Revisiting the SABRA model: Statics and dynamics

¹ Department of Physics, Indian Institute of Science - Bangalore 560012, India
² Department of Physics, Carnegie Mellon University - 5000 Forbes Avenue, Pittsburgh, PA 15213-3890, USA
³ International Centre for Theoretical Sciences, Tata Institute of Fundamental Research - Bangalore 560089, India

Received: 31 August 2017
Accepted: 5 January 2018

Abstract

We revisit the two-dimensional SABRA model, in the light of the recent results of Frisch et al. (Phys. Rev. Lett., 108 (2012) 074501) 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 .