F Ur Mathematik in Den Naturwissenschaften Leipzig Phase Transition in the Passive Scalar Advection Phase Transition in the Passive Scalar Advection
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چکیده
The paper studies the behavior of the trajectories of uid particles in a compress-ible generalization of the Kraichnan ensemble of turbulent velocities. We show that, depending on the degree of compressibility, the trajectories either explosively separate or implosively collapse. The two behaviors are shown to result in drastically diierent statistical properties of scalar quantities passively advected by the ow. At weak compressibility, the explosive separation of trajectories induces a familiar direct cascade of the energy of a scalar tracer with a short-distance intermittency and dissipative anomaly. At strong compressibility, the implosive collapse of trajectories leads to an inverse cascade of the tracer energy with suppressed intermittency and with the energy evacuated by large scale friction. A scalar density whose advection preserves mass exhibits in the two regimes opposite cascades of the total mass squared. We expect that the explosive separation and collapse of Lagrangian trajectories occur also in more realistic high Reynolds number velocity ensembles and that the two phenomena play a crucial role in fully developed turbulence.
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تاریخ انتشار 1998