Desingularization of steady vortex of perturbation type in the lake equations

TL;DR

This paper develops a method to smooth out singular vortices in steady lake equations with general nonlinearities, constructing solutions that approximate singular vortices by controlling circulation decay.

Contribution

It introduces a novel desingularization approach for steady vortex solutions in lake equations using the modified vorticity method with general nonlinearities.

Findings

Constructed steady solutions with vanishing circulation

Established localization based on circulation decay rate

Analyzed qualitative and asymptotic properties

Abstract

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