An example of anomalous dissipation for passive scalars

We study anomalous dissipation in hydrodynamic turbulence in the context of passive scalars. We give an example of a rough divergence-free velocity field that explicitly exhibits anomalous dissipation for passive scalars. The mechanism for scalar dissipation is a built-in direct energy cascade in the synthetic velocity field. Connections to the Obukhov–Corrsin monofractal theory of scalar turbulence will be discussed.