Revisiting the SABRA Model: Statics and Dynamics

TL;DR

This paper re-examines the two-dimensional SABRA turbulence model, analyzing static and dynamic properties across different regimes, and finds it only mimics true 2D turbulence asymptotically as a key parameter approaches -2.

Contribution

It provides a systematic analysis of the SABRA model's equilibrium and turbulent states, clarifying the nature of the transition and asymptotic behavior.

Findings

No sharp transition from equipartition to turbulence.

Static and dynamic exponents are consistent with previous studies.

Model mimics 2D turbulence asymptotically as parameter b approaches -2.

Abstract

We revisit the two-dimensional SABRA model, in the light of recent results of Frisch {\it et al.} [Phys. Rev. Lett. {\bf 108}, 074501 (2012)] and examine, systematically, the interplay between equilibrium states and cascade (turbulent) solutions, characterised by a single parameter $b$, via equal-time and time-dependent structure functions. We calculate the static and dynamic exponents across the equipartition as well as turbulent regimes which are consistent with earlier studies. Our results indicate the absence of a sharp transition from equipartition to turbulent states. Indeed, we find that the SABRA model mimics true two-dimensional turbulence only asymptotically as $b\to-2$.