On the general impossibility of controllable axisymmetric NavierStokes motions
Abstract
Steady NavierStokes motion of an incompressible linearly viscous fluid of uniform density and viscosity is considered. The motion is called controllable if the velocity field is independent of the kinematic viscosity. A condition for controllable steady NavierStokes motion is that the motion be circulationpreserving. For steady isochoric axisymmetric motions, a necessary and sufficient conditions for circulationpreserving flow is that the ratio of the vorticity magnitude to the distance from a representative point to the axis of symmetry be constant on a Lamb surface. In this paper a theorem is proved, stating that the only steady controllable rotational axisymmetric NavierStokes motions are motions for which this ratio is spatially constant and motions whose streamlines are parallel straight lines.
 Publication:

Archive for Rational Mechanics and Analysis
 Pub Date:
 June 1977
 DOI:
 10.1007/BF00280601
 Bibcode:
 1977ArRMA..63..107M
 Keywords:

 Axisymmetric Flow;
 Incompressible Fluids;
 NavierStokes Equation;
 Steady Flow;
 Viscous Fluids;
 Algebra;
 Equations Of Motion;
 Existence Theorems;
 Polynomials;
 Vortices;
 Fluid Mechanics and Heat Transfer;
 Neural Network;
 Complex System;
 Nonlinear Dynamics;
 Electromagnetism;
 General Impossibility