Dynamical Model for the Anomalous Transport of a Passive Scalar in a Reverse Barotropic Jet Flow
Received 22 July 2019; accepted 08 August 2019
2019, Vol. 15, no. 3, pp. 251-260
Author(s): Reutov V. P., Rybushkina G. V.
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”.
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