Author:
MIYAZAKI TAKESHI,HUNT JULIAN C. R.
Abstract
The structure of initially isotropic homogeneous turbulence interacting with a columnar
vortex (with circulation Γ and radius σ), idealized both as a solid cylinder
and a hollow core model is analysed using the inhomogeneous form of linear rapid distortion
theory (RDT), for flows where the r.m.s. turbulence velocity u0 is small
compared with Γ/σ. The turbulent eddies with scale Γ
are distorted by the mean velocity gradient and also, over a distance Γ
from the surface of the vortex, by their direct impingement onto it, whether it is solid or
hollow. The distortion of the azimuthal component of turbulent vorticity by the differential
rotation in the mean flow around the columnar vortex causes the mean-square radial velocity
away from the cylinder to increase as
(Γt/2πr2)2
(Γx/r)u20, when
(r − σ) > Γx, but on the surface of
the vortices ((r − σ) < Γx) where
〈u2r〉 is reduced,
〈u2z〉 increases to the same order, while the
other components do not grow. Statistically, while the vorticity field remains asymmetric,
the velocity field of small-scale eddies near the vortex core rapidly becomes
axisymmetric, within a period of two or three revolutions of the columnar vortex.
Calculation of the distortion of small-scale initially random velocity fields shows
how the turbulent eddies, as they are wrapped around the columnar vortex, become
like vortex rings, with similar properties to those computed by Melander & Hussain
(1993) using a fully nonlinear direct numerical simulation. A mechanism is proposed
for how interactions between the external turbulence and the columnar vortex can
lead to non-axisymmetric vortex waves being excited on the vortex and damped
fluctuations in its interior. If the columnar vortex is not significantly distorted by
these linear effects, estimates are made of how nonlinear effects lead to the formation
of axisymmetric turbulent vortices which move as result of their image vorticity (in
addition to the self-induction velocity) at a velocity of order
u0tΓ/σ2 parallel to the vortex. Even
when the circulation (γ) of the turbulent vortices is a small fraction of
Γ, they can excite self-destructive displacements through resonance on a time
scale σ/u0.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
30 articles.
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