Dynamical Model for the Anomalous Transport of a Passive Scalar in a Reverse Barotropic Jet Flow

The anomalous transport of a passive scalar at the excitation of immovable chains of wave structures with closed streamlines in a barotropic reverse jet flow is studied. The analysis is performed for a plane-parallel flow in a channel between rigid walls in the presence of the beta effect and external friction. Periodic boundary conditions are set along the channel, while nonpercolation and sticking conditions are adopted on the channel walls. The equations of a barotropic (quasi-two-dimensional) flow are solved numerically using a pseudospectral method. A reverse jet with a “two-hump” asymmetric velocity profile facilitating the faster transition to the complex dynamics of the Eulerian flow fields is considered. Unlike the most developed kinematic models of anomalous transport, the basic chain of structures becomes unsteady due to the birth of supplementary perturbations at saturation of barotropic instability. A regular (multiharmonic) regime of wave generation is shown to appear due to the excitation of a new flow mode. Immovable structure chains giving rise to anomalous transport are obtained in the multiharmonic and chaotic regimes. The velocity of the chains of structures was determined by watching movies made according to the computations of the streamlines. It is revealed that the onset of anomalous transport in a regular regime is possible at essentially lower supercriticality compared to the chaotic regime. Trajectories of the tracer particles containing alternations of long flights and oscillations are drawn in the chaotic regime. The time dependences of the averaged (over ensemble) displacement of the tracer particles and its variance are obtained for two basic regimes of generation with immovable chains of structures, and the corresponding exponents of the power laws are determined. Normal advection is revealed in the regular regime, while anomalous diffusion arises in both regimes and may be classified as a “superdiffusion”.