196 research outputs found
The Strange Eigenmode in Lagrangian Coordinates
For a distribution advected by a simple chaotic map with diffusion, the
"strange eigenmode" is investigated from the Lagrangian (material) viewpoint
and compared to its Eulerian (spatial) counterpart. The eigenmode embodies the
balance between diffusion and exponential stretching by a chaotic flow. It is
not strictly an eigenmode in Lagrangian coordinates, because its spectrum is
rescaled exponentially rapidly.Comment: 15 pages, 6 figures. RevTeX4 format with psfra
Stirring by swimming bodies
We consider the stirring of an inviscid fluid caused by the locomotion of
bodies through it. The swimmers are approximated by non-interacting cylinders
or spheres moving steadily along straight lines. We find the displacement of
fluid particles caused by the nearby passage of a swimmer as a function of an
impact parameter. We use this to compute the effective diffusion coefficient
from the random walk of a fluid particle under the influence of a distribution
of swimming bodies. We compare with the results of simulations. For typical
sizes, densities and swimming velocities of schools of krill, the effective
diffusivity in this model is five times the thermal diffusivity. However, we
estimate that viscosity increases this value by two orders of magnitude.Comment: 5 pages, 5 figures. PDFLaTeX with RevTeX 4 macros. Final versio
Energy-Conserving Truncations for Convection with Shear Flow
A method is presented for making finite Fourier mode truncations of the
Rayleigh--Benard convection system that preserve invariants of the full partial
differential equations in the dissipationless limit. These truncations are
shown to have no unbounded solutions and provide a description of the thermal
flux that has the correct limiting behavior in a steady-state. A particular
low-order truncation (containing 7 modes) is selected and compared with the 6
mode truncation of Howard and Krishnamurti (1986), which does not conserve the
total energy in the dissipationless limit. A numerical example is presented to
compare the two truncations and study the effect of shear flow on thermal
transport.Comment: 18 pages, 5 Postscript figures, uses RevTeX and epsf. Accepted for
publication in Physics of Fluid
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
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