The Stability of a Vortex Pair in the Presence of a Ground Plane,
Abstract
The configuration stability of a vortex pair in the presence of a ground plane is examined. First the motion of a vortex in three dimensions is examined by the method of matched asymptotic expansions in which the solution of the Navier-Stokes equations are constructed asymptotically. The dependence of the velocity and stability of the vortex on factors such as the outer(inviscid) flow field and viscosity in the inner (vortical core) region is clearly established. The proximity of the ground plane enters through the outer solution which is matched to the inner, viscosity dependent, solution. The vortex pair in ground effect is shown to be unstable to disturbances of all wavelengths with increasing amplification rate as the ground is approached. Indications are that the present analysis predicts a more stable (less unstable) vortex system than does the inviscid theory. Comparison of the present analysis, in the limit of zero ground effect, with photographs of vortices undergoing a configuration instability is made. The viscosity necessary for agreement is found to be on the order of the eddy viscosity for the turbulent line vortex, indicating the existence of turbulence in the vortex core. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1971
- Accession Number
- AD0732473
Entities
People
- Nicholas R. Rotta