The influence of turbulence on a columnar vortex

Abstract

The interaction between a columnar vortex and external turbulence is investigated numerically. A Lamb–Oseen vortex is immersed in an initially isotropic homogeneous turbulence field, which itself is produced numerically by a direct numerical simulation of decaying turbulence. The formation of inhomogeneous fine turbulent eddies around the columnar vortex and the vortex-core deformations are studied in detail by visualizing the flow field. The initially random turbulent eddies (worms) are wrapped around the columnar vortex and become spirals. Statistical quantities, such as two-point-energy spectra and two-point-enstrophy spectra, are evaluated and compared with the theoretical predictions from rapid distortion theory. The axial velocity correlation dominates near the vortex surface, whereas the radial velocity correlation becomes larger where the worms are wrapped. Where the columnar vortex is strong compared with the external turbulence, external velocity disturbances are blocked by the vortex and they cannot penetrate into the vortex core directly, whereas various types of vortex waves (Kelvin waves) are excited.

Stochastic forcing of the Lamb–Oseen vortex

“…This scenario gives a theoretical counterpart to the observation of the recurrent development of vortex rings at the periphery of vortices when submerged in an ambient turbulence (Melander & Hussain 1993;Risso et al 1997;Takahashi et al 2005).…”

“…, saturation). In the case of a transient forcing induced by an initially homogeneous isotropic turbulence, Takahashi et al (2005) performed such analysis. The departure from the linear regime happens when the bending wave growing in the core reaches a finite amplitude.…”

“…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.…”

Horizontal Vortex Tubes near a Simulated Tornado: Three-Dimensional Structure and Kinematics

“…In their study, the interaction of the sustained vortex and the worms is shown to induce disturbances in the larger vortex core flow that can affect its dynamics. Given the vorticity arrangement shown in Figure 5, it seems plausible to hypothesize that vortex-vortex interactions analogous to those shown by Takahashi et al [49] may occur between tornadoes and surrounding HVs.…”

“…In both observed and simulated tornadoes, the HVs revolve counter-clockwise in the tornadic outer wind field and tend to align azimuthally around (but outside) the tornado core, thus, forming ring-like structures encircling the tornado. Although in a different context, this behavior bears remarkable resemblance to the process by which elongated vortices in isotropic homogeneous turbulence, the so-called "worms" (e.g., [48]), interact with a large, sustained columnar vortex in the DVRs of Takahashi et al [49]. In their study, the interaction of the sustained vortex and the worms is shown to induce disturbances in the larger vortex core flow that can affect its dynamics.…”