Vortex Breakdown and Instability.
Final rept. 1 Mar-30 Sep 81,
KENTUCKY UNIV LEXINGTON DEPT OF MECHANICAL ENGINEERING
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Solutions of the full steady axisymmetric Navier-Stokes equations for breakdown in an unconfined viscous vortex have been obtained by Grabowski and Berger. The core Reynolds numbers were varied up to 200 and a two-parameter family of velocity distributions was assumed upstream as the boundary condition. In this report, the Richardson numbers corresponding to the developing solution profiles of Grabowski and Berger are calculated and shown graphically. The inviscid linear stability of thw swirling velocity profiles as calculated by Grabowski and Berger is investigated with repsect to non-axisymmetric disturbances. This eigen-value problem is solved numerically for various wave numbers and it is shown that the developing velocity profiles lead to instability. These results are believed to be useful in analyzing instabilities for a trailing vortex from an aircraft. Author
- Fluid Mechanics