Anisotropic energy transfers in quasi-static magnetohydrodynamic turbulence

Abstract

We perform direct numerical simulations of quasi-static magnetohydrodynamic turbulence, and compute various energy transfers including the ring-to-ring and conical energy transfers, and the energy fluxes of the perpendicular and parallel components of the velocity field. We show that the rings with higher polar angles transfer energy to ones with lower polar angles. For large interaction parameters, the dominant energy transfer takes place near the equator (polar angle θ ≈ π 2 ). The energy transfers are local both in wavenumbers and angles. The energy flux of the perpendicular component is predominantly from higher to lower wavenumbers (inverse cascade of energy), while that of the parallel component is from lower to higher wavenumbers (forward cascade of energy). Our results are consistent with earlier results, which indicate quasi two-dimensionalization of quasi-static magnetohydrodynamic (MHD) flows at high interaction parameters.

Anisotropy in Quasi-Static Magnetohydrodynamic Turbulence

“…In Fig. 13(d,e,f) we exhibit the J (k, θ) that exhibits the above properties for N = 0, 18, 130 respectively [56] . The ring spectra demonstrates that the flow is strongly anisotropic for large N with strong concentration of energy near k ≈ 0 plane.…”

“…Thus, for k > k f , where k f is the forcing wavenumber, F (k) = 0. In this regime, the flux Π(k) will decrease with k since J (k) is active at all scales [57,58,72,74]. This result is contrary to the constant energy flux observed in fluid turbulence in which ν is effective only at large k's (also see Sec.…”

“…The ratio of the angular distribution of the dissipation rates is given by [57] Thus, ν (k, θ) = J (k, θ) at…”

“…In Fig. 16 we plot the Joule dissipation spectrum [56] J (k) = 2B 2 0 cos 2 θE(k, θ)dθ (100) and the viscous dissipation…”

Statistical features of rapidly rotating decaying turbulence: Enstrophy and energy spectra and coherent structures

“…Note that u ⊥ = u xx + u yŷ and ω z (k) = [ik × u(k)] z . For the cross section at z = π, Figure 4(b,d) illustrates the plots Π (k) in stronglyrotating turbulence is due to the viscous effects, as in Equation (14), and due to energy transfer from u ⊥ to u z , analogous to that in quasi-static MHD 59,79 ; this is in contrast to constant Π starts to decrease at small k itself because the enstrophy dissipation wavenumber, k d , is quite small (see Table III). We compute the enstrophy dissipation wavenumber k d using Equation (15).…”