Transition from dissipative to conservative dynamics in equations of hydrodynamics
Abstract
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 →∞ [U. Frisch et al., Phys. Rev. Lett. 101, 144501 (2008), 10.1103/PhysRevLett.101.144501], is now shown to be true for any large, but finite, value of α greater than a crossover value α_{crossover}. We thus provide a selfconsistent picture of how dissipative systems, under certain conditions, start behaving like conservative systems and hence elucidate the subtle connection between equilibrium statistical mechanics and outofequilibrium turbulent flows.
 Publication:

Physical Review E
 Pub Date:
 October 2014
 DOI:
 10.1103/PhysRevE.90.041001
 arXiv:
 arXiv:1403.6599
 Bibcode:
 2014PhRvE..90d1001B
 Keywords:

 47.27.Gs;
 05.20.y;
 47.10.ad;
 Isotropic turbulence;
 homogeneous turbulence;
 Classical statistical mechanics;
 NavierStokes equations;
 Nonlinear Sciences  Chaotic Dynamics;
 Physics  Fluid Dynamics
 EPrint:
 12 pages, 4 figures