EGU21-7768, updated on 04 Mar 2021
https://doi.org/10.5194/egusphere-egu21-7768
EGU General Assembly 2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Proof of the zeroth law of turbulence in one-dimensional compressible magnetohydrodynamics and heating of the sawtooth solar wind

Vincent David1,2 and Sébastien Galtier1,2,3
Vincent David and Sébastien Galtier
  • 1Laboratoire de Physique des Plasmas, Ecole Polytechnique, Palaiseau, France (vincent.david@lpp.polytechnique.fr)
  • 2Université Paris-Saclay
  • 3Institut universitaire de France

The zeroth law of turbulence is one of the oldest conjecture in turbulence that is still unproven. We consider weak solutions of one-dimensional (1D) compressible magnetohydrodynamics (MHD) and demonstrate that the lack of smoothness of the fields introduces a new dissipative term, named inertial dissipation, into the expression of energy conservation that is neither viscous nor resistive in nature. We propose exact solutions assuming that the kinematic viscosity and the magnetic diffusivity are equal, and we demonstrate that the associated inertial dissipation is, on average, positive and equal to the mean viscous dissipation rate in the limit of small viscosity, proving the conjecture of the zeroth law of turbulence.

We show that discontinuities commonly de- tected by Voyager 1 & 2 in the solar wind at 2–10AU can be fitted by the inviscid analytical profiles. We deduce a heating rate of ∼ 10−18 Jm−3s−1 , which is significantly higher than the value obtained from the turbulent fluctuations. This suggests that collisionless shocks are a dominant source of heating in the outer solar wind.

How to cite: David, V. and Galtier, S.: Proof of the zeroth law of turbulence in one-dimensional compressible magnetohydrodynamics and heating of the sawtooth solar wind, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7768, https://doi.org/10.5194/egusphere-egu21-7768, 2021.

Corresponding presentation materials formerly uploaded have been withdrawn.