Stationary, isotropic and homogeneous two-dimensional turbulence: a first non-perturbative renormalization group approach

We study the statistical properties of stationary, isotropic and homogeneous turbulence in
two-dimensional (2D) flows, focusing on the direct cascade, that is on large wave-numbers compared
to the integral scale, where both energy and enstrophy are provided to the fluid. Our starting point
is the 2D Navier–Stokes equation in the presence of a stochastic forcing, or more precisely the
associated field theory. We unveil two extended symmetries of the Navier–Stokes action which were
not yet identified, one related to time-dependent (or time-gauged) shifts of the response fields and
existing in both 2D and 3D, and the other to time-gauged rotations and specific to 2D flows. We
derive the corresponding Ward identities, and exploit them within the non-perturbative
renormalization group formalism, and the large wave-number expansion scheme developed in Tarpin et
al (2018 Phys. Fluids 30 055102). We consider the flow equation for a generalized n -point

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