Distortion and evolution of a localized vortex in an irrotational flow

Abstract

This paper examines the interaction of an axisymmetric vortex monopole, such as a Lamb vortex, with a background irrotational liow. At leading order, the monopole is advected with the background flow velocity at the center of vorticity. However, inhomogeneities of the llow will cause the monopole to distort. It is shown that a shear-diffusion mechanism, familiar from the study of mixing of passive scalars, plays an important role in the evolution of the vorticity distribution. Through this mechanism, nonaxisymmetric vorticity perturbations which do not shift the center of vorticity are homogenized along streamlines on a Ren3 time scale, much faster than the Re decay time scale of an axisymmetric monopole. This separation of time scales leads to the quasisteady evolution of a monopole in a slowly varying flow. The asymptotic theory is verified by numerically computing the linear response of a Lamb monopole to a time-periodic straining flow and it is shown that a large amplitude, @(Ren3), distortion results when the monopole is forced at its resonant frequency. 6

Accelerated diffusion in the centre of a vortex

“…The case n = 2 represents the leading vorticity fluctuations generated by straining a coherent vortex, for example in two-dimensional turbulence. The case n = 1 corresponds to the homogenization of a uniform vorticity gradient, a Poiseuille flow, by the vortex, but also includes the steady solutions corresponding to infinitesimal translations of the vortex, which do not undergo spiral wind-up (see Lingevitch & Bernoff 1995;Llewellyn Smith 1995). We assume that spiral wind-up of vorticity occurs (see for example the 'mixing hypothesis' of Bernoff & Lingevitch 1994), and seek an exact solution to the equation (5.2) that describes this process.…”

“…These processes are important in the behaviour of coherent vortices evolving freely in two-dimensional turbulence; in this case the leading effect on the internal dynamics of a coherent vortex is a time-dependent strain from other vortices (see Lingevitch & Bernoff 1995). This can generate spiral arms of vorticity with azimuthal wavenumber n = 2 which are subject to accelerated diffusion as the vortex regains axisymmetry through spiral wind-up (e.g.…”

Vortex motion in a weak background shear flow

“…This can be considered as a coupling to a mode with angular wavenumber n = 1, and this mode includes infinitesimal translations of the vortex (Smith & Rosenbluth 1990;Ting & Klein 1991;Lingevitch & Bernoff 1995;Llewellyn Smith 1995). In this paper we consider flows confined to the plane, and the case where the coherent vortex is immersed in a weak background gradient of vorticity; an example is that of a point vortex introduced at the midline of a weak plane Poiseuille shear flow.…”

The spiral wind-up and dissipation of vorticity and a passive scalar in a strained planar vortex

“…These vortices have a high Reynolds number Re and tend to be isolated, there being a disparity between the length scale l of a typical vortex and that of the separation L between vortices. On the large scale L the vortices move under their mutual interactions, and at leading order are governed by the dynamics of a number of point vortices (excepting collisions) (Ting & Klein 1991;Lingevitch & Bernoff 1995). On the moderate scale l, an individual vortex can be considered an approximately axisymmetric distribution of vorticity immersed in the time-dependent irrotational flow generated by the remaining vortices (cf.…”