Unsteady chains of wave structures and anomalous transport of а passive scalar in a barotropic jet flow

Abstract

The onset of anomalous transport of a passive scalar at the excitation of unsteady chains of wave structures with closed streamlines in a barotropic jet flow modeling zonal flows in the Earths atmosphere and ocean and in laboratory experiments is investigated. The analysis is performed within a dynamical model describing saturation of the barotropic instability in a plane-parallel channel flow with allowance for the beta-effect and external friction. The equations of a quasi-two-dimensional flow are solved numerically with the aid of a pseudospectral method. It is found that the generation of high modes in a jet with a two-hump velocity profile leads to accelerated transition to the complex dynamics, at which an increase in supercriticality first gives rise to а multiharmonic regime with a discrete spectrum. The exponents of the power dependence on the time of the averaged (over the ensemble) tracer particle displacement and its variance are computed for the basic generation regimes, which confirms the occurrence of anomalous diffusion of the scalar. A self-similar probability density function of tracer displacements is obtained and the dependence of the transition to complex dynamics on the number of vortices in the chain and on the strength of the beta-effect is elucidated. Numerical estimates are presented, which confirm the possibility of generation of unsteady vortex chains and the related anomalous transport of the scalar.barotropic flow; chains of wave structures; dynamical chaos; anomalous advection and diffusion