Stability of Kolmogorov scaling in anisotropically forced turbulence

Abstract

Renormalization-group analysis of randomly stirred fluid with anisotropic distribution of random force is carried out at one-loop order. The axial anisotropy is introduced by free parameters of external forcing in the Navier-Stokes equation, but the anisotropy parameters are not assumed to be small. The region of stability of the Kolmogorov scaling regime in the space of anisotropy parameters has been determined for several space dimensionalities 2\ensuremath{\leqslant}3. The Kolmogorov constant and the amplitudes of longitudinal and transverse projection operators with respect to the preferred direction in the energy spectrum have been calculated in situations where the competition between the anisotropy of the external forcing and the Navier-Stokes dynamics may affect the stability of the Kolmogorov regime. Extension to more complex magnetohydrodynamic systems is under investigation.