Richardson’s criterion for the stability of stratified shear flow

Abstract

Chandrasekhar’s derivation, from energy considerations, of the sufficient condition R>1/4 for stability of a stratified shear flow, in which R is the local Richardson number, is amended to obtain R>1, in agreement with the earlier arguments of Richardson, Taylor, and Prandtl(L. F. Richardson, Proc. R. Soc. London Ser. A 97, 354 (1920); G. I. Taylor, Rapp. P. V. Reun. Cons. Permanent Int. d’Exploration Mer 76, 35 (1931); Sci. Pap. 2, 240; L. Prandtl, Vorträge aus dem Gebiete der Aerodynamik und verwandten Gebieten (Springer, Berlin, 1930), pp. 1–7; L. Prandtl, Führer durch die Strömungslehre (Vieweg, Braunschweig, 1942), p. 337; Essentials of Fluid Dynamics [English translation of 1949 edition of Führer durch die Strömungslehre (Hafner, New York, 1952), pp. 381 and 382]).