An explicit incompressible flow on the 2-torus is constructed that simultaneously causes anomalous dissipation, Richardson dispersion, anomalous regularization, and spatial intermittency for every Hölder exponent below 1.
Anomalous Regularization in Kraichnan's Passive Scalar Model
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abstract
We consider the advection of a passive scalar by a divergence free random Gaussian field, white in time and H\"older regular in space (rough Kraichnan's model), a well established synthetic model of passive scalar turbulence. By studying the evolution of negative Sobolev norms, we show an anomalous regularization effect induced by the dynamics: distributional initial conditions immediately become functions of positive Sobolev regularity.
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Turbulent and intermittent phenomena in a universal total anomalous dissipator
An explicit incompressible flow on the 2-torus is constructed that simultaneously causes anomalous dissipation, Richardson dispersion, anomalous regularization, and spatial intermittency for every Hölder exponent below 1.