer of an incompressible fluid with rigid boundaries. A linear temperature distribution is set on the upper boundary of the layer while the lower boundary is thermally insulated. The plane-parallel flow due to the action of horizontal convection is described analytically as an exact solution of the Navier–Stokes equations in the Boussinesq approximation. In the linear theory, the stability of an advective flow to normal perturbations is studied at various values of the Prandtl number. The most dangerous modes are determined, and neutral curves are plotted. In the nonlinear formulation of the problem, the structure of finite-amplitude perturbations in the supercritical region near the minima of the neutral curves is studied.

previous article On the Value of the Second Invariant of the Strain Rate Tensor at the Point of Minimum Pressure on the Plane of Symmetry of Non-Barotropic Flow

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Title: Stability of an Advective Flow in a Horizontal Fluid Layer Heat-Insulated from Below with Rigid Boundaries
Authors: K. G. Shvarts
Yu. A. Shvarts
Publication date: 01-12-2022
Publisher: Pleiades Publishing
Published in: Fluid Dynamics / Issue 8/2022
Print ISSN: 0015-4628
Electronic ISSN: 1573-8507
DOI: https://doi.org/10.1134/S0015462822080055

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