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 ($\alpha$) in equations of hydrodynamics, there is a transition from a dissipative to a conservative system. This remarkable result, already conjectured for the asymptotic case $\alpha \to \infty$ [U. Frisch et al., Phys. Rev. Lett. {\bf 101}, 144501 (2008)], is now shown to be true for any large, but finite, value of $\alpha$ greater than a crossover value $\alpha_{\rm crossover}$. 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.Comment: 12 pages, 4 figure

Droplets in isotropic turbulence: deformation and breakup statistics

The statistics of the deformation and breakup of neutrally buoyant sub-Kolmogorov ellipsoidal drops is investigated via Lagrangian simulations of homogeneous isotropic turbulence. The mean lifetime of a drop is also studied as a function of the initial drop size and the capillary number. A vector model of drop previously introduced by Olbricht, Rallison and Leal [J. Non-Newtonian Fluid Mech. $\mathbf{10}$, 291 (1982)] is used to predict the behaviour of the above quantities analytically.Comment: 16 pages, 16 figure

Elastic turbulence in a shell model of polymer solution

We show that, at low inertia and large elasticity, shell models of viscoelastic fluids develop a chaotic behaviour with properties similar to those of elastic turbulence. The low dimensionality of shell models allows us to explore a wide range both in polymer concentration and in Weissenberg number. Our results demonstrate that the physical mechanisms at the origin of elastic turbulence do not rely on the boundary conditions or on the geometry of the mean flow.Comment: 6 pages; 8 figure

Bending dynamics of semi-flexible macromolecules in isotropic turbulence

We study the Lagrangian dynamics of semi-flexible macromolecules in laminar as well as in homogeneous and isotropic turbulent flows by means of analytically solvable stochastic models and direct numerical simulations. The statistics of the bending angle is qualitatively different in laminar and turbulent flows and exhibits a strong dependence on the topology of the velocity field. In particular, in two-dimensional turbulence, particles are either found in a fully extended or in a fully folded configuration; in three dimensions, the predominant configuration is the fully extended one.Comment: 5 pages, 4 figure

Revisiting the SABRA Model: Statics and Dynamics

We revisit the two-dimensional SABRA model, in the light of recent results of Frisch {\it et al.} [Phys. Rev. Lett. {\bf 108}, 074501 (2012)] and examine, systematically, the interplay between equilibrium states and cascade (turbulent) solutions, characterised by a single parameter $b$, via equal-time and time-dependent structure functions. We calculate the static and dynamic exponents across the equipartition as well as turbulent regimes which are consistent with earlier studies. Our results indicate the absence of a sharp transition from equipartition to turbulent states. Indeed, we find that the SABRA model mimics true two-dimensional turbulence only asymptotically as $b\to-2$.Comment: 6 pages; 5 figure