Some Cases of Instability in Fluid Motion

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 ( d 2/ d ζ2 - a 2)3 Z = -λ a 2Z. (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 a 2 = ( l 2 + m 2) h 2. (3)