Exact decomposition of energy and helicity fluxes in (magneto-)hydrodynamic turbulence

Recently, an exact decomposition of the energy flux from large to small scales in three-dimensional turbulence into contributions associated with vortex stretching and strain self-amplification has been derived (P. Johnson, Phys. Rev. Lett., 124, 104501 (2020)). Applied to data from direct numerical simulations, this decomposition results in a quantification of the relative contributions of the respective terms to the energy cascade.

Here, we extend the formalism to general, including coupled, advection-diffusion equations. The resulting flux decompositions can thus be readily applied to problems involving the dynamics of active and passive scalars and vectors. Here we use the method to calculate (a) kinetic helicity fluxes for homogeneous and isotropic turbulence, (b) magnetic and kinetic energy fluxes, and cross- and magnetic helicity fluxes for homogeneous magnetohydrodynamic (MHD) turbulence in two and three dimensions. The aim is to disentangle and quantify the relative contributions of vortex stretching by vorticity gradients and strain-vorticity coupling to the kinetic helicity cascade and similarly for the corresponding quantities in MHD.