You have probably seen the “Add a Vector Field” option under the Graph menu in CalcPlot3D which allows you to create some nifty three-dimensional vector fields like the one below.
But did you know that you can add a parameter (t) to the vector field to create and animate time dependent vector fields by controlling the slide bar for t in the Animate Parameters pop-up window? Bonus: Click on the 2D graph and view the flow lines!
Below is a screenshot. Go to the CalcPlot3D applet and try for yourself!