In a variety of circumstances, it is common to find fluid motions that have a cellular character;…

In a variety of circumstances, it is common to find fluid motions that have a cellular character; i.e. the fluid streamlines form closed loops in the form of a cell. An example of a two-dimensional cellular flow (sketched below) is u = (ux(x, y), uy(x, y), 0) = (sin px cos py, – cos px sin py, 0) . (75) (a) Verify that the flow is solenoidal, i.e. ? · u = 0.