Effect of variation in density on the stability of superposed streams of Fluid

Abstract

1. The chief part of the work described in this paper was done in 1914 and formed part of the essay for which the Adams Prize was awarded in 1915. During the war years it was laid aside, and since then I have delayed publica­tion, hoping to be able to undertake experiments designed to verify, or otherwise, the results. Lately, however, Mr. Goldstein has told me that he is engaged on similar problems and he has encouraged me to publish the work without waiting for experimental results. It is well known that when the wind near the ground drops at night owing to the cooling of the ground, the wind at a higher level frequently remains unchanged so that the effect of a decrease in density with height is to enable a large velocity gradient to be maintained. This implies that the turbulence is suppressed or at any rate much reduced by the density gradient. To the mathematician this at once presents the problem of the stability of a fluid in which the density and velocity vary with height above the ground, regarded as a horizontal plane.