Linear and nonlinear interactions between a columnar vortex and external turbulence

被引:31
|
作者
Miyazaki, T [1 ]
Hunt, JCR [1 ]
机构
[1] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 9EW, England
关键词
D O I
10.1017/S0022112099006990
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
The structure of initially isotropic homogeneous turbulence interacting with a columnar vortex (with circulation Gamma and radius sigma), 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 u(0) is small compared with Gamma/sigma. The turbulent eddies with scale L are distorted by the mean velocity gradient and also, over a distance L 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 (Gamma t/2 pi r(2))(2)(L-x/r)u(0)(2), when (r - sigma) > L-x, but on the surface of the vortices ((r - sigma) < L-x) where (u(r)(2)) is reduced, (u(z)(2)) 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 u(0)t Gamma/sigma(2) parallel to the vortex. Even when the circulation (gamma) of the turbulent vortices is a small fraction of Gamma, they can excite self-destructive displacements through resonance on a time scale sigma/u(0).
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页码:349 / 378
页数:30
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