7,793 research outputs found
Vortex motion around a circular cylinder above a plane
The study of vortex flows around solid obstacles is of considerable interest
from both a theoretical and practical perspective. One geometry that has
attracted renewed attention recently is that of vortex flows past a circular
cylinder placed above a plane wall, where a stationary recirculating eddy can
form in front of the cylinder, in contradistinction to the usual case (without
the plane boundary) for which a vortex pair appears behind the cylinder. Here
we analyze the problem of vortex flows past a cylinder near a wall through the
lenses of the point-vortex model. By conformally mapping the fluid domain onto
an annular region in an auxiliary complex plane, we compute the vortex
Hamiltonian analytically in terms of certain special functions related to
elliptic theta functions. A detailed analysis of the equilibria of the model is
then presented. The location of the equilibrium in front of the cylinder is
shown to be in qualitative agreement with the experimental findings. We also
show that a topological transition occurs in phase space as the parameters of
the systems are variedComment: 17 pages, 8 figure
Velocity selection (without surface tension) in multi-connected Laplacian growth
We predict a novel selection phenomenon in nonlinear interface dynamics out
of equilibrium. Using a recently developed formalism based on the
Schottky-Klein prime functions, we extended the existing integrable theory from
a single interface to multiple moving interfaces. After applying this extended
theory to the two-dimensional Laplacian growth, we derive a new rich class of
exact (non-singular) solutions for the unsteady dynamics of an arbitrary
assembly of air bubbles within a layer of a viscous fluid in a Hele-Shaw cell.
These solutions demonstrate that all bubbles reach an asymptotic velocity, ,
which is {\it precisely twice} greater than the velocity, , of the uniform
background flow, i.e., . The result does not depend on the number of
bubbles. It is worth to mention that contrary to common belief, the predicted
velocity selection does not require surface tension.Comment: 5 pages, 1 figure. Updated versio
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