You guys are totally overthinking the Zelda water. Those "spikes" are just two copies of an alpha mask, scrolling in opposite directions. The mask image is low frequency waves, with a few larger "spikes" in it. As the two scroll, the "spike" waves cross over, causing the bigger spikes. You can really see it if you pick a spot in the scroll and follow it with your eyes as it pans - it will reveal the two layers.
Keep in mind, the Gamecube used very limited pixel shaders. It wasn't very fast. Computing arc tangents per pixel would likely be prohibitively expensive on an actual Gamecube.
While that doesn't apply as much to today's graphics processors, it's a good idea to keep up the same mindset. The more reuse you can get out of your shaders, the better off you'll be. You don't want infinite different shaders for every new object or effect, for the sake of batching, resources, etc.
If you can accomplish something with a simpler shader, do it