Stochastic magnetohydrodynamic turbulence in space dimensions d > or =2

Area of Science:

• Physics
• Fluid Dynamics
• Plasma Physics

Background:

• Magnetohydrodynamics (MHD) describes the dynamics of electrically conducting fluids.
• Understanding scaling regimes in randomly driven MHD is crucial for astrophysical and geophysical applications.
• Previous studies faced challenges with divergences at two spatial dimensions.

Purpose of the Study:

• To analyze the interplay of kinematic and magnetic forcing in randomly driven MHD.
• To investigate the stability of scaling regimes in different spatial dimensions (d >= 2).
• To address and resolve inconsistencies in treating divergences at d=2.

Main Methods:

• Renormalization group (RG) analysis in spatial dimensions d >= 2.
• Perturbative expansion using deviations from critical values for spatial dimension and forcing correlation exponent.
• One-loop approximation incorporating additional divergences at d=2.

Main Results:

• The kinetic fixed point, linked to Kolmogorov scaling, remains stable for d >= 2 with sufficiently decaying magnetic forcing correlations.
• A novel scaling regime driven by thermal velocity field fluctuations was identified and analyzed.
• The absence of a magnetic field fluctuation-driven scaling regime near d=2 was confirmed.

Conclusions:

• The study confirms the stability of the Kolmogorov scaling regime in randomly driven MHD for d >= 2, despite divergences.
• New insights into thermal fluctuation-driven scaling regimes were provided.
• A robust renormalization scheme was developed and numerically validated for interpolating between different expansion methods.