Dynamics of Parcels of Fluids when psi = sin(2 x) sin(2 y)
This animation is the result of solving the dynamical system one obtains from the stream function psi = sin 2 x sin 2 y. There are nine equilibrium (stagnation) points present in this flow located at (0,0), (pi/2, 0), (pi, 0), (0, pi/2), (pi/2, pi/2), (pi, pi/2), (0, pi), (pi/2, pi) and (pi, pi). The effect of the circulation near these points is felt by the five parcels of fluid, whose centers have the same horizontal components at time zero but experience vastly different deformations as time evolves. The evolution of the parcels is superimposed on the contours of the stream function. The Mathematica program that produced the gif files is written in a rather generic form to allow for use with other stream functions with minimal changes in syntax.