Fluid of density ½1 occupies the region z > 0 and overlies another fluid of density ½2 (with ½2 > ½1), which occupies the region z < 0. Show that the frequencies of small amplitude oscillations of the interface between the regions are given by !2 = gk µ½2 – ½1 ½2 + ½1¶ . [Hint: You will need different potentials Á1 and Á2 for the two regions, and you should apply the kinematic boundary condition to the flow in each region.]


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