Convection and gravity waves in two layer models. I - Overstable modes driven in conducting boundary layers

Details Convection and gravity waves in two layer models. I - Overstable modes driven in conducting boundary layers Convection and gravity waves in two layer models. I - Overstable modes driven in conducting boundary layers

Dec 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982gapfd..22..305k&link_type=abstract

Geophysical and Astrophysical Fluid Dynamics, vol. 22, no. 3-4, 1982, p. 305-324.

Statistics

Computation

5

Boundary Layer Stability, Boussinesq Approximation, Convective Flow, Gravity Waves, Propagation Modes, Stellar Models, Thermal Conductivity, Boundary Value Problems, Computational Fluid Dynamics, Eigenvalues, Viscous Flow, Wave Propagation

Scientific paper

Stability analysis is formulated for a two-layer fluid model in which the upper and lower layers are, respectively, convectively stable and unstable. Given discontinuities in viscosity and conductivity at the interface, the exchange of stability in general does not hold, and overstability is a possibility. A detailed analytical treatment is given for the case of small viscosity and conductivity in which viscous and conducting boundary layers are formed at the interface. The usual damping effect arising from the energy dissipation by viscosity and thermal conductivity exists irrespective of whether the mode is the convection or the gravity wave, but for larger horizontal wavelengths, the effect of the boundary layer can cause overstability of the gravity wave, in agreement with Souffrin and Spiegel (1967). The jump in the viscosity provides a self-catalytic action for the unstable flow if the viscosity is assumed to be the nonlinear turbulent viscosity arising from the motion itself. This effect is not, however, strong enough to overcome the usual viscous damping.

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