An extension of Prandtl-Batchelor theory and consequences for chaotic advection
Abstract
We extend the Prandtl-Batchelor theory of steady laminar motion at large Reynolds number to derive conditions that steady three-dimensional Navier-Stokes flows have to satisfy. We combine these results with ergodic theory to show that flows with strong Beltrami property (e.g., ABC flows) cannot be a paradigm for chaotic advection in inertia-dominated boundary-driven three-dimensional flows. Our results indicate that viscous forces are responsible for chaotic advection in steady, three-dimensional boundary-driven Navier-Stokes flows at large Reynolds numbers.
- Publication:
-
Physics of Fluids
- Pub Date:
- September 2002
- Bibcode:
- 2002PhFl...14Q..61M
- Keywords:
-
- Chaos;
- Fluid Dynamics;
- Laminar Flow;
- Navier-Stokes Equation;
- Prandtl Number;
- Reynolds Number;
- Three Dimensional Flow;
- Fluid Mechanics and Thermodynamics