Texturing an animated fluid is a useful way to augment the visual complexity of pictures without increasing the simulation time. But texturing flowing fluids is a complex issue, as it creates conflicting requirements: we want to keep the texture properties (features, spectrum) while conforming to the underlying flow --- which distorts the attached texture. In this paper, we present a new method for texturing animated fluids. Our method ensures that the moving texture always follows the velocity field of the fluid, while maintaining key properties of the original texture. Our algorithm runs in real-time; our experiments show that it is well suited for a wide range of input texture, including, but not limited to, noise textures.