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The evolution of piecewise constant distributions of a conserved quantityrelated to the frozen-in canonical vorticity in effectively two-dimensionalincompressible ideal EMHD flows is analytically investigated by the Hamiltonianmethod. The study includes the case of axisymmetric flows with zero azimuthalvelocity component and also the case of flows with the helical symmetry ofvortex lines. For sufficiently large size of such a patch of the conservedquantity, a local approximation in the dynamics of the patch boundary issuggested, based on the possibility to represent the total energy as the sum ofarea and boundary terms. Only the boundary energy produces deformation of theshape with time. Stationary moving configurations are described.

Local Approximation for Contour Dynamics in Effectively Two-Dimensional Ideal Electron-Magnetohydrodynamic Flows