Then, this criterion was used for a “heuristic calculation” of the Dimits shift. However, that calculation is not entirely satisfactory, because deriving the actual Dimits shift takes more than a sufficient condition of ZF stability. The direct relation between @St-Onge17’s criterion and the Dimits shift is only an assumption. As a result, the agreement of @St-Onge17’s theory with numerical simulations is limited (section \[sec:DSPrediction\]). Besides, the 4MT model is only a rough approximation and cannot capture essential features of the TI in principle, as we shall discuss below. Therefore, a transparent theory of the TI and the Dimits shift within the mTHE model is yet to be developed.

In our recent letter [@Zhu20], we sketched a theory of the TI and the Dimits shift within the modified Hasegawa–Wakatani model, where the mTHE was briefly mentioned as the “adiabatic limit”. This limit is important in that the mTHE permits a detailed analytic study of the TI and an explicit quantitative prediction of the Dimits shift; thus, it deserves further investigation. Here, we present an in-depth study of the mTHE by expanding on the results presented in [@Zhu20]. We show that assuming a sufficient scale separation between ZFs and DWs, TI modes 