  The tertiary instability is believed to be important for governing magnetised
plasma turbulence under conditions of strong zonal flow generation, near
marginal stability. In this work, we investigate its role for a collisionless
strongly driven fluid model, self-consistently derived as a limit of
gyrokinetics. It is found that a region of absolute stability above the linear
threshold exists, beyond which significant nonlinear transport rapidly
develops. While within this range a complex pattern of transient zonal
evolution is observed before a stable profile is found, the Dimits transition
itself is found to coincide with a tertiary instability threshold so long as
linear effects are included. Through a simple and readily extendable procedure
tracing its origin to St-Onge 2017 (arXiv:1704.05406) the stabilising effect of
the typical zonal profile can be approximated and the accompanying reduced mode
estimate is found to be in good agreement with nonlinear simulations.
