Asymptotic structure of the stress field in flow past a cylinder at high Weissenberg number

We study the flow of an upper convected Maxwell fluid past a cylinder in th e limit of high Weissenberg number. We make the simplifying assumption that the velocity field is given and similar to the Newtonian case (as discusse d below, this assumption is likely to be wrong) and consider the integratio n of the stress equations. The asymptotic behavior at high Weissenberg numb er leads to boundary layers along the edge of the cylinder as well as stres s concentration in the wake. The stresses in the boundary layer are of orde r W while the width of the boundary layer is of order W-1. The stresses in the wake are of order W-3, and the width of the wake is of order W-2. Just outside the boundary layer near the cylinder and wake, there is a region wh ere the stresses are much larger (order W-3 near the cylinder and W-5 near the wake). The origin of these stresses is in the stretching flow near the upstream stagnation point. (C) 2000 Elsevier Science B.V. All rights reserv ed.