On the decay of Saffman turbulence subject to rotation, stratification or an imposed magnetic field

Abstract

We consider freely decaying, statistically axisymmetric turbulence evolving in the presence of a background rotation, an imposed stratification or a uniform magnetic field. We focus on the case of Saffman turbulence in which E(k → 0) ~ k2 and show that, if the large scales evolve in a self-similar manner, then u⊥2 ℓ⊥2 ℓ∥ = constant in rotating, stratified and magnetohydrodynamic turbulence. This may be contrasted with E(k → 0) ~ k4 turbulence, in which u⊥2 ℓ⊥4 ℓ∥ ≈ constant. (Here the subscripts ⊥ and ∥ indicate directions perpendicular and parallel to the axis of symmetry, and ℓ⊥, ℓ∥ and u⊥ are suitably defined integral scales.) This constraint on the integral scales allows us to make simple, testable predictions for the temporal evolution of ℓ⊥, ℓ∥ and u⊥ in all three systems. There are only limited data sets against which to compare these predictions, but they are consistent with those data which are currently available.