Publications [#361920] of Tarek M Elgindi

Papers Published

1. Drivas, TD; Elgindi, TM; Iyer, G; Jeong, IJ, Anomalous Dissipation in Passive Scalar Transport, Archive for Rational Mechanics and Analysis, vol. 243 no. 3 (March, 2022), pp. 1151-1180 [doi]
   (last updated on 2024/04/23)

   Abstract:
   We study anomalous dissipation in hydrodynamic turbulence in the context of passive scalars. Our main result produces an incompressible C∞([0 , T) × Td) ∩ L1([0 , T] ; C1 -(Td)) velocity field which explicitly exhibits anomalous dissipation. As a consequence, this example also shows the non-uniqueness of solutions to the transport equation with an incompressible L1([0 , T] ; C1 -(Td)) drift, which is smooth except at one point in time. We also give a sufficient condition for anomalous dissipation based on solutions to the inviscid equation becoming singular in a controlled way. Finally, we discuss connections to the Obukhov-Corrsin monofractal theory of scalar turbulence along with other potential applications.