ON THE THEORY OF SLOPE FLOWS

Paradoxical properties of the classical Prandtl solution for fl ows occurring in a semibounded liquid (gaseous) medium above an infi nite homogeneously cooled/heated inclined plane are analyzed. In particular, the maximum velocity of steady-state slope fl ow is independent, according to this solution, of the angle of inclination. Consequently, there is no passage to the limit to the case of zero angle where the cooling/heating is unlikely to give rise to homogeneous horizontal fl ows. It is shown that no paradoxes arise if we do not consider buoyancy sources of infi nite spatial scale, which act infi nitely long. It follows from the results that, in particular, the solution of the problem for a semibounded medium above a homogeneously cooled surface in the gravity fi eld is unstable to small deviations of this surface from horizontal.
   
Author:  L. Kh. Ingel′
Keywords:  slow fl ows, analytical solutions, Prandtl model, asymptotics at small angles of inclination, thermal inhomogeneities
Page:  641