3 research outputs found
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
Tailored mixing inside a translating droplet
Tailored mixing inside individual droplets could be useful to ensure that
reactions within microscopic discrete fluid volumes, which are used as
microreactors in ``digital microfluidic'' applications, take place in a
controlled fashion. In this article we consider a translating spherical liquid
drop to which we impose a time periodic rigid-body rotation. Such a rotation
not only induces mixing via chaotic advection, which operates through the
stretching and folding of material lines, but also offers the possibility of
tuning the mixing by controlling the location and size of the mixing region.
Tuned mixing is achieved by judiciously adjusting the amplitude and frequency
of the rotation, which are determined by using a resonance condition and
following the evolution of adiabatic invariants. As the size of the mixing
region is increased, complete mixing within the drop is obtained
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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