= Goldreich–Sridhar turbulence
{c}
{title2=$E(k_\perp)\propto k_\perp^{-5/3}$}
= Goldreich–Sridhar theory
{c}
{synonym}
<Goldreich–Sridhar turbulence> combines <critical balance>, balanced counterpropagating <Alfvén waves>, a local perpendicular cascade, and constant <energy> flux per unit mass $\mathcal E$. With $\tau_{\mathrm{nl}}\sim\ell_\perp/\delta u_\ell$ and $\mathcal E\sim\delta u_\ell^2/\tau_{\mathrm{nl}}$, one obtains $\delta u_\ell\sim(\mathcal E\ell_\perp)^{1/3}$. Defining the one-dimensional perpendicular <turbulent energy spectrum> by $\delta u_\ell^2\sim k_\perp E(k_\perp)$ gives $E(k_\perp)\sim\mathcal E^{2/3}k_\perp^{-5/3}$. <Critical balance> also gives $k_\parallel\sim\mathcal E^{1/3}k_\perp^{2/3}/v_A$. This scaling argument neglects scale-dependent alignment and intermittency corrections, which are additional physical effects rather than consequences of the stated assumptions.
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