A minimal stochastic model of the influence of turbulence intermittency on scalar structure-function exponents

Hierarchical parcel-swapping (HiPS) predicts scalar structure-function exponent values that compare favorably to DNS results that exhibit anomalous scaling attributed to turbulence intermittency. To illustrate the mechanism by which HiPS captures intermittent behavior, a simpler model is introduced. JELLIED (jump events, logarithmic ladder, intervening exponential decay) is an event-based Monte-Carlo simulation in which scalar differences at logarithmically spaced length scales decay exponentially after a scale-dependent delay but sporadically jump to the difference value at the next larger scale, where the dependencies of jump frequency and decay rate on length scale are prescribed in conformance with inertial-range scaling. This is roughly analogous to a noise-coupled hierarchy of Langevin processes. The associated physical picture is that the scalar difference at a given length scale decays owing to cascading to dissipative scales while being sporadically pumped by cascading of scalar difference at the next larger scale. Tuning of model parameters yields moment-order-dependent scalar structure-function exponent values close to HiPS predictions and a corresponding DNS case. Implications of model results with regard to the phenomenology of exponent saturation are noted.