Fluid Layer Heated from Above

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Abstract
The stability of an inviscid layer of homogeneous fluid was confined between two rigid horizontal parallel plates is investigated under the action of a uniform nonadverse temperature gradient while the fluid has a general streaming which depends only on the vertical coordinate (z). The main results established in the paper are as follows: (i) A sufficient condition of stability is obtained for the above problem and further it is shown that the rate of growth of any arbitrary periodic disturbance for an unstable mode must be less than the maximum of 1/2|d U/d z| in the flow region. (ii) Taking the coefficient of thermometric conductivity of the fluid to be very small, the problem is shown to depend on a single nondimensional number R 2 and a variational method is given for its calculation at the marginal state when the principle of exchange of stability is satisfied. Moreover for a given wave number, the complex wave velocity for an arbitrary unstable mode is shown to be confined within a semicircle in the complex plane of wave velocity.

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