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The Motion of a Vortex Pair in a Stratified Atmosphere
Author(s) -
Saffman P. G.
Publication year - 1972
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1972512107
Subject(s) - vortex , inviscid flow , laminar flow , entrainment (biomusicology) , mechanics , stratification (seeds) , turbulence , physics , classical mechanics , amplitude , stratified flow , constant (computer programming) , vortex stretching , vortex ring , optics , seed dormancy , germination , botany , dormancy , rhythm , acoustics , computer science , biology , programming language
The movement of a horizontal vortex pair through an inhomogeneous fluid is considered. The problem is formulated first for the case when the ambient fluid is uniform, the fluid moving with the vortex pair has a different density, and the motion is supposed laminar and inviscid. An approximate solution is obtained, which predicts that the distance between the vortices stays constant and the vortices accelerate at a constant rate. This solution is then applied to motion in a stratified atmosphere and it is found that the vortices oscillate vertically with a frequency and amplitude depending on the initial conditions and the stratification. Finally, approximate equations are constructed to describe the effects of turbulent entrainment into the fluid moving with the vortex pair, and an estimate of the damping is obtained.