Vladimir Reutov

The transition to dynamical chaos and the related lateral (cross-flow) transport of a passive scalar in the reverse annular jet flow generating two chains of wave-vortex structures are studied. The quasi-geostrophic equations for the barotropic (quasi-two-dimensional) flow written in polar coordinates with allowance for the beta-effect and external friction are solved numerically using a pseudospectral method. The critical parameters of the equilibrium flow with a complex “two-hump” azimuth velocity profile facilitating a faster transition to the complex dynamics are determined. Two regular multiharmonic regimes of wave generation are revealed with increasing flow supercriticality before the onset of Eulerian chaos. The occurrence of the complex flow dynamics is confirmed by a direct calculation of the largest Lyapunov exponent. The evolution of streamline images is analyzed by making video, thereby chains with single and composite structures are distinguished. The wavenumber-frequency spectra confirming the possibility of chaotic transport of the passive scalar are drawn for the basic regimes of wave generation. The power law exponents for the azimuth particle displacement and their variance, which proved the occurrence of the anomalous azimuth transport of the passive scalar, are determined. Lagrangian chaos is studied by computing the finite-time Lyapunov exponent and its distribution function. The internal chain (with respect to the annulus center) is found to be totally subject to Lagrangian chaos, while only the external chain boundary is chaotic. It is revealed that the cross-flow transport occurs only in the regime of Eulerian dynamical chaos, since there exists a barrier to it in the multiharmonic regimes. The images of fluid particles confirming the presence of lateral transport are obtained and their quantitative characteristics are determined.

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”.