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Selective withdrawal of a two-layer fluid is considered. The fluid layers are weakly compressible, miscible and viscous and therefore flow rotationally. The lower, denser fluid flows with constant velocity out through one or more drain holes in the bottom of a rectangular tank. The drain is opened impulsively and the subsequent draw-down produces waves in the interface which travel outward to the edges of the tank and are reflected back with a 180 • change of phase. The points on the interface that have the highest absolute gradient form regions of high vorticity in the tank, enabling mixing of the fluids. An inviscid linearized interface is computed and compared to contour plots of density for the viscous solution. The two agree closely at early times in the withdrawal process, but as time increases, nonlinear and viscous effects take over. The time at which the lighter fluid starts to flow out of the tank is dependent on the number of drains, their width, and the fluid flow rate and density, and is investigated here.

Saturn's North Polar Hexagon was discovered by Godfrey who pieced together map projections of images captured by the Voyager mission to unveil a hexagonal structure over the north pole of Saturn. This article attempts to answer whether or not a hexagonal structure can be formed through anticyclones impinging on the dominant eastward circumpolar flow and is in part based upon the proposed theory by Allison et al. that the Hexagon may be the result of at least one impinging anticyclone perturbing a circumpolar jet centrally located around the 76 • N latitude. A high-latitude δ-plane approximation is used to simulate the interaction between an initially circular circumpolar jet and at least one perturbing anticyclone. Our simulations with one perturbing anticyclone failed to form a hexagonal structure; yet by including an additional anticyclone it was found that depending on the strength, location and radius of the perturbing anticyclones a hexagonal feature could develop. However, the longevity and drift rate of the actual Hexagon must be attributed to other factors not considered in this paper.