Abstract:The motion of a two-dimensional buoyant vortex patch, i.e. a vortex patch with a uniform density different from the uniform density of the surrounding fluid, is analysed in terms of evolution equations for the motion of its centroid, deformation of its boundary and the strength of a vortex sheet which is essential to enforce pressure continuity across the boundary. The equations for the centroid are derived by a linear momentum analysis and that for the sheet strength by applying Euler's equations on the bound… Show more
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