Theory for helical turbulence under fast rotation

Abstract

Recent numerical simulations have shown the strong impact of helicity on \ADD{homogeneous} rotating hydrodynamic turbulence. The main effect can be summarized through the following law, $n+\tilde{n}=-4$, where $n$ and $\tilde{n}$ are respectively the power law indices of the one-dimensional energy and helicity spectra. We investigate this rotating turbulence problem in the small Rossby number limit by using the asymptotic weak turbulence theory derived previously. We show that the empirical law is an exact solution of the helicity equation where the power law indices correspond to perpendicular (to the rotation axis) wave number spectra. It is proposed that when the cascade towards small-scales tends to be dominated by the helicity flux the solution tends to $\tilde{n}=-2$, whereas it is $\tilde{n}=-3/2$ when the energy flux dominates. The latter solution is compatible with the so-called maximal helicity state previously observed numerically and derived theoretically in the weak turbulence regime when only the energy equation is used, whereas the former solution is constrained by a locality condition.

4 pages

References in corpus (4)

• Wave turbulence in incompressible Hall MHD
• Scale interactions and scaling laws in rotating flows at moderate Rossby numbers and large Reynolds numbers
• Helicity cascades in rotating turbulence
• Signatures of two-dimensionalisation of 3D turbulence in presence of rotation

Cited by in corpus (10)

• Cascades and transitions in turbulent flows
• Rotating Taylor-Green Flow
• An alternative formulation for exact scaling relations in hydrodynamic and magnetohydrodynamic turbulence
• Weak turbulence theory for rotating magnetohydrodynamics and planetary dynamos
• Entanglement of helicity and energy in kinetic Alfven wave/whistler turbulence
• Small-scale anisotropy induced by spectral forcing and by rotation in non-helical and helical turbulence
• Complete Hamiltonian formalism for inertial waves in rotating fluids
• Non-universal behaviour of helical two-dimensional three-component turbulence
• Intermittency in Weak Magnetohydrodynamic Turbulence
• Multiple scales kinetic theory for rotationally constrained slow inertial waves and anisotropic dynamics