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In this paper, we study the desingularization of steady lake model ofperturbation type with general nonlinearity f. Using the modified vorticitymethod, we construct a family of steady solutions with vanishing circulation,which constitute a desingularization of a singular vortex. The localization ofthe singular vortex is determined only by the vanishing rate of thecirculation. Some qualitative and asymptotic properties are also established.

Desingularization of steady vortex of perturbation type in the lake equations