Wakes as Topological Limit sets.

The long lived features of observable hydrodynamic wakes in otherwise diffusive and dissipative media implies that these tangential discontinuities are related to topological limit sets generated by harmonic vector fields. Recall that harmonic vector fields are the generators of minimal surfaces, and contribute nothing to the power dissipated by viscosity in a Navier-Stokes fluid. An argument is made that on the limit set that represents the discontinuity, two dimensional flow lines will have a Frenet curvature that depends only upon the arc length. Remarkably, this approach leads to closed form results for the two extremes of two dimensional instability patterns: The Kelvin-Helmoltz instability and the Rayliegh-Taylor instability.


Copyright © 1995-2009, CSDC Inc. All rights reserved.
Last update 01/23/2009
to HomePage