Functional Renormalization for Elastic Burgulence

Abstract

We formulate elastic and elasto-inertial turbulence in the Martin-Siggia-Rose path-integral formalism and develop a systematic source-extended symmetry algorithm to derive Ward identities directly from the Euler-Lagrange equations. These identities provide nonperturbative constraints and a principled foundation for constructing closure schemes. As a dimensionally reduced model for elastic turbulence, we propose an extended Burgers equation that preserves the characteristic coupling between the extra stress and velocity gradient, while remaining simple enough for first controlled calculations. In particular, we obtain an extended set of Ward identities that strongly constrains admissible closures and provides insight into the scaling behaviour near the fixed point.