For the "Twilight of the Gods" Demo I had to make an animated Water Texture as well. It was hard work. First a little app created a serie of sin/cos-distorted versions of a simple water texture. I had then to retouche the seams manually, for 14 animation-frames.
The texture was then mixed with a copy of it self that was rotated 90 degrees. Additionally in the game the animated texture is moved in the way you mentioned.
The texture was then mixed with a copy of it self that was rotated 90 degrees. Additionally in the game the animated texture is moved in the way you mentioned.