Past exam of the mathematics course of the University of Cambridge / 2007 / ib / Paper 1 / 5D / iv / Solution

If $\alpha =\beta$, $\psi =-\alpha (x-y{)}^2/2$. Its contours are the parallel lines $x-y=d$. On each such line,For $d\ne 0$ this is an unbounded straight streamline. Every point on $x=y$ has zero velocity, so that diagonal is a line of equilibria, rather than one moving streamline.