Alternative exact law for homogeneous compressible turbulent flows: from Hall-MHD to hydrodynamics

Renaud Ferrand
Laboratoire de Physique des Plasmas, Ecole polytechnique, 91128 Palaiseau, France

Fluid and plasma turbulence is a longstanding problem in physics. Studying its dynamics can help understanding various processes such as mass transport and energy dissipation, in particular in collisionless systems like most of the astrophysical plasmas. The solar wind heating problem, which is manifested by a slower decrease of the ion temperature as function of the heliocentric distance than the prediction from the adiabatic expansion model of the wind, is one example of such problems where turbulence can help give an explanation.

A way to study fluid or plasma turbulence is to estimate the total energy cascade rate, which is the energy transferred from the largest scales into the dissipative scales of the system. This is made possible by the use of exact laws, which link the energy cascade rate to the physical variables of the flow. Significant progress has been made in recent years on deriving various forms of exact laws for different compressible flows: HydroDynamics (HD), MagnetoHydroDynamics (MHD) and Hall-MagnetoHydroDynamics (HMHD). Some of them were used successfully to estimate the energy cascade rate in the solar wind and the magnetosheath, but at the expense of making additional assumptions that made different mathematical terms involved in the laws accessible to in-situ measurements.

Here we present an alternative exact law for compressible Hall-MHD turbulence. This law is more compact and easier to compute in numerical simulations and spacecraft data, thus reducing the memory load and time required to compute the energy cascade rate. We also show the validity of this new law in the limit of compressible HD using high-resolution simulation data of HD turbulence spanning the subsonic and supersonic regimes.