Transport of a Vortex Wake in a Stably Stratified Atmosphere
Atmospheric stratification affects the downward motion of an aircraft vortex wake and may influence the persistence and stability of the vortex pair configuration. Observations of actual wakes have shown significant variation in the distance to which they descend and in their lifetimes under different degrees of atmospheric stability. This behavior has been modeled analytically in this paper as a pair of infinite vortices in an inviscid, compressible, stably stratified atmosphere with entrainment characterized by a single parameter which is related to the difference between the density in a particular region of the wake and that external to the wake. It has been found that the motion of such a vortex system is governed by a parameter Q which depends on the initial circulation and vortex spacing, on the atmospheric stability, and on the entrainment parameter.
The nature of the transport follows one of two patterns, depending on whether Q is less than or greater than a critical value Qcrit. If Q < Qcrit, the circulation decreases more rapidly than the momentum and the vortices separate as they descend to an equilibrium level. If Q > Qcrit, the momentum of the vortices decreases more rapidly than the circulation and, after an initial period of slow divergence, the vortices attempt to converge as they descend. In both cases, the descent takes place in a well-defined characteristic time which depends solely on the atmospheric density gradient.
KeywordsVortex Ring Atmospheric Stability Vortex Wake Entrainment Rate Vortex System
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