Author:
ZHANG CHIONG,SHEN LIAN,YUE DICK K. P.
Abstract
Vortex connections at the surface are fundamental and prominent
features in free-surface vortical flows. To understand the detailed mechanism of such connection,
we
consider, as a canonical problem, the laminar vortex connections at a free
surface when
an oblique vortex ring impinges upon that surface. We perform numerical
simulations
of the Navier–Stokes equations with viscous free-surface boundary
conditions. It is
found that the key to understanding the mechanism of vortex connection
at a free
surface is the surface layers: a viscous layer resulting from the dynamic
zero-stress
boundary conditions at the free surface, and a thicker blockage layer which
is due to
the kinematic boundary condition at the surface. In the blockage layer,
the vertical
vorticity component increases due to vortex stretching and vortex turning
(from the
transverse vorticity component). The vertical vorticity is then transported
to the free
surface through viscous diffusion and vortex stretching in the viscous
layer leading to
increased surface-normal vorticity. These mechanisms take place at the
aft-shoulder
regions of the vortex ring. Connection at the free surface is different
from that at a
free-slip wall owing to the generation of surface secondary vorticity.
We study the
components of this surface vorticity in detail and find that the presence
of a free
surface accelerates the connection process. We investigate the connection
time scale
and its dependence on initial incidence angle, Froude and Reynolds numbers.
It is
found that a criterion based on the streamline topology provides a precise
definition
for connection time, and may be preferred over existing definitions, e.g.
those based
on free-surface elevation or net circulation.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
28 articles.
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