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In this work we address the open problem of high Reynolds number limit inhydrodynamic turbulence, which we modify by considering a vanishing random(instead of deterministic) viscosity. In this formulation, a small-scale noisepropagates to large scales in an inverse cascade, which can be described usingqualitative arguments of the Kolmogorov-Obukhov theory. We conjecture that thelimit of the resulting probability distribution exists as $\mathrm{Re} \to\infty$, and the limiting flow at finite time remains stochastic even ifforcing, initial and boundary conditions are deterministic. This conjecture isconfirmed numerically for the Sabra model of turbulence, where the solution isdeterministic before and random immediately after a blowup. Then, we derive apurely inviscid problem formulation with a stochastic boundary conditionimposed in the inertial interval.

Stochastic anomaly and large Reynolds number limit in hydrodynamic turbulence models