The large-scale structure of compressible convection

Details The large-scale structure of compressible convection The large-scale structure of compressible convection

Mar 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981aj.....86..496d&link_type=abstract

Astronomical Journal, vol. 86, Mar. 1981, p. 496-512.

Astronomy and Astrophysics

Astronomy

31

Compressible Flow, Convective Flow, Convective Heat Transfer, Ideal Gas, Polytropic Processes, Solar Atmosphere, Boundary Layers, Boussinesq Approximation, Finite Element Method, Rayleigh Number, Stellar Evolution, Thermal Conductivity, Thermodynamic Properties, Two Dimensional Flow, Velocity Distribution

Scientific paper

We study convection of small but finite amplitude in plane-parallel layer of perfect gas. The conductivity is assumed constant, hence the static state is polytropic. The heat flux on the boundaries is held fixed. When the polytropic index is not too large, the critical horizontal wave number for the onset of convection is zero and there is finite-amplitude instability. The finite-amplitude instability persists into the thin-layer limit provided that there are no geometrical limits to the horizontal scale of the convection. This result contradicts conclusions drawn from the strict Boussinesq approximation and it suggests that results based on that approximation are not generic for convection with flux prescribed on the boundaries. For all the Rayleigh numbers and layer thicknesses accessible to our amplitude expansions, convection with very large horizontal extent is expected to be prevalent at significant amplitudes. We suggest ways in which the nonlinear solutions found here may be useful in the interpretation of large-scale solar convection.

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