Publication 19-CNA-018
Anomalous Dissipation in Passive Scalar Transport
Theodore D. Drivas
Department of Mathematics
Princeton University
tdrivas@math.princeton.edu
Tarek M. Elgindi
Department of Mathematics
UC San Diego
telgindi@ucsd.edu
Gautam Iyer
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
gautam@math.cmu.edu
In-Jee Jeong
School of Mathematics
Korea Institute for Advanced Study
ijeong@kias.re.kr
Abstract: We study anomalous dissipation in hydrodynamic turbulence in the context of passive scalars. Our main result produces an incompressible $C^\infty([0,T)\times \mathbb{T}^d)\cap L^1([0,T];
C^{1-}(\mathbb{T}^d))$ velocity field which explicitly exhibits anomalous dissipation. As a consequence, this example also shows non-uniqueness of solutions to the transport equation with an incompressible $L^1([0,T]; C^{1-}(\mathbb{T}^d))$ drift, which is smooth
except at one point in time. We also provide three sufficient conditions for anomalous dissipation provided solutions to the inviscid equation become singular in a controlled way. Finally, we discuss connections to the Obukhov-Corrsin monofractal theory of scalar turbulence along with other potential applications.
Get the paper in its entirety as 19-CNA-018.pdf
« Back to CNA Publications
