# Animations

**Tearing-mediated turbulence via collisions of 3D Alfvén-wave packets**

[ **Reference:** Cerri, Passot, Laveder, Sulem & Kunz, *"Turbulent regimes in collisions of 3D Alfvén-wave packets" *ApJ **939**:36 (2022) ]

*Basic ideas:*

- If some sort of
*dynamic alignment*takes place as the turbulent fluctuations cascade towards smaller and smaller scales, then in addition to the usual fluctuations' anisotropy with respect to the mean magnetic field, turbulent eddies become increasingly more sheared also in the field-perepndicular plane (i.e., fluctuations become more and more*3D anisotropic*with decreasing scale). - The above mechanism sets up a tearing-unstable configuration in the plane perpendicular to the mean magnetic field. If the turbulent eddies at a certain scale live long enough to allow the tearing instability to grow and disrupt them, then the turbulent cascade transtitions into the so-called
*tearing-mediated range*. - The turbulent-eddies' lifetime depends upon the large-scale nonlinearities (the strength of which can be defined through a
*nonlinearity parameter χ*, defined as the ratio between the Alfvén-wave linear propagation time and the nonlinear turnover time). The lower the nonlinearities are, the longer the lifetime of turbulent eddies will be. Therefore, by decreasing the nonlinearities at large scales (_{0}*"weak cascade"*,*χ*), one may expect to meet the conditions for a transition to the tearing-mediated range at scales that can be larger than those predicted for a cascade with strong large-scale nonlinearities (_{0}< 1*"critically balanced cascade",*).*χ*_{0}~ 1

*Bottom line:*

*An initially weak cascade could allow tearing instability to onset and mediate the cascade at scales much larger than those predicted for a critically balanced cascade. Such a weak-to-tearing transition may even supplant the usual weak-to-strong transition in plasma turbulence.*

**Note: **if html embedding of .mov videos right below does not work on your web browser, the same videos are also embedded as YouTube videos at the bottom of the page.

**1.** Very weak non-linearities at large scales (emerging tearing-mediated range)

**Figure.** Iso-contours of δB_{⊥}/B_{rms} for initial non-linearity parameter χ_{0} ∼ 0.1. *Left:* view of a slice in the x-y plane (i.e., plane perpendicular to B_{0}) at z = L_{0}/2. *Right:* view of δB⊥/B_{rms} averaged over z.

**2.** Intermediate non-linearities at large scales (emerging tearing-mediated range)

**Figure.** Iso-contours of δB_{⊥}/B_{rms} for initial non-linearity parameter χ_{0} ∼ 0.5. *Left:* view of a slice in the x-y plane (i.e., plane perpendicular to B_{0}) at z = L_{0}/2. *Right:* view of δB⊥/B_{rms} averaged over z.

**3.** Strong non-linearities at large scales (no tearing-mediated range):

**Figure.** Iso-contours of δB_{⊥}/B_{rms} for initial non-linearity parameter χ_{0} ∼ 1. *Left:* view of a slice in the x-y plane (i.e., plane perpendicular to B_{0}) at z = L_{0}/2. *Right:* view of δB⊥/B_{rms} averaged over z.

**1.** Very weak non-linearities at large scales (emerging tearing-mediated range)

**Figure.** Iso-contours of δB_{⊥}/B_{rms} for initial non-linearity parameter χ_{0} ∼ 0.1 taken on a x-y plane (i.e., plane perpendicular to B_{0}) at z = L_{0}/2.

**Figure.** Iso-contours of δB_{⊥}/B_{rms} for initial non-linearity parameter χ_{0} ∼ 0.1 when an average over z is performed (z is the direction along B_{0}).

**2.** Intermediate non-linearities at large scales (emerging tearing-mediated range)

**Figure.** Iso-contours of δB_{⊥}/B_{rms} for initial non-linearity parameter χ_{0} ∼ 0.5 taken on a x-y plane (i.e., plane perpendicular to B_{0}) at z = L_{0}/2.

**Figure.** Iso-contours of δB_{⊥}/B_{rms} for initial non-linearity parameter χ_{0} ∼ 0.5 when an average over z is performed (z is the direction along B_{0}).

**3.** Strong non-linearities at large scales (no tearing-mediated range):

**Figure.** Iso-contours of δB_{⊥}/B_{rms} for initial non-linearity parameter χ_{0} ∼ 1 taken on a x-y plane (i.e., plane perpendicular to B_{0}) at z = L_{0}/2.

**Figure.** Iso-contours of δB_{⊥}/B_{rms} for initial non-linearity parameter χ_{0} ∼ 1 when an average over z is performed (z is the direction along B_{0}).