Gregory L. Eyink

Singular or weak solutions of the incompressible Euler equations have been hypothesized to acccount for anomalous dissipation at very high Reynolds numbers and, in particular, to explain the d'Alembert paradox of nonvanishing drag. A possible objection to this explanation is the mathematical property called “weak-strong uniqueness,” which requires that any admissable weak solution of the Euler equations must coincide with the smooth Euler solution for the same initial data.

How predictable are turbulent flows? Here, we use theoretical estimates and shell model simulations to argue that Eulerian spontaneous stochasticity, a manifestation of the nonuniqueness of the solutions to the Euler equation that is conjectured to occur in Navier-Stokes turbulence at high Reynolds numbers, leads to universal statistics at finite times, not just at infinite time as for standard chaos. These universal statistics are predictable, even though individual flow realizations are not.