Some cases of instability in fluid motion

Abstract

Abstract 1. In a recent paper I obtained a numerical solution of some problems concerning the stability of a layer of incompressible fluid when the temperature decreases upwards. The results depended on the solution of the sixth-order differential equation (d2/dζ2 - a2)3 Z = -λa2Z. (1) In this solution the co-ordinates were x, y and z, the last being taken vertically. The depth of the fluid is h, and ζ = z/h. (2) Z is the factor of the disturbance of temperature that involves Z. The other factor is supposed to be of the form sin lx sin my, and a2 = (l2 + m2) h2. (3)