Critical gradient response of the Weiland model

The success the Weiland model has had in reproducing modulation experiments prompted this in-depth investigation into its behaviour as a critical gradient model (CGM). The critical gradient properties of the Weiland model is examined analytically and numerically and compared with the, empirical CGM commonly used in experiment. A simplified Weiland CGM is derived in which the height-above-threshold, dependence is not necessarily linear. Simultaneously, the validity of the empirical CGM was examined. It is shown that an effective threshold, which is higher than the instability threshold, can be obtained if pinches influence the diffusivity.