COEXISTENCE OF REGIONS OF EQUILIBRIUM AND NON-EQUILIBRIUM TWO-POINT TURBULENCE DYNAMICS IN GRID-GENERATED TURBULENCE BOTH WITH -5/3 SPECTRA BUT DIFFERENT UNDERLYING PHYSICS

Abstract

In this paper we present results concerning the spatial development of energy spectra E11( f ) and their associated integral and Taylor scales in conjunction with the spatial developments of vorticity, strain and production rates of vorticity and strain obtained from Direct Numerical Simulations of spatially developing grid-generated turbulence. We use a fractal square grid and a single mesh grid where the mesh is similar to the largest square on the fractal square grid. We find two adjacent but physically different regions in these flows relatively close to the grid: one where the Q-R diagram has not yet formed its well-known, presumed universal, tear-drop shape (Tsinober (2009)) but E11( f ) ∼ f−5/3 over more than a decade of a frequency range which is set by inlet conditions rather than Kolmogorov scalings: and one where theQ-R diagram immediately adopts the well-known tear-drop shape and E11( f ) ∼ f−5/3 over a Kolmogorov range of frequencies which increases as the local Reynolds number increases. In the one case with the higher local Reynolds numbers, the first region gives rise, as one moves downstream, to the non-equilibrium behaviour Cε ∼ 1/Reλ whilst the second region leads to Cε =Const.