Abstract

In the great tradition linking turbulence and statistical physics, we discuss new connections that hold great promise for important progress, mainly for high Reynolds number turbulence but also for transitional turbulence and bridging the wide range of intermediate Reynolds numbers. First we discuss recent work showing that thermal noise become significant already at the Kolmogorov scale, making it clear that deterministic Navier-Stokes equation is inadequate to describe the turbulent dissipation range in molecular fluids. Second, we discuss how indeterminacy from molecular noise propagates to any length scale in the turbulent flow within one eddy turnover time at that scale, and relations with “spontaneous stochasticity” of Lagrangian particle trajectories and the Nash non-rigidity phenomenon discovered in the convex integration constructions of weak Euler solutions.  Finally, in wall-bounded flows we discuss a classical Josephson-Anderson relation, analogous to those in superfluids and superconductors, which explains drag by the flux of spanwise vorticity away from the wall and across the streamlines of the background potential Euler flow. This relation makes important connections with the Onsager theory for wall-bounded turbulence, the D’Alembert paradox, and large-eddy simulation modelling of turbulence in the presence of solid boundaries.