Stability of Steady Flow in a Vertical Layer in the Microconvection Model

The stability of steady flow in a vertical gap is analyzed using the perturbation method within the framework of the microconvection model. The resulting spectral problem is not self-conjugate. The stability of the flow to long-wave perturbations is established. It is shown that if the Boussinesq parameter is small, the spectrum of this problem approximates the spectra of the corresponding problems for a viscous heat-conducting fluid and thermogravitational convection with a finite Rayleigh number. The numerical calculations indicate that in the microconvection model the instability develops at smaller wave numbers.