A VORTEX IN AN INFINITE VISCOUS FLUID
Abstract
A solution is given for a viscous vortex in an infinite liquid. Similarity arguments lead to a reduction of the equations of motion to a set of ordinary differential equations. These are integrated numerically. A uniform feature is the constant circulation, K, outside the vortex core, which is also a viscous boundary layer. The circulation decreases monotonically toward the axis. The axial velocity profiles and the radial velocity profiles have several characteristic shapes, depending on the value of the non-dimensional momentum transfer, M. The solution has a singular point on the axis of the vortex. The radius of the core increases linearly with distance along the axis from the singularity, and, at a given distance, is proportional to the coefficient of viscosity and inversely proportional to K. Finally a discussion is given to indicate that intense vortices above a plate, like the confined experimental vortex, or above the ground, like the atmospheric tornado and dust whirl, will not resemble the theoretical vortex except, possibly, far above the plate. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1961
- Accession Number
- AD0257756
Entities
People
- Robert R. Long
Organizations
- Johns Hopkins University