On the anisotropy of a low-Reynolds-number grid turbulence

The anisotropy of a low-Reynolds-number grid turbulence is investigated through direct numerical simulations based on the lattice Boltzmann method. The focus is on the anisotropy of the Reynolds-stress (b(ij)) and Reynolds-stress dissipation-rate (d(ij)) tensors and the approach taken is that using the invariant analysis introduced by Lumley & Newman (J. Fluid Mech., vol. 82, 1977, pp. 161-178). The grid is made up of thin square floating elements in an aligned configuration. The anisotropy is initially high behind the grid and decays quickly as the downstream distance increases. The anisotropy invariant map (AIM) analysis shows that the return-to-isotropic trend of both b(ij) and d(ij) is fast and follows a perfectly axisymmetic expansion, although just behind the grid there is an initial tendency toward a one-component state. It is found that the linear relation d(ij) = Ab(ij) with A = 0.21 is satisfied during the return-to-isotropy phase of the turbulence decay, although close to the grid a form d(ij) = f(b(ij)), where f is a nonlinear function of b(ij), is more appropriate. For large downstream distances, d(ij) becomes almost independent of b(ij), suggesting that despite the absence of an inertial range, the (dissipative) small scales present a high degree of isotropy. It is argued that (i) the very small values of the mean strain rate and (ii) the weak anisotropy of the large scales are in fact responsible for this result.