Accelerated diffusion in the centre of a vortex

Abstract

The spiral wind-up and diffusive decay of a passive scalar in circular streamlines is considered. An accelerated diffusion mechanism operates to destroy scalar fluctuations on a time scale of order P 1/3 times the turn-over time, where P is a Péclet number. The mechanism relies on differential rotation, that is, a non-zero gradient of angular velocity. However if the flow is smooth, the gradient of angular velocity necessarily vanishes at the centre of the streamlines, and the time scale becomes greater. The behaviour at the centre is analysed and it is found that scalar there is only destroyed on a time scale of order P 1/2 . Related results are obtained for magnetic field and for weak vorticity, a scalar coupled to the stream function of the flow. Some exact solutions are presented.

Dynamics of lean blowout of a swirl-stabilized flame in a gas turbine model combustor

“…The inner vortex core featuring solid-body rotation is surrounded by a zone where velocities decrease with distance from the center. The decrease of velocity implies high strain rates, leading to accelerated mixing [29,30] and thereby to a supply of heat and radicals to the unburned gas.…”

Vortex motion in a weak background shear flow

“…The flow field of the vortex wraps up the passive scalar to form a spiral structure, leading to the diffusive decay of scalar fluctuations in the vicinity of the vortex. Several time scales are involved: in particular there is an enhanced shear-diffusion time scale for the destruction of scalar fluctuations on given closed streamlines (Moffatt & Kamkar 1983;Rhines & Young 1983;Bajer, Bassom & Gilbert 2001). The spiral distribution of the passive scalar also has a fractal nature, with a non-trivial box-counting dimension which can determine spectral power laws and anomalous diffusion properties (for example , Gilbert 1988;Vassilicos 1995).…”

Intermittency of passive-scalar decay: Strange eigenmodes in random shear flows

“…The result is a decay rate proportional to κ 3/8 . In a natural way, this is larger than the O(κ 1/2 ) decay rate achieved for time-independent flows with extrema, but smaller than the O(κ 1/3 ) found for monotonic velocity profiles [23,24]. Of course, the latter cannot be continuous in periodic domains.…”

“…by a number of authors [23][24][25] who found that the concentration decreases to zero very rapidly outside narrow regions around the velocity extrema. The width of these regions then scales with the diffusivity κ like κ 1/4 , leading to a decay rate proportional to κ 1/2 .…”