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 and to inviscid mixing will be discussed. This is joint work with T. Elgindi, G. Iyer and I-J Jeong.
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