Hysteresis behavior across the nonlinear ITG transition

Investigate whether the standard ITG and potential-vorticity-conserving ITG fluid models exhibit hysteresis associated with the transition between zonal-flow-dominated and high-transport states.

Background

The paper studies two-dimensional fluid models of ion-temperature-gradient turbulence that display a transition from a zonal-flow-dominated regime to a high-transport turbulent regime. The authors note that analogous hysteresis has been observed in related drift-wave, gyrofluid, and gyrokinetic systems, but they do not investigate it in the two ITG models considered here.

The unresolved issue is whether sufficiently resolved simulations of these simple fluid models reproduce hysteresis around the nonlinear threshold, rather than merely exhibiting distinct regimes at selected temperature-gradient values.

References

Ideally, one would like to recover the hysteresis associated with the transition using the simple fluid models with high resolution simulations. However, the additional flexibility provided by using fluid models make the choice of model an essential issue. Therefore, here we focus on the physics of the system when it is in either of the states that it presents and try to characterize the effects of different nonlinearities, leaving the investigation of possible hysteresis behavior to a future study.

— The role of different nonlinearities and potential vorticity conservation in two-dimensional fluid ITG models  (2609.01414 - Paramasivam et al., 1 Sep 2026) in Section 1, Introduction

Note also that the inevitable requirement of hypoviscosity may in fact be stemming from the use of local gradient-driven simulations with periodic boundary conditions instead of flux driven system with boundary conditions. This is because, in a flux driven system, whenever there is a jump in the flux, the profile relaxes, mitigating the increase and thereby allowing the simulation to saturate eventually. Therefore, a flux-driven code with fixed boundary conditions should elucidate the behavior of the diamagnetic nonlinearity better and also improve the system from a modeling perspective. These extensions, too, are left for future studies.

— The role of different nonlinearities and potential vorticity conservation in two-dimensional fluid ITG models  (2609.01414 - Paramasivam et al., 1 Sep 2026) in Section 6, Conclusion