Table 1.
Quasi-parallel Alfvén waves in MHD turbulence.
Background | Scale range of validity | Scaling of background | Nonlinear parameter of | Nonlinear parameter | |
---|---|---|---|---|---|
cascade | turbulent fluctuations | background turbulence | of quasi-parallel AWs | ||
(acronym) | λ⊥, max | λ⊥, min | δzλ⊥ | ![]() |
![]() |
Without scale-dependent alignment | |||||
sub-Alfvénic injection (MA, 0 < 1): | |||||
(W0) | ℓ0 | ![]() |
vA, 0 MA, 0 (λ⊥/ℓ0)1/2 | MA, 0 (λ⊥/ℓ0)−1/2 | ![]() |
(GS95) | ![]() |
![]() |
![]() |
∼1 | ![]() |
trans-Alfvénic injection (MA, 0 ≈ 1): | |||||
(GS95) | ℓ0 | ![]() |
vA, 0 (λ⊥/ℓ0)1/3 | ∼1 | (λ⊥/ℓ0)2/3 |
super-Alfvénic injection (MA, 0 > 1): | |||||
(K41) | ℓ0 | ![]() |
vA, 0 MA, 0 (λ/ℓ0)1/3 | MA, 0 (λ/ℓ0)1/3 | MA, 0 (λ/ℓ0)1/3 |
(GS95) | ![]() |
(MA, 0 S0)−3/4 ℓ0 | vA, 0 MA, 0 (λ⊥/ℓ0)1/3 | ∼1 | ![]() |
With scale-dependent alignment | |||||
sub-Alfvénic injection (MA, 0 < 1): | |||||
(W0) | ℓ0 | ![]() |
vA, 0 MA, 0 (λ⊥/ℓ0)1/2 | MA, 0 (λ⊥/ℓ0)−1/2 | ![]() |
(B06) | ![]() |
![]() |
![]() |
∼1 | ![]() |
(TMT) | ![]() |
![]() |
![]() |
∼1 | ![]() |
trans-Alfvénic injection (MA, 0 ≈ 1): | |||||
(B06) | ℓ0 | ![]() |
vA, 0 (λ⊥/ℓ0)1/4 | ∼1 | (λ⊥/ℓ0)1/2 |
(TMT) | ![]() |
![]() |
![]() |
∼1 | ![]() |
super-Alfvénic injection (MA, 0 > 1): | |||||
(K41) | ℓ0 | ![]() |
vA, 0 MA, 0 (λ/ℓ0)1/3 | MA, 0 (λ/ℓ0)1/3 | MA, 0 (λ/ℓ0)1/3 |
(B06) | ![]() |
![]() |
![]() |
∼1 | ![]() |
(TMT) | ![]() |
(MA, 0 S0)−3/4 ℓ0 | ![]() |
∼1 | ![]() |
Notes. Summary of the relevant scaling relations for balanced MHD turbulence in the different regimes mentioned in Section 4 (see Appendix A for the derivation). The last two columns explicitly show the difference between the intrinsic nonlinear parameter χ z of background fluctuations and the nonlinear parameter χw, q∥ of a quasi-parallel Alfvén wave interacting with those fluctuations. The locality of interactions has been implied everywhere and that in all the regimes with dynamic alignment, a transition to a tearing-mediated range (TMT) has been assumed, i.e., that the injection-scale Lunquist number satisfies the inequality
(
) for sub-Alfvénic (super-Alfvénic) injection. See Table 2 for the consequences of not taking into account this difference between χw, q∥ and χ z on the inferred turbulent damping rate of quasi-parallel Alfvén waves.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.