Imbalanced Strong MHD Turbulence

By Y. Lithwick, Peter Goldreich, S. Sridhar. 2006

156 citations recorded by the source corpus.

We present a phenomenological model of imbalanced MHD turbulence in an incompressible magnetofluid. The steady state cascades, of waves traveling in opposite directions along the mean magnetic field, carry unequal energy fluxes to small length scales, where they decay as a result of viscous and resistive dissipation. The inertial range scalings are well understood when both cascades are weak. We study the case in which both cascades are, in a sense, strong. The inertial range of this imbalanced cascade has the following properties: (1) The ratio of the rms Elsässer amplitudes is independent of scale and is equal to the ratio of the corresponding energy fluxes. (2) In common with the balanced strong cascade, the energy spectra of both Elsässer waves are of the anisotropic Kolmogorov form, with their parallel correlation lengths equal to each other on all scales, and proportional to the two-thirds power of the transverse correlation length. (3) The equality of cascade time and wave period (critical balance) that characterizes the strong balanced cascade does not apply to the Elsässer field with the larger amplitude. Instead, the more general criterion that always applies to both Elsässer fields is that the cascade time is equal to the correlation time of the straining imposed by oppositely directed waves. (4) In the limit of equal energy fluxes, the turbulence corresponds to the balanced strong cascade. Our results are particularly relevant for turbulence in the solar wind. Spacecraft measurements have established that in the inertial range of solar wind turbulence, waves traveling away from the Sun have higher amplitudes than those traveling toward it. Result 1 allows us to infer the turbulent flux ratios from the amplitude ratios, thus providing insight into the origin of the turbulence.

Subfields: Astronomy and Astrophysics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/ff541d45b1613780607d6ec2547dff979c4f85b4

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Citations in the corpus

INCORPORATING KINETIC PHYSICS INTO A TWO-FLUID SOLAR-WIND MODEL WITH TEMPERATURE ANISOTROPY AND LOW-FREQUENCY ALFVÉN-WAVE TURBULENCE (2011, background): “However, Equation (46) is not consistent with three competing (and mutually inconsistent) models of AW turbulence with cross helicity (Lithwick et al. 2007; Beresnyak & Lazarian 2008; Chandran 2008a).”
ASTROPHYSICAL GYROKINETICS: KINETIC AND FLUID TURBULENT CASCADES IN MAGNETIZED WEAKLY COLLISIONAL PLASMAS (2007, background): “The GS theory can be generalized to this case ofimbalancedAlfvénic cascades (Lithwick et al. 2007; Beresnyak & Lazarian 2008a; Chandran 2008), but here we will focus on the balanced turbulence,ε+ ∼ ε−.”
NUMERICAL TESTS OF FAST RECONNECTION IN WEAKLY STOCHASTIC MAGNETIC FIELDS (2009, result): “We also do not consider imbalanced MHD turbulence (see Lithwick et al. 2007; Chandran 2008; Beresnyak & Lazarian 2008a, 2009), although for the modest degrees of imbalance between the turbulent energy fluxes moving in the opposite directions, we do not expect substantial changes in our results 6…”
DEPENDENCE OF SOLAR-WIND POWER SPECTRA ON THE DIRECTION OF THE LOCAL MEAN MAGNETIC FIELD (2009, background): “This inconsistency is easily remedied and the perpendicular energy spectra of the two Elsasser fields still have the same k−5/3⊥ scaling found by Lithwick et al. (2007).”
The Evolution and Role of Solar Wind Turbulence in the Inner Heliosphere (2019, background): “These spectra are similar to, although a little flatter than, the spectra predicted by Lithwick et al. (2007), whose model relies upon assumptions that may also describe reflection-driven turbulence in the solar wind (see Chandran & Perez (2019) for a more detailed discussion of this point).”
Evaluation of the turbulent energy cascade rates from the upper inertial range in the solar wind at 1 AU (2007, methodology): “Moreover, for cascades where sc 6 0i n the lower and middle inertial range, an analysis by Lithwick and Goldreich [2003] for weak turbulence determined that sc will approach zero in the high end and vanish at the point where the dissipation range begins [see also Grappin et al., 1983], while for str”
A Model of Turbulence in Magnetized Plasmas: Implications for the Dissipation Range in the Solar Wind (2007, background): “Later studies have examined the effects of compressibility [Lithwick and Goldreich, 2001; Cho and Lazarian, 2003; Vestuto et al., 2003], imbalanced Elsa¨sser fluxes [Maron and Goldreich, 2001; Cho et al. ,2 002; Lithwick et al., 2007 ], and a host of other refinements [Oughton et al., 2004; Oughton”
FAST MAGNETIC RECONNECTION AND SPONTANEOUS STOCHASTICITY (2011, background): “4 Among the existing theories of imbalanced turbulence (see Lithwick et al. (2007); Beresnyak & Lazarian (2008); Chandran (2008); Perez & Boldyrev (2009), all, but Beresnyak & Lazarian Similarly, we shall not discuss MHD turbulence at high magnetic Prandtl numbers, when the field-parallel viscosity…”