824 research outputs found
Tauberian identities and the connection to Wile E. Coyote physics
The application of the motion of a vertically suspended mass-spring system
released under tension is studied focusing upon the delay timescale for the
bottom mass as a function of the spring constants and masses. This
``hang-time", reminiscent of the Coyote and Road Runner cartoons, is quantified
using the far-field asymptotic expansion of the bottom mass' Laplace transform.
These asymptotics are connected to the short time mass dynamics through
Tauberian identities and explicit residue calculations. It is shown, perhaps
paradoxically, that this delay timescale is maximized in the large mass limit
of the top ``boulder". Experiments are presented and compared with the
theoretical predictions. This system is an exciting example for the teaching of
mass-spring dynamics in classes on Ordinary Differential Equations, and does
not require any normal mode calculations for these predictions
Vortex Induced Oscillations of Cylinders
This article submitted to the APS-DFD 2008 conference, accompanies the fluid
dynamics video depicting the various orientational dynamics of a hinged
cylinder suspended in a flow tank. The different behaviors displayed by the
cylinder range from steady orientation to periodic oscillation and even
autorotation. We illustrate these features using a phase diagram which captures
the observed phenomena as a function of Reynolds number and reduced inertia. A
hydrogen bubble flow visualization technique is also used to show vortex
shedding structure in the cylinder's wake which results in these oscillations.Comment: 3 page
A Higher Public Purpose - The Constitutionality of Mississippi\u27s Public Trust Tidelands Legislation
Commentary on Professor Tarlock's Paper: The Influence of International Environmental Law on United States Pollution Control Law
Enhanced diffusivity and skewness of a diffusing tracer in the presence of an oscillating wall
We examine a passive scalar diffusing in time-varying flows which are induced
by a periodically oscillating wall in a Newtonian fluid between two infinite
parallel plates as well as in an infinitely long duct. These shear flows yield
the generalized Ferry waves which are exact solutions of the Navier-Stokes
equations. First, we calculate the second Aris moment for all time, and its
long time limiting effective diffusivity as a function of the geometrical
parameters, frequency, viscosity, and diffusivity. We show that the viscous
dominated limit results in a linear shear layer for which the effective
diffusivity is bounded with upper bound , where
is the tracer diffusivity, is the amplitude of oscillation, and is the
gap thickness. Alternatively, we show that for finite viscosities the enhanced
diffusion is unbounded, diverging in the high frequency limit. Physical
arguments are given to explain these striking differences. Asymptotics for the
high frequency behavior as well as the low viscosity limit are computed. Study
of the exact formula shows that a maximum exists as a function of the
viscosity, suggesting a possible optimal temperature for mixing in this
geometry. Physical experiments are performed in water using Particle Tracking
Velocimetry to quantitatively measure the fluid flow. Using fluorescein dye as
the passive tracer, we document that the theory is quantitatively accurate.
Further, we show that the scalar skewness is zero for linear shear at all
times, whereas for the nonlinear Ferry wave, using Monte-Carlo simulations, we
show the skewness sign (as well as front versus back loaded distributions) can
be controlled through the phase of the oscillating wall. Lastly, short time
skewness asymptotics are computed for the Ferry wave and compared to the
Monte-Carlo simulations
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