Violation of the zeroth law of turbulence in space plasmas. (arXiv:2009.02828v1 [physics.space-ph] CROSS LISTED)
<a href="http://arxiv.org/find/physics/1/au:+Meyrand_R/0/1/0/all/0/1">Romain Meyrand</a>, <a href="http://arxiv.org/find/physics/1/au:+Squire_J/0/1/0/all/0/1">Jonathan Squire</a>, <a href="http://arxiv.org/find/physics/1/au:+Schekochihin_A/0/1/0/all/0/1">Alexander A. Schekochihin</a>, <a href="http://arxiv.org/find/physics/1/au:+Dorland_W/0/1/0/all/0/1">William Dorland</a>
The zeroth law of turbulence states that, for fixed energy input into
large-scale motions, the statistical steady state of a turbulent system is
independent of microphysical dissipation properties. The behavior, which is
fundamental to nearly all fluid-like systems from industrial processes to
galaxies, occurs because nonlinear processes generate smaller and smaller
scales in the flow, until the dissipation—no matter how small—can
thermalize the energy input. Using direct numerical simulations and theoretical
arguments, we show that in strongly magnetized plasma turbulence such as that
recently observed by the Parker Solar Probe (PSP) spacecraft, the zeroth law is
routinely violated. Namely, when such turbulence is “imbalanced”—when the
large-scale energy input is dominated by Alfv’en waves propagating in one
direction (the most common situation in space plasmas)—nonlinear conservation
laws imply the existence of a “barrier” at scales near the ion gyroradius. This
causes energy to build up over time at large scales. The resulting
magnetic-energy spectra bear a strong similarity to those observed in situ,
exhibiting a sharp, steep kinetic transition range above and around the
ion-Larmor scale, with flattening at yet smaller scales, thus resolving the
decade-long puzzle of the position and variability of ion-kinetic spectral
breaks in plasma turbulence. The “barrier” effect also suggests that how a
plasma is forced at large scales (the imbalance) may have a crucial influence
on thermodynamic properties such as the ion-to-electron heating ratio.
The zeroth law of turbulence states that, for fixed energy input into
large-scale motions, the statistical steady state of a turbulent system is
independent of microphysical dissipation properties. The behavior, which is
fundamental to nearly all fluid-like systems from industrial processes to
galaxies, occurs because nonlinear processes generate smaller and smaller
scales in the flow, until the dissipation—no matter how small—can
thermalize the energy input. Using direct numerical simulations and theoretical
arguments, we show that in strongly magnetized plasma turbulence such as that
recently observed by the Parker Solar Probe (PSP) spacecraft, the zeroth law is
routinely violated. Namely, when such turbulence is “imbalanced”—when the
large-scale energy input is dominated by Alfv’en waves propagating in one
direction (the most common situation in space plasmas)—nonlinear conservation
laws imply the existence of a “barrier” at scales near the ion gyroradius. This
causes energy to build up over time at large scales. The resulting
magnetic-energy spectra bear a strong similarity to those observed in situ,
exhibiting a sharp, steep kinetic transition range above and around the
ion-Larmor scale, with flattening at yet smaller scales, thus resolving the
decade-long puzzle of the position and variability of ion-kinetic spectral
breaks in plasma turbulence. The “barrier” effect also suggests that how a
plasma is forced at large scales (the imbalance) may have a crucial influence
on thermodynamic properties such as the ion-to-electron heating ratio.
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