Lucas oil makes a great power steering fluid. This stuff works wonders.
Has worked on all of my whining pumps.
You can pick it up at any auto parts store. It's much thinker than the normal fluid.
First try and get as much of the fluid as you can from the top of the pump. A turkey baster works good. (don't use your mom's or wifes she will be mad)
You dont need to get it all out, just the more you get the more of the lucas will fit.
Once you get all you think you can fill back up with the lucas to the proper level.
Start car, Give a few minutes to work threw the system, you could even turn the wheels from right to left full travel to help it out.
If this does not get rid of the whine it will make it quiet enough to were you won't notice it.