Resonance-driven intermittency and extreme events in turbulent scalar transport with a mean gradient

Abstract We study the statistical properties of passive tracer transport in turbulent flows with a mean gradient, emphasizing tracer intermittency and extreme events. An analytically tractable model is developed, coupling zonal and shear velocity components with both linear and non-linear stochastic dynamics. Formulating the model in Fourier space, a simple explicit solution for the tracer invariant statistics is derived. Through this model we identify the resonance condition responsible for non-Gaussian behaviour and bursts in the tracer. Resonant conditions, that lead to a peak in the tracer variance, occur when the zonal flow and the shear flow phase speeds are equivalent. Numerical experiments across a range of regimes, including different energy spectra and zonal flow models, are performed to validate the theoretical findings and demonstrate how the velocity field and stochasticity determines tracer extremes. These results provide additional insight into the mechanisms underlying turbulent tracer transport, with implications for uncertainty quantification and data assimilation in geophysical and environmental applications.