 Weak Alfvénic cascade

For balanced anisotropic Alfvénic turbulence, suppose ${\tau }_A=l_{\parallel }/v_A\ll {\tau }_{\mathrm{nl}}=l_{\perp }/\delta z$ and resonant interactions preserve the parallel scale during the perpendicular cascade. Random encounter accumulation gives ${\tau }_{\mathrm{cas}}=v_A{l}_{\perp }^2/(\delta z^2{l}_{\parallel })$. Constant energy flux then gives $\delta z\propto l_{\perp }^{1/2}$ and the displayed perpendicular turbulent energy spectrum. Unlike isotropic phenomenology, the fixed parallel scale is independent of the decreasing perpendicular scale.