Cascade properties of shear Alfvén wave turbulence
Abstract
Nonlinear threewave interactions of linear normal modes are investigated for twodimensional incompressible magnetohydrodynamics and the weakly threedimensional Strauss equations in the case where a strong uniform background field B_{0} is present. In both systems the only resonant interaction affecting Alfvén waves is caused by the shear of the background field plus the zero frequency (ω=k ṡ B_{0}=0) components of the perturbation. It is shown that the Alfvén waves are cascaded in wavenumber space by a mechanism equivalent to the resonant absorption at the Alfvén resonance. For large wavenumbers perpendicular to B_{0}, the cascade is described by Hamilton's ray equations, dk/dt=∂ω/∂r, where ω includes the effects of the zero frequency perturbations.
 Publication:

Physics of Fluids
 Pub Date:
 August 1985
 DOI:
 10.1063/1.865246
 Bibcode:
 1985PhFl...28.2406B
 Keywords:

 Magnetohydrodynamic Shear Heating;
 Magnetohydrodynamic Waves;
 Plasma Turbulence;
 Wave Interaction;
 Cascades;
 Tokamak Devices;
 Two Dimensional Flow;
 Wave Attenuation;
 Plasma Physics