Critical balance in magnetohydrodynamic, rotating and stratified turbulence: towards a universal scaling conjecture

• Published in: Journal of fluid mechanics Vol. 677; pp. 134 - 153
• Main Authors: NAZARENKO, SERGEI V., SCHEKOCHIHIN, ALEXANDER A.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.06.2011
• Subjects: Anisotropy; Computational fluid dynamics; Exact sciences and technology; Fluid flow; Fluid mechanics; Magnetohydrodynamic waves (e.g., alfven waves); Magnetohydrodynamics; Physics; Physics of gases, plasmas and electric discharges; Physics of plasmas and electric discharges; Plasma turbulence; Propagation; Reynolds number; Rotating; Spectra; Turbulence; Turbulent flow; Waves, oscillations, and instabilities in plasmas and intense beams; stratified turbulence; rotating turbulence; MHD turbulence; Alfven waves; Rotating system; Anisotropy; Digital simulation; Scaling laws; Layered fluid; Modelling
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S002211201100067X

It is proposed that critical balance – a scale-by-scale balance between the linear propagation and nonlinear interaction time scales – can be used as a universal scaling conjecture for determining the spectra of strong turbulence in anisotropic wave systems. Magnetohydrodynamic (MHD), rotating and stratified turbulence are considered under this assumption and, in particular, a novel and experimentally testable energy cascade scenario and a set of scalings of the spectra are proposed for low-Rossby-number rotating turbulence. It is argued that in neutral fluids the critically balanced anisotropic cascade provides a natural path from strong anisotropy at large scales to isotropic Kolmogorov turbulence at very small scales. It is also argued that the k−2⊥ spectra seen in recent numerical simulations of low-Rossby-number rotating turbulence may be analogous to the k−3/2⊥ spectra of the numerical MHD turbulence in the sense that they could be explained by assuming that fluctuations are polarised (aligned) approximately as inertial waves (Alfvén waves for MHD).