The effect of viscosity on the rotating waves and polygonal patterns within a hollow vortex core

The question of how viscosity influences the development of instabilities within a rotating shallow layer of liquid, which gives rise to polygonal patterns, has been investigated experimentally. A phase diagram of the existence regions of these polygonal patterns is constructed in (Fr,Ta) plane, where Fr is the Froude number and Ta is the Taylor number. The results show that the effect of the viscosity on the domain of existence of the patterns depends on the initial fluid height above the rotating disc. The results also show that the variation of viscosity does not affect the locking ratio between the rotational frequencies of the pattern to the disc; the two frequencies remain locked at approximately 1/3.