Zum Energiespektrum der isotropen hydromagnetischen Turbulenz

Abstract

The physical consequences emerging from a theory stated byKraichnan are considered with regard to isotropic hydromagnetic turbulence. This theory involves the direct-interaction approximation retaining the phase correlation within each triad of Fourier amplitudes. These interactions are suggested to be very important in hydromagnetic turbulence.

Hydrodynamic as well as magnetic impulse-response function and time-correlation are unequivocally the same. This result suggests the existence of a universal equilibrium range. Within the inertial range the total energy spectrumE _g (k)=E(k)+E _m (k) obeys the same law as in hydrodynamic turbulenceE(k). The valueE _m (k)≈E(k) corresponds roughly to maximum energy flux through this range. The magnetic energy flux decreases rapidly for eddies with larger wave-numbers within the range of ohmic ≫ viscous dissipation.