Space–time structure of weak magnetohydrodynamic turbulence
The two-time energy spectrum of weak magnetohydrodynamic turbulence is found by applying a wave-turbulence closure to the cumulant hierarchy constructed from the dynamical equations. Solutions are facilitated via asymptotic expansions in terms of the small parameter $$\varepsilon$$ , describing the ratio of time scales corresponding to Alfvénic propagation and nonlinear interactions between counter-propagating Alfvén waves. The strength of nonlinearity at a given spatial scale is further quantified by an integration over all possible delta-correlated modes compliant in a given set of three-wave interactions that are associated with energy flux through the said scale. The wave-turbulence closure for the two-time spectrum uncovers a secularity occurring on a time scale of order $$\varepsilon ^{-2}$$ , and the asymptotic expansion for the spectrum is reordered in a manner comparable to the one-time case. It is shown that for the regime of stationary turbulence, the two-time energy spectrum exponentially decays on a lagged time scale $$(\varepsilon ^2 \gamma _k^s)^{-1}$$ in proportion to the strength of the associated three-wave interactions, characterized by nonlinear decorrelation frequency $$\gamma _k^s$$ . The scaling of the form $$k_{\perp } v_0 \chi _0$$ exhibited by this frequency is reminiscent of random sweeping by the outer scale with characteristic fluctuation velocity $$v_0$$ that is modified due to competition with Alfvénic propagation (characterized by $$\chi _0$$ ) at the said scale. A brief calculation of frequency broadening of the power spectrum due to nonlinear interactions is also presented.
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- FG02-89ER53291
- OSTI ID:
- 2283590
- Alternate ID(s):
- OSTI ID: 2577228
- Journal Information:
- Journal of Plasma Physics, Journal Name: Journal of Plasma Physics Journal Issue: 1 Vol. 90; ISSN 0022-3778
- Publisher:
- Cambridge University Press (CUP)Copyright Statement
- Country of Publication:
- United Kingdom
- Language:
- English
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