Richardson criteria for stratified vortex motions under gravity
Abstract
Three sufficient conditions for stability are established for a general class of rotating flows with the velocity and the density distribution varying in both the axial and radial directions. Two are the classical Richardson criteria in the axial and radial directions. The third, measured by a newly defined Richardson number, acts as a constraint on the other two. The newly defined Richardson number is a ratio between the interaction of the density variations with the force fields and the interaction of the velocity gradients in two directions. The former interaction is a result of the pressure restraint condition and is measured by a new BruntVäisälä frequency. The latter interaction determines whether the velocity gradients in the second direction strengthen or weaken the resultant shear effect. Because of the generality of the flow profiles being considered, the criteria established in this investigation are valid for a wide range of problems in oceanographic and atmospheric studies.
 Publication:

Physics of Fluids
 Pub Date:
 February 1986
 DOI:
 10.1063/1.866011
 Bibcode:
 1986PhFl...29..368F
 Keywords:

 Computational Fluid Dynamics;
 Flow Stability;
 Gravitational Effects;
 Richardson Number;
 Stratified Flow;
 Vortex Shedding;
 Atmospheric Circulation;
 BruntVaisala Frequency;
 Density Distribution;
 Oceanography;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer