16 research outputs found
Turbulence has its limits : a priori estimates of transport properties in turbulent fluid flows
EThOS - Electronic Theses Online ServiceGBUnited Kingdo
Optimizing the Source Distribution in Fluid Mixing
A passive scalar is advected by a velocity field, with a nonuniform spatial
source that maintains concentration inhomogeneities. For example, the scalar
could be temperature with a source consisting of hot and cold spots, such that
the mean temperature is constant. Which source distributions are best mixed by
this velocity field? This question has a straightforward yet rich answer that
is relevant to real mixing problems. We use a multiscale measure of
steady-state enhancement to mixing and optimize it by a variational approach.
We then solve the resulting Euler--Lagrange equation for a perturbed uniform
flow and for simple cellular flows. The optimal source distributions have many
broad features that are as expected: they avoid stagnation points, favor
regions of fast flow, and their contours are aligned such that the flow blows
hot spots onto cold and vice versa. However, the detailed structure varies
widely with diffusivity and other problem parameters. Though these are model
problems, the optimization procedure is simple enough to be adapted to more
complex situations.Comment: 19 pages, 23 figures. RevTeX4 with psfrag macro
Stirring up trouble: Multi-scale mixing measures for steady scalar sources
The mixing efficiency of a flow advecting a passive scalar sustained by
steady sources and sinks is naturally defined in terms of the suppression of
bulk scalar variance in the presence of stirring, relative to the variance in
the absence of stirring. These variances can be weighted at various spatial
scales, leading to a family of multi-scale mixing measures and efficiencies. We
derive a priori estimates on these efficiencies from the advection--diffusion
partial differential equation, focusing on a broad class of statistically
homogeneous and isotropic incompressible flows. The analysis produces bounds on
the mixing efficiencies in terms of the Peclet number, a measure the strength
of the stirring relative to molecular diffusion. We show by example that the
estimates are sharp for particular source, sink and flow combinations. In
general the high-Peclet number behavior of the bounds (scaling exponents as
well as prefactors) depends on the structure and smoothness properties of, and
length scales in, the scalar source and sink distribution. The fundamental
model of the stirring of a monochromatic source/sink combination by the random
sine flow is investigated in detail via direct numerical simulation and
analysis. The large-scale mixing efficiency follows the upper bound scaling
(within a logarithm) at high Peclet number but the intermediate and small-scale
efficiencies are qualitatively less than optimal. The Peclet number scaling
exponents of the efficiencies observed in the simulations are deduced
theoretically from the asymptotic solution of an internal layer problem arising
in a quasi-static model.Comment: 37 pages, 7 figures. Latex with RevTeX4. Corrigendum to published
version added as appendix
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
Large scale dynamics in turbulent Rayleigh-Benard convection
The progress in our understanding of several aspects of turbulent
Rayleigh-Benard convection is reviewed. The focus is on the question of how the
Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the
Prandtl number Pr, and on how the thicknesses of the thermal and the kinetic
boundary layers scale with Ra and Pr. Non-Oberbeck-Boussinesq effects and the
dynamics of the large-scale convection-roll are addressed as well. The review
ends with a list of challenges for future research on the turbulent
Rayleigh-Benard system.Comment: Review article, 34 pages, 13 figures, Rev. Mod. Phys. 81, in press
(2009