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On Stratified Vortex Motions under Gravity.

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Summary rept. 1981-1984,

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A general class of stratified vortex flows in investigated in order to understand the vortex patterns developed in stratified late wakes. The flow profiles to be considered vary in both the radial and the axial directions. Three necessary conditions obtained by the method of generalized progressing wave expansion and three sufficient conditions obtained by the integral method of complex conjugation are discussed for stability of the present flow. As a result, the three necessary and sufficient conditions require that the flow be stable in the centrifugal force field, in the gravitational force field, and in the pressure field that restrains the density variations in the two force fields. A new Brunt-Vaisala frequency and a new Richardson number are proposed as a result of the third stability condition. The newly defined Brunt-Vaisala frequency can be viewed as a measure of the interaction of the density variation in one direction with the force field in the other direction. This Richardson number is a ratio between the interactions of the density variations with the force fields and the interactions of the velocity gradients in two direction. The former interaction is a result of the third stability condition. The newly defined Brunt-Vaisala frequency. The latter interaction determines whether the velocity gradients in the second direction strengthens or weakens 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. Keywords include Kelvin-Helmholtz instability Rayleigh-Taylor instability Shear effect.

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  • Numerical Mathematics
  • Fluid Mechanics

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