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Topology and stability of a water-soybean-oil swirling flow

Abstract:

This paper reveals and explains the flow topology and instability hidden in an experimental study by Tsai et al. [Tsai, Phys. Rev. E 92, 031002(R) (2015)]10.1103/PhysRevE.92.031002. Water and soybean oil fill a sealed vertical cylindrical container. The rotating top disk induces the meridional circulation and swirl of both fluids. The experiment shows a flattop interface shape and vortex breakdown in the oil flow developing as the rotation strength Reo increases. Our numerical study shows that vortex breakdown occurs in the water flow at Reo=300 and in the oil flow at Reo=941. As Reo increases, the vortex breakdown cell occupies most of the water domain and approaches the interface at Reo around 600. The rest of the (countercirculating) water separates from the axis as the vortex breakdown cells in the oil and water meet at the interface-axis intersection. This topological transformation of water flow significantly contributes to the development of the flattop shape. It is also shown that the steady axisymmetric flow suffers from shear-layer instability, which emerges in the water domain at Reo=810.