On Kelvin-Stuart vortices in a viscous fluid

Reference:

Fraenkel, L. E., 2008. On Kelvin-Stuart vortices in a viscous fluid. Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences, 366 (1876), pp. 2717-2728.

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Abstract

When one contemplates the one-parameter family of steady inviscid shear flows discovered by J. T. Stuart in 1967, an obvious thought is that these flows resemble a row of vortices diffusing in a viscous fluid, with the parameter playing the role of a reversed time. In this paper, we ask how close this resemblance is. Accordingly, the paper begins to explore Navier-Stokes solutions having as initial condition the classical, irrotational flow due to a row of point vortices. However, since we seek explicit answers, such exploration seems possible only in two relatively easy cases: that of small time and arbitrary Reynolds number and that of small Reynolds number and arbitrary time.

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