52 research outputs found
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 () in equations of hydrodynamics, there is a
transition from a dissipative to a conservative system. This remarkable result,
already conjectured for the asymptotic case [U. Frisch et
al., Phys. Rev. Lett. {\bf 101}, 144501 (2008)], is now shown to be true for
any large, but finite, value of greater than a crossover value
. 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. , 291 (1982)] is used to predict the behaviour of the
above quantities analytically.Comment: 16 pages, 16 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 , 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
.Comment: 6 pages; 5 figure
Persistence Problem in Two-Dimensional Fluid Turbulence
We present a natural framework for studying the persistence problem in
two-dimensional fluid turbulence by using the Okubo-Weiss parameter
to distinguish between vortical and extensional regions. We then use a direct
numerical simulation (DNS) of the two-dimensional, incompressible
Navier--Stokes equation with Ekman friction to study probability distribution
functions (PDFs) of the persistence times of vortical and extensional regions
by employing both Eulerian and Lagrangian measurements. We find that, in the
Eulerian case, the persistence-time PDFs have exponential tails; by contrast,
this PDF for Lagrangian particles, in vortical regions, has a power-law tail
with an exponent .Comment: consistent with the published versio
Nelkin scaling for the Burgers equation and the role of high-precision calculations
Nelkin scaling, the scaling of moments of velocity gradients in terms of the
Reynolds number, is an alternative way of obtaining inertial-range information.
It is shown numerically and theoretically for the Burgers equation that this
procedure works already for Reynolds numbers of the order of 100 (or even lower
when combined with a suitable extended self-similarity technique). At moderate
Reynolds numbers, for the accurate determination of scaling exponents, it is
crucial to use higher than double precision. Similar issues are likely to arise
for three-dimensional Navier--Stokes simulations.Comment: 5 pages, 2 figures, Published in Phys. Rev E (Rapid Communications
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