Characteristics of the intense vorticity structures in isotropic turbulence at high Reynolds numbers

Abstract

Direct numerical simulations (DNS) of forced (statistically stationary) isotropic turbulence are used to assess the characteristics of the intense vorticity structures (IVS) or "worms"at higher Reynolds numbers than previously available. The simulations cover a range of Taylor-based Reynolds numbers in the range 90≤Reλ≤399, for a resolution of kmaxη≈2.0, where kmax is the maximum resolved wave number and η is the Kolmogorov microscale. Most of the IVS characteristics are confirmed at the higher Reynolds numbers analyzed in this work; e.g., the results confirm that the mean radius of the IVS (Rivs) is approximately equal to (Rivs)/η≈4-5 and that the mean radius is equal to the radius of the stationary Burgers vortex (Rivs/RB)≈1.0, with RB=2(ν/α)1/2, where ν is the kinematic viscosity and α is the (locally) imposed rate of strain. Moreover, the tangential velocity of the IVS scales with the root-mean-square velocity of the flow Uivs∼u′. These IVS characteristics seem to be robust and relatively independent of the Reynolds number; however, there are other quantities for which the classical results do not hold. A notable example is the mean length of the IVS (Livs), which previous works, carried out at smaller Reynolds numbers, claimed to scale with either the Taylor microscale λ or the integral scale of turbulence L. It turns out that the correct scaling for this quantity can be observed only at Reλ200, and the results consistently show that Livs scales with the Kolmogorov microscale Livs∼η, with a mean value equal to (Livs)≈60η. The present findings provide further evidence that Reλ200 is required for the small scales to be fully developed.