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 symmetry-breaking bifurcations. A group theory approach is taken to present a formal mathematical proof of the invariance of the Navier-Stokes equations with respect to spatial transformations, i.e., planar translations and rotations. The invariance is applied to the classical problems of describing patterns in Taylor-Couette 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;
- Navier-Stokes Equation;
- Rayleigh-Benard Convection;
- Taylor Instability;
- Benard Cells;
- Broken Symmetry;
- Computational Fluid Dynamics;
- Group Theory;
- Invariance;
- Fluid Mechanics and Heat Transfer