175 research outputs found
Generalised Quasilinear Approximation of the Interaction of Convection and Mean Flows in a Thermal Annulus
In this paper, we examine the interaction of convection, rotation and mean flows in a thermal annulus. In this system, mean flows are driven by correlations induced by rotation leading to non-trivial Reynolds stresses. The mean flows act back on the convective turbulence acting as a barrier to transport. For this system, we demonstrate that the generalized quasilinear approximation (Marston et al. 2016 Phys. Rev. Lett.116, 214501. (doi:10.1103/PhysRevLett.116.214501)) may provide a much better approximation to the complicated full nonlinear dynamics than the widely used quasilinear approximation. This result will enable the construction of more accurate statistical theories for the description of geophysical and astrophysical flows
Conformal invariance in two-dimensional turbulence
Simplicity of fundamental physical laws manifests itself in fundamental
symmetries. While systems with an infinity of strongly interacting degrees of
freedom (in particle physics and critical phenomena) are hard to describe, they
often demonstrate symmetries, in particular scale invariance. In two dimensions
(2d) locality often promotes scale invariance to a wider class of conformal
transformations which allow for nonuniform re-scaling. Conformal invariance
allows a thorough classification of universality classes of critical phenomena
in 2d. Is there conformal invariance in 2d turbulence, a paradigmatic example
of strongly-interacting non-equilibrium system? Here, using numerical
experiment, we show that some features of 2d inverse turbulent cascade display
conformal invariance. We observe that the statistics of vorticity clusters is
remarkably close to that of critical percolation, one of the simplest
universality classes of critical phenomena. These results represent a new step
in the unification of 2d physics within the framework of conformal symmetry.Comment: 10 pages, 5 figures, 1 tabl
Efficient Mixing at low Reynolds numbers using polymer additives
Mixing in fluids is a rapidly developing field of fluid mechanics
\cite{Sreen,Shr,War}, being an important industrial and environmental problem.
The mixing of liquids at low Reynolds numbers is usually quite weak in simple
flows, and it requires special devices to be efficient. Recently, the problem
of mixing was solved analytically for a simple case of random flow, known as
the Batchelor regime \cite{Bat,Kraich,Fal,Sig,Fouxon}. Here we demonstrate
experimentally that very viscous liquids at low Reynolds number, . Here we
show that very viscous liquids containing a small amount of high molecular
weight polymers can be mixed quite efficiently at very low Reynolds numbers,
for a simple flow in a curved channel. A polymer concentration of only 0.001%
suffices. The presence of the polymers leads to an elastic instability
\cite{LMS} and to irregular flow \cite{Ours}, with velocity spectra
corresponding to the Batchelor regime \cite{Bat,Kraich,Fal,Sig,Fouxon}. Our
detailed observations of the mixing in this regime enable us to confirm sevearl
important theoretical predictions: the probability distributions of the
concentration exhibit exponential tails \cite{Fal,Fouxon}, moments of the
distribution decay exponentially along the flow \cite{Fouxon}, and the spatial
correlation function of concentration decays logarithmically.Comment: 11 pages, 5 figure
Kolmogorov scaling and intermittency in Rayleigh-Taylor turbulence
The Rayleigh--Taylor (RT) turbulence is investigated by means of high
resolution numerical simulations. The main question addressed here is on
whether RT phenomenology can be considered as a manifestation of universality
of Navier--Stokes equations with respect to forcing mechanisms. At a
theoretical level the situation is far from being firmly established and,
indeed, contrasting predictions have been formulated. Our first aim here is to
clarify the above controversy through a deep analysis of scaling behavior of
relevant statistical observables. The effects of intermittency on the mean
field scaling predictions is also discussed.Comment: 4 pages, 5 figure
Macroscopic effects of the spectral structure in turbulent flows
Two aspects of turbulent flows have been the subject of extensive, split
research efforts: macroscopic properties, such as the frictional drag
experienced by a flow past a wall, and the turbulent spectrum. The turbulent
spectrum may be said to represent the fabric of a turbulent state; in practice
it is a power law of exponent \alpha (the "spectral exponent") that gives the
revolving velocity of a turbulent fluctuation (or "eddy") of size s as a
function of s. The link, if any, between macroscopic properties and the
turbulent spectrum remains missing. Might it be found by contrasting the
frictional drag in flows with differing types of spectra? Here we perform
unprecedented measurements of the frictional drag in soap-film flows, where the
spectral exponent \alpha = 3 and compare the results with the frictional drag
in pipe flows, where the spectral exponent \alpha = 5/3. For moderate values of
the Reynolds number Re (a measure of the strength of the turbulence), we find
that in soap-film flows the frictional drag scales as Re^{-1/2}, whereas in
pipe flows the frictional drag scales as Re^{-1/4} . Each of these scalings may
be predicted from the attendant value of \alpha by using a new theory, in which
the frictional drag is explicitly linked to the turbulent spectrum. Our work
indicates that in turbulence, as in continuous phase transitions, macroscopic
properties are governed by the spectral structure of the fluctuations.Comment: 6 pages, 3 figure
Energy Transfer and Spectra in Simulations of Two-dimensional Compressible Turbulence
We present results of high-resolution numerical simulations of compressible
2D turbulence forced at intermediate spatial scales with a solenoidal
white-in-time external acceleration. A case with an isothermal equation of
state, low energy injection rate, and turbulent Mach number
without energy condensate is studied in detail. Analysis of energy spectra and
fluxes shows that the classical dual-cascade picture familiar from the
incompressible case is substantially modified by compressibility effects. While
the small-scale direct enstrophy cascade remains largely intact, a large-scale
energy flux loop forms with the direct acoustic energy cascade compensating for
the inverse transfer of solenoidal kinetic energy. At small scales, the direct
enstrophy and acoustic energy cascades are fully decoupled at small Mach
numbers and hence the corresponding spectral energy slopes comply with
theoretical predictions, as expected. At large scales, dispersion of acoustic
waves on vortices softens the dilatational velocity spectrum, while the
pseudo-sound component of the potential energy associated with coherent
vortices steepens the potential energy spectrum.Comment: 10 pages, 6 figures. To appear in: Turbulence in Complex Conditions,
Proc. Euromech/Ercoftac Colloquium 589, ed. M. Gorokhovski, Springer, 201
Vortices in (2+1)d Conformal Fluids
We study isolated, stationary, axially symmetric vortex solutions in
(2+1)-dimensional viscous conformal fluids. The equations describing them can
be brought to the form of three coupled first order ODEs for the radial and
rotational velocities and the temperature. They have a rich space of solutions
characterized by the radial energy and angular momentum fluxes. We do a
detailed study of the phases in the one-parameter family of solutions with no
energy flux. This parameter is the product of the asymptotic vorticity and
temperature. When it is large, the radial fluid velocity reaches the speed of
light at a finite inner radius. When it is below a critical value, the velocity
is everywhere bounded, but at the origin there is a discontinuity. We comment
on turbulence, potential gravity duals, non-viscous limits and non-relativistic
limits.Comment: 39 pages, 10 eps figures, v2: Minor changes, refs, preprint numbe
Towards DNS of the Ultimate Regime of Rayleigh--B\'enard Convection
In this contribution we have briefly introduced the problem of turbulent
thermal convection with a particular look at its transition to the ultimate
regime and the resolution requirements needed for the direct numerical
simulation of this flow.Comment: 10 pages, 6 figure
Wall roughness induces asymptotic ultimate turbulence
Turbulence is omnipresent in Nature and technology, governing the transport
of heat, mass, and momentum on multiple scales. For real-world applications of
wall-bounded turbulence, the underlying surfaces are virtually always rough;
yet characterizing and understanding the effects of wall roughness for
turbulence remains a challenge, especially for rotating and thermally driven
turbulence. By combining extensive experiments and numerical simulations, here,
taking as example the paradigmatic Taylor-Couette system (the closed flow
between two independently rotating coaxial cylinders), we show how wall
roughness greatly enhances the overall transport properties and the
corresponding scaling exponents. If only one of the walls is rough, we reveal
that the bulk velocity is slaved to the rough side, due to the much stronger
coupling to that wall by the detaching flow structures. If both walls are
rough, the viscosity dependence is thoroughly eliminated in the boundary layers
and we thus achieve asymptotic ultimate turbulence, i.e. the upper limit of
transport, whose existence had been predicted by Robert Kraichnan in 1962
(Phys. Fluids {\bf 5}, 1374 (1962)) and in which the scalings laws can be
extrapolated to arbitrarily large Reynolds numbers
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