Stability of a Heterogeneous Fluid Layer Heated from Above

Abstract

Stability of a heterogeneous layer of an inviscid incompressible fluid confined between two rigid horizontal parallel planes heated uniformly from above is discussed. The basic nonhomogeneity of the fluid which depends on the vertical coordinate (z) is assumed to be of the form ρ=ρ₀[1+δz], δ being positive and of the order of αβ, where α is the coefficient of volume expansion of the fluid and β is the uniform non-adverse temperature gradient which is maintained. The necessary and sufficient condition for the stability of the system is found that (δ−αβ) should be negative or equal to zero. Bound on the square of the growth rate of unstable modes is found to be g(δ−αβ), where g is the acceleration due to gravity.