Material frame-indifference in turbulence modeling
Abstract
Theoretical support is developed for the acceptability of the application of the principle of material frame-indifference to turbulence modeling. The Reynolds stress tensor has been proven frame-independent in two-dimensional turbulence, such as for upper atmospheric modeling. Observer-independent velocity fluctuations are discussed, showing that ensemble mean velocities are frame-indifferent. The frame-indifferent stress tensor is therefore only a special solution to the Navier-Stokes equations, which are frame-dependent. However, at distances sufficiently far from the boundaries three-dimensional eddies are aligned with the axis of rotation, as proven by the Taylor-Proudman theory, and thus become two-dimensional and frame-independent.
- Publication:
-
ASME Journal of Applied Mechanics
- Pub Date:
- December 1984
- Bibcode:
- 1984ATJAM..51..942S
- Keywords:
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- Closure Law;
- Computational Fluid Dynamics;
- Flow Theory;
- Reynolds Stress;
- Stress Tensors;
- Turbulent Flow;
- Flow Velocity;
- Invariance;
- Navier-Stokes Equation;
- Rotating Fluids;
- Fluid Mechanics and Heat Transfer