Turbulence and laminar structures: Can they co-exist?

Abstract

Schwarzschild first suggested that the laminar structures observed in the high Reynolds number Re = UL/v ≈ O (1012) solar photosphere are the result of turbulence rather than a proof of its absence. He reasoned that, since turbulence generates large turbulent viscosities vt ≫ v, the 'effective' Reynolds number Re = UL/vt ≈ O(1). Schwarzschild's argument is, however, incomplete, for it assumes that the entire role of the non-linear interactions is to 'enhance' viscosity. While this is not true in general, we present a proof of how and why it may occur, thus completing Schwarzschild's argument. We further discuss the fact that the same non-local turbulence models reproduce Large Eddy Simulation (LES) data for a variety of flows pertaining to astrophysics, geophysics and laboratory situations (in a fraction of the time).