Extremal energy properties and construction of stable solutions of the Euler equations
Abstract
Certain modifications of the Euler equations of fluid motion lead to systems in which the energy decays or grows monotonically, yet which preserve other dynamically important characteristics of the field. In particular, all topological invariants associated with the vorticity field are preserved. In cases where isolated energy extrema exist, a stable steady flow can be found. In two dimensions, highly constrained by vorticity invariants, it is shown that the modified dynamics will lead to at least one nontrivial stationary, generally stable, solution of the equations of motion from any initial conditions. Numerical implementation of the altered dynamics is straightforward, and thus provides a practical method for finding stable flows. The method is sufficiently general to be of use in other dynamical systems.
- Publication:
-
Journal of Fluid Mechanics
- Pub Date:
- October 1989
- DOI:
- 10.1017/S0022112089002533
- Bibcode:
- 1989JFM...207..133V
- Keywords:
-
- Computational Fluid Dynamics;
- Dynamic Characteristics;
- Energy Distribution;
- Euler Equations Of Motion;
- Turbulent Flow;
- Vorticity Equations;
- Fluid Flow;
- Three Dimensional Flow;
- Two Dimensional Flow;
- Fluid Mechanics and Heat Transfer