Anomalous transport of a passive scalar at the transition to dynamical chaos in a barotropic shear layer

Abstract

Abstract In this paper we are concerned with the problem of anomalous transport in a quasi-two-dimensional (barotropic) shear layer localized in the horizontal channel with rigid walls and subjected to the beta-effect. The flow may be regarded as a model of a zonal shear layer in the Earth’s atmosphere and ocean as well as in laboratory experiments. External (bottom) friction is taken into account by adding Rayleigh damping to two-dimensional equations. The attention is focused on a new mechanism of anomalous wave transport, when the disturbances producing stochastic layers in the vicinity of a vortex chain are caused by the transition to dynamical chaos. The problem is solved numerically using a pseudospectral method. The supercriticality is defined as the ratio of the characteristic flow velocity to the critical one. The critical wavenumber of the linear eigenvalue problem is such that 7 vortices are excited on a flow period, while the transition to chaos begins when 5 vortices are excited. The anomalous transport is examined at the first stage of the chaos onset, when the frequency spectra of spatial harmonics are quite narrow, thereby the trajectories of tracer particles are formed like in the kinematic model. The self-similarity property of variance in the ensemble of tracers is confirmed and the exponents of time power law are obtained. The Poincare map is drawn and the average displacements of the tracers are computed.