External turbulence interaction with a columnar vortex

Abstract

A study was performed using direct numerical simulation to examine the interaction of external turbulence with a nominally columnar, large-scale vortex at a vortex Reynolds number $\hbox{\it Re}_V \,{\equiv}\, \Gamma / \nu \,{=}\, 3000$. A multi-step procedure is used to generate initial conditions in which the external turbulence has the wrapped, nearly azimuthal form characteristic of turbulence around a large-scale vortex structure. The proper-orthogonal decomposition method is used to extract specific modes of the vortex turbulence that dominate the kinetic energy and enstrophy fields. The effect of turbulence initial intensity and length scale on the turbulence structure and its influence on the large-scale vortex are examined. It is observed that the external turbulence wraps around the large-scale vortex and advects radially inward toward the vortex core. The dominant axial length scale of the external turbulence appears to scale with the vortex core diameter, with the mode with the largest enstrophy having a wavelength of about twice the core diameter. The turbulence induces a bending wave on the vortex core with axial wavelength approximately equal to the dominant wavelength of the external turbulence. The turbulent enstrophy decays according to a power-law expression for cases with moderate initial turbulence intensity. For sufficiently strong initial turbulence intensity, the turbulence breaks up the large-scale vortex core, creating strong turbulence within the vortex core.

Evolution of isolated turbulent trailing vortices

“…Many of the existing computational works (for instance, [10,14]) on trailing vortices assume periodicity in the cross-stream directions. This means that the tangential velocity (and hence, the circulation) has to vanish at the boundaries, thus making the vortex unstable according to…”

An experimental investigation of wing-tip vortex decay in turbulence

“…It has been suggested that a vortex under conditions of moderate turbulence intensity will produce secondary vortical structures, i.e., in turbulence with kinetic energy sufficiently high to influence the vortex, yet insufficient to destroy the vortex through excessive deformation, coherent structures form through an interaction between the vortex and external turbulence. The secondary structures form azimuthally around the primary vortex and have been observed in both experiments 5,6 and simulation, 17,22,23,27,32 and it has been hypothesized that they form via stretching of azimuthally aligned vorticity around the primary vortex. The secondary vortices tend to become axisymmetric within two or three revolutions of the primary vortex, 24 form at a radial position twice the radius of the primary vortex, and have a longitudinal scale in the same order as the core radius.…”

Stochastic forcing of the Lamb–Oseen vortex

“…The studies of perturbed vortices generally focus on the former point, the evolution of initial conditions, such as temporal modal stability analyses (see Fabre et al (2006) for the Lamb-Oseen vortex), optimal perturbation analyses (Antkowiak & Brancher 2004, 2007Pradeep & Hussain 2006) or theoretical and numerical investigations of the response of vortices to initially injected turbulence (Melander & Hussain 1993;Risso et al 1997;Miyazaki & Hunt 2000;Takahashi et al 2005;Marshall & Beninati 2005). More particularly in the latter case, the objective is to understand how the vortex immersed in an initial turbulent field responds to this perturbation and how in return the initial turbulence is affected by the presence of the vortex and the associated shear and rotation which are known to drastically alter the statistics of turbulence on a short time scale.…”