Had the cup been circular we would see vortex shaped upper surface deeper at the center than at edges with polar circular symmetry as there is no radial component. When boundary is a regular polygon of $n$ sides we can see _standing wave_ interference patterns caused by vibration frequency due to radial and circumferential component streamline flow interfering to form $n$ spiral arms.
An attempt at modeling should include the two interactions.
EDIT1:
If such a cup is placed and rotated sufficiently fast on a turntable I suspect it may give rise to some similar pattern, that is if viewing at all is possible.