Abstract-
We consider a model of incompressible trailing vortices consisting of an array
of counter-rotating structures in a doubly periodic domain, infinite in the
vertical direction. The two-dimensional vortex array of Mallier and Maslowe is
combined with an axial velocity profile chosen proportional to the initial
axial vorticity to provide an initial condition for the vortex wake. This base
flow is a weak solution of the 2D-3C steady Euler equations thus allowing its
linear stability properties to be investigated. These are used to interpret
several stages in the development of vortex structure observed in 3D-3C DNS at
Reynolds numbers of O(1000). For sufficiently high axial velocity, its effect
can be seen, in that each vortex in the linear array first develops helical
structures before undergoing a period of relaminarization. At later times the
more slowly growing co-operative elliptical instabilities become apparent;
however, the helical structure persists and the observed vortical structures
remain coherent for longer periods than in the absence of axial velocity.
Using the stretched vortex subgrid model, large-eddy simulation runs are
performed at higher Reynolds numbers and a mixing transition identified at
about Re =1-2 x 10^4. Similar phenomena are observed in these simulations as
are seen in the DNS. Finally, a model for the average axial pressure gradient
present in the true spatially evolving wake, but
absent in the numerical simulations is formulated and its affect investigated.
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