= Iroshnikov-Kraichnan spectrum
{c}
{title2=$E(k)\sim(\epsilon v_A)^{1/2}k^{-3/2}$}
The <Iroshnikov-Kraichnan spectrum> phenomenology assumes balanced, isotropic local <Alfvénic turbulence> with $\delta z_l\ll v_A$, decorrelated counterpropagating encounters, $\tau_A=l/v_A$ and $\tau_{\rm nl}=l/\delta z_l$. A <weak wave cascade> takes $\tau_{\rm cas}\sim\tau_{\rm nl}^2/\tau_A=v_Al/\delta z_l^2$. Constant <energy flux> gives $\delta z_l^4\sim\epsilon v_Al$ and the displayed shell-integrated <turbulent energy spectrum>. Isotropy is an additional assumption, not a consequence of a strong guide field.
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