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

• Published in: Journal of fluid mechanics Vol. 663; pp. 268 - 292
• Main Author: DAVIDSON, P. A.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.11.2010
• Subjects: Decay; Exact sciences and technology; Fluid dynamics; Fluid flow; Fundamental areas of phenomenology (including applications); homogeneous turbulence; Integrals; Isotropic turbulence; homogeneous turbulence; Magnetic fields; Physics; Physics of gases, plasmas and electric discharges; Physics of plasmas and electric discharges; Plasma turbulence; rotating turbulence; Stratification; Turbulence; Turbulence models; turbulence theory; Turbulent flow; Turbulent flows, convection, and heat transfer; Waves, oscillations, and instabilities in plasmas and intense beams; homogeneous turbulence; rotating turbulence; turbulence theory; Rotating system; Turbulent flow; Plasma turbulence; Decay; Theoretical study; Magnetic fields; Conducting fluid; Turbulence structure; MHD turbulence; Stratified flow; Homogeneous turbulence
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112010003496

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.