The reason for this is the difference in the refractive index between cold and hot water. Mixing cold and hot water cause wavy appearance because there is motion of cold and hot wateruntil equilibrium is achieved. The light is then scattered non-uniformly by the hot and cold domains.

Water at different temperatures has different densities, in much the same way that air has a different density from water (although the difference within water is much less). Light passing through a density gradient is refracted. The "waves" that you see are the turbulent, convective motion of the water. They're currents, not waves.

Water's density is strongly effected by its temperature. Water density increases until about 34 F (1.5C) when it begins to decrease until it freezes (big decrease in density). Water's refractive index (there lative speed of light in water relative to space) is proportional to its density. So the diffraction patterns happen for the same reason that hot water rises in cold water.

If you mix hot and cold water, you see a complex diffraction which depends on the type of mixing flow-- however, these variations are not 'waves' in the normal sense. On the other hand, since the hot water tries to rise and the cold water tries to fall, in a special container, it is possible to set up convection waves and other interesting phenomena.