Unsteady Chains of Wave Structures and Anomalous Transport of Passive Admixture in a Barotropic Jet Flow

Abstract

The anomalous transport of passive admixture is studied when unsteady chains of wave structures with closed streamlines are excited in a barotropic jet flow that models the zonal flows in the Earth’s atmosphere and ocean, as well as in the laboratory experiments. The analysis is performed within a dynamical model describing saturation of the barotropic instability of the jet current in a plane channel with rigid parallel walls with account for the beta effect and external friction. The equations of a barotropic current are solved numerically using the pseudospectral approach. It is found that the generation of high modes in a jet with a “two-hump” velocity profile leads to the accelerated transition to the complex dynamics. A multiharmonic regime with a discrete spectrum appears in the initial stage of this motion. The exponents of the power dependence on the time of the average (over the ensemble) displacement of tracer particles and its dispersion are found for the basic generation regimes of the wave structure, which confirm the occurrence of the anomalous diffusion of the admixture. A self-similar probability density function of tracer displacements has been found and the dependence of the transition to the complex dynamics on the number of vortices in the chain and on the intensity of the beta effect has been revealed. Numerical estimates are presented which confirm the possibility of generating unsteady vortex chains and the related anomalous transport of the passive admixture.