Elastic turbulence – a functional renormalization group approach

With its remarkable success in both statistical and quantum field theory—and more recently in Navier-Stokes turbulence—we apply the functional renormalization group to elastic turbulence.

While the vanishing-momentum sector in Navier-Stokes turbulence is fully determined by the Galilean-gauged Ward identity and related symmetries, this is not the case for elastic turbulence. In particular, for the extra-stress and response-stress sectors of the correlation functions, there are few, if any, Ward identities that can be exploited in closure schemes. To address this difficulty, we consider a generalized viscoelastic Burgers equation as a simplified model and perform a systematic symmetry and Ward identity classification of the governing action. In the purely elastic (Stokesian) regime, we derive a Ward identity that elucidates the coupling between the velocity and stress sectors, enabling a first-order closure of the former. Finally, a closure scheme in the spirit of the Blaizot Mendez Wschebor scheme, improved by the usage of Ward identities, is employed to obtain insights into the underlying fixed-point structure of elastic Burgers turbulence. JC is supported by the Graduate School CE at TU Darmstadt.