Viscous Stability Criterion for Hydrodynamic Differential Rotation

Abstract

Viscous stability criterion in a thin layer on a rotating sphere is studied. The case when the fluid is inviscid was explained by Watson in 1981, the work was motivated by the idea suggested by Drazin and Ried in their celebrated text "Hydrodynamic Stability"; here  we will investigate the model worked out by B. Sherif and C. Jones in the year 2005, and show the necessary condition for instability which depends on the energy that is provided by the shear motion of the fluid in spherical thin layer.