Mechanism study of free-surface polygons formation in rotating fluids

In order to study the formation mechanism of the polygon phenomenon in rotating fluid, a test set-up of a rotating cylinder which can produce rotating fluid was designed. Experiments on rotating fluid for different rotational frequencies, liquid heights and radii of the cylinder were performed. Based on experimental results, a composite wave theoretical model of the intersection point between the free surface of the fluid and the bottom of the container was established according to the wave equation while ignoring the specific movement inside the fluid. On this basis, the theoretical model was verified by experiments, and the rotation state on the experimental phenomenon was further studied. Based on the experimental data and previous work, this paper made empirical formula fitting to the data, and found that the fitting effect of the blackbody radiation model is the best. The results can be further applied to theoretical research to determine the physical mechanism of the phenomenon.