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