248,677 research outputs found
Mixing of asymmetric logarithmic suspension flows over interval exchange transformations
We consider suspension flows built over interval exchange transformations
with the help of roof functions having an asymmetric logarithmic singularity.
We prove that such flows are strongly mixing for a full measure set of interval
exchange transformations
Computation of three-dimensional flow in turbofan mixers and comparison with experimental data
A three dimensional, viscous computer code was used to calculate the mixing downstream of a typical turbofan mixer geometry. Experimental data obtained using pressure and temperature rakes at the lobe and nozzle exit stations were used to validate the computer results. The relative importance of turbulence in the mixing phenomenon as compared with the streamwise vorticity set up by the secondary flows was determined. The observations suggest that the generation of streamwise vorticity plays a significant role in determining the temperature distribution at the nozzle exit plane
Short- and Long- Time Transport Structures in a Three Dimensional Time Dependent Flow
Lagrangian transport structures for three-dimensional and time-dependent
fluid flows are of great interest in numerous applications, particularly for
geophysical or oceanic flows. In such flows, chaotic transport and mixing can
play important environmental and ecological roles, for examples in pollution
spills or plankton migration. In such flows, where simulations or observations
are typically available only over a short time, understanding the difference
between short-time and long-time transport structures is critical. In this
paper, we use a set of classical (i.e. Poincar\'e section, Lyapunov exponent)
and alternative (i.e. finite time Lyapunov exponent, Lagrangian coherent
structures) tools from dynamical systems theory that analyze chaotic transport
both qualitatively and quantitatively. With this set of tools we are able to
reveal, identify and highlight differences between short- and long-time
transport structures inside a flow composed of a primary horizontal
contra-rotating vortex chain, small lateral oscillations and a weak Ekman
pumping. The difference is mainly the existence of regular or extremely slowly
developing chaotic regions that are only present at short time.Comment: 9 pages, 9 figure
From large deviations to semidistances of transport and mixing: coherence analysis for finite Lagrangian data
One way to analyze complicated non-autonomous flows is through trying to
understand their transport behavior. In a quantitative, set-oriented approach
to transport and mixing, finite time coherent sets play an important role.
These are time-parametrized families of sets with unlikely transport to and
from their surroundings under small or vanishing random perturbations of the
dynamics. Here we propose, as a measure of transport and mixing for purely
advective (i.e., deterministic) flows, (semi)distances that arise under
vanishing perturbations in the sense of large deviations. Analogously, for
given finite Lagrangian trajectory data we derive a discrete-time and space
semidistance that comes from the "best" approximation of the randomly perturbed
process conditioned on this limited information of the deterministic flow. It
can be computed as shortest path in a graph with time-dependent weights.
Furthermore, we argue that coherent sets are regions of maximal farness in
terms of transport and mixing, hence they occur as extremal regions on a
spanning structure of the state space under this semidistance---in fact, under
any distance measure arising from the physical notion of transport. Based on
this notion we develop a tool to analyze the state space (or the finite
trajectory data at hand) and identify coherent regions. We validate our
approach on idealized prototypical examples and well-studied standard cases.Comment: J Nonlinear Sci, 201
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