Authors: Subash Adhikari (University of Delaware), Riddhi Bandyopadhyay (University of Delaware), Yan Yang (University of Delaware), William H. Matthaeus (University of Delaware)
A central assumption in most turbulence theories is that the mean energy dissipation rate remains finite as viscosity approaches zero, a concept known as the zeroth law of turbulence. While this behavior is well established in both hydrodynamic and magnetohydrodynamic (MHD) turbulence, its applicability to weakly collisional plasmas, where conventional viscous and resistive closures are absent, has remained unclear. Using a set of fully kinetic two-dimensional simulations of decaying plasma turbulence, we present the first evidence that the mean energy dissipation rate in a nearly collisionless plasma converges to a finite, system-independent value when expressed using an effective Reynolds number based on a heuristic effective collisionless viscosity (Adhikari et al. ApJ 2025). These findings confirm the presence of a so-called dissipation anomaly in collisionless plasma turbulence, demonstrating that the zeroth law extends beyond the collisional MHD regime. Evidently, in systems displaying this property, the turbulent dissipation is imposed by large scale dynamics, effectively at the energy containing scales. We believe this to offer a quantitative framework for estimating turbulent heating in space plasmas.
