## Gravitational instability of a liquid layer flowing down an induced plane and heated from below.(English)Zbl 0145.23102

The author develops a linearized analysis for the title problem. In a few asymptotic limits surface tension effects are considered. The analysis is based on a conventional normal mode reduction followed by a parameter expansion in powers of the relevant wave number. It is found, after many approximations, that (1) the critical Reynolds number does not depend on the Rayleigh number for long waves, (2) a boundary condition which leaves some effects of surface waves in the problem yields a smaller value for the critical Rayleigh number than symmetric boundary condition, (3) the stability limit for heated from below is decreased as the angle of inclination rises.
Reviewer: D. D. Joseph

### MSC:

 7.6e+21 Stability and instability of geophysical and astrophysical flows

fluid mechanics