Effect of a Standing Acoustic Wave on the Development of Large-Scale Convection in a Horizontal Layer

Authors: Lyubimov D.V.; Lyubimova T.P.; Shklyaev S.V.

Source: Fluid Dynamics, Volume 39, Number 2, March 2004 , pp. 169-180(12)

Publisher: Springer

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Abstract:

The effect of a standing acoustic wave on the development of long-wave convective perturbations in a horizontal layer with thermally insulated boundaries is investigated. The main two-dimensional flow is determined. A nonlinear amplitude equation with spatially-periodic coefficients is derived for investigating the stability of the main flow and secondary convection flows in the neighborhood of the stability threshold. The intensity of the acoustic field is assumed to be low. It is shown that the acoustic action leads to destabilization of the layer. Plane and three-dimensional perturbations are critical at large and small Prandtl numbers, respectively. Nonlinear one-dimensional steady-state solutions of the amplitude equation are obtained and their stability is investigated.

Keywords: convection; acoustic wave; stability limit; three-dimensional perturbations

Document Type: Research article

DOI: http://dx.doi.org/10.1023/B:FLUI.0000030301.26416.bc

Publication date: 2004-03-01