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.
|Number of pages||12|
|Journal||Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences|
|Publication status||Published - 2008|
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), 2717-2728. https://doi.org/10.1098/rsta.2008.0064