Some reversed and non-reversed flows of a second grade fluid (Q1209089)

We study steady plane incompressible second grade fluid flow by assuming that the stream function has the form \(\psi(x,y)=y+f(x)e^{ky}\), where \(k\) is a real constant and \(f(x)\) is a function to be determined. These flows are extensions of the planar generalized Beltrami flows. When the Weissenberg number is zero, some of the results of \textit{W. H. Hui} [Z. Angew. Math. Phys. 38, 689-702 (1987; Zbl 0629.76030)] and \textit{S. P. Lin} and \textit{M. Tobak} [AIAA J. 24, 334-335 (1986)] are realized. Reversed and non-reversed flows are obtained.