On Some Generalization of the Rayleigh Problem on a Convective Instability

Previous investigations using the numerical modeling of moist convection in the atmosphere found an interesting effect: clouds arising through the water vapor condensation shield partially the underlying surface and change its radiation balance. The vertical heat fluxes on the surface become horizontally inhomogeneous, that can exert a back profound effect on the convection and dynamics of clouds, in particular, resulting in their horizontal transference (a cloud "runs away from its own shadow"). This paper is dedicated to the corresponding generalization of the classical Rayleigh problem on the convective instability of horizontal layer of a fluid. This generalization has as its object to describe the effect mentioned above – the influence of partial surface shielding on convection. The results show that the given relatively small modification of the Rayleigh problem, taking into account the possibility of the horizontally shifted thermal response to the vertical motions, leads to qualitatively new results. There appears a new, easily realizable type of instability, for which the strengthening of disturbances moving horizontally is typical.