Transition from dissipative to conservative dynamics in equations of hydrodynamics

We show, by using direct numerical simulations and theory, how, by increasing the order of dissipativity ($α$) in equations of hydrodynamics, there is a transition from a dissipative to a conservative system. This remarkable result, already conjectured for the asymptotic case $α\to \infty$ [U. Frisch et al., Phys. Rev. Lett. {\bf 101}, 144501 (2008)], is now shown to be true for any large, but finite, value of $α$ greater than a crossover value $α_{\rm crossover}$. We thus provide a self-consistent picture of how dissipative systems, under certain conditions, start behaving like conservative systems and hence elucidate the subtle connection between equilibrium statistical mechanics and out-of-equilibrium turbulent flows.

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