#
65th Annual Meeting of the APS Division of Fluid Dynamics

## Volume 57, Number 17

##
Sunday–Tuesday, November 18–20, 2012;
San Diego, California

### Session M12: Vortex VII

8:00 AM–9:57 AM,
Tuesday, November 20, 2012

Room: 26B

Chair: Dustin Kleckner, University of Chicago

Abstract ID: BAPS.2012.DFD.M12.3

### Abstract: M12.00003 : Regenerative centrifugal instability on a vortex column

8:26 AM–8:39 AM

Preview Abstract
Abstract

####
Authors:

Eric Stout

(University of Houston)

Fazle Hussain

(University of Houston)

The limitation and renewal of centrifugal instability of a vortex column
(due to a sheath of negative axial vorticity, -\textit{$\Omega $}$_{z}$, surrounding the
+\textit{$\Omega $} core, i.e. a circulation overshoot) is studied via the transport dynamics
of perturbations to the initially unstable vortex using DNS of the
incompressible Navier-Stokes equations for a range of vortex Reynolds
numbers (Re=circulation/viscosity). Any radial perturbation vorticity,
\textit{$\omega $'}$_{r}$, is tilted by the column's mean shear to form filaments with
azimuthal vorticity, \textit{$\omega $'}$_{\theta }$, generating positive Reynolds stress,
+$u'v'$ ($u'$,$ v'$ are the radial and azimuthal perturbation velocities), required for
energy growth. This \textit{$\omega $'}$_{\theta }$ in turn tilts -\textit{$\Omega $}$_{z}$ to amplify \textit{$\omega $'}$_{r}$
(and consequently \textit{$\omega $'}$_{\theta })$ -- thus causing instability. Limitation of
\textit{$\omega $'}$_{r}$ growth, thus also energy production, occurs as the perturbation
transports angular momentum (\textit{rV}) radially outward from the overshoot, moving
the overshoot outward, hence lessening and shifting -\textit{$\Omega $}$_{z}$, while also
transporting core +\textit{$\Omega $}$_{z}$, around the location of the filament. After the
overshoot shifts, tilting of -\textit{$\Omega $}$_{z}$ reverses \textit{$\omega $'}$_{r}$ (hence reducing
\textit{$\omega $'}$_{\theta })$, causing the filament to generate --$u'v'$, i.e. energy decay, and
hence self-limitation of growth. Associated with $--u'v'$ is the filament's radially
inward transport of \textit{rV}, which can produce a new circulation overshoot and
renewed instability. New overshoot formation and renewed generation of
$+u'v'$ is examined using a helical ($m=1)$ mode -- a promising scenario for
regenerative transient growth and possible turbulence generation on a vortex
column.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2012.DFD.M12.3