The Clebsch form of the Euler equations provides an intuitive picture as to how the circulation constraints direct the spatial organization of vorticity and favor the formation of vortex sheets. Porous media convection models the basic mechanism and is also the simplest generalization of the inviscid Burgers equation that allows for an incompressible velocity field. The finite time singularities of the model are studied numerically. A related convection analog to the axisymmetric Euler equations is discussed for comparison.
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Pumir et al. (1992) studied this question.