Bifurcations in the presence of symmetry in classical problems of hydrodynamics
Abstract
Analytical techniques are discussed for modeling the hydrodynamics of flows subjected to spontaneous symmetrybreaking bifurcations. A group theory approach is taken to present a formal mathematical proof of the invariance of the NavierStokes equations with respect to spatial transformations, i.e., planar translations and rotations. The invariance is applied to the classical problems of describing patterns in TaylorCouette flow and planar and spherical Benard convection.
 Publication:

Journal de Mecanique Theorique et Appliquee Supplement
 Pub Date:
 1984
 Bibcode:
 1984JMTAS......157C
 Keywords:

 Branching (Mathematics);
 Couette Flow;
 Flow Stability;
 Hydrodynamics;
 NavierStokes Equation;
 RayleighBenard Convection;
 Taylor Instability;
 Benard Cells;
 Broken Symmetry;
 Computational Fluid Dynamics;
 Group Theory;
 Invariance;
 Fluid Mechanics and Heat Transfer