We construct a family of steady solutions of the lake model perturbed by some small Coriolis force, that converge to a singular vortex pair. The desingularized solutions are obtained by maximization of the kinetic energy over a class of rearrangements of sign changing functions. The precise localization of the asymptotic singular vortex pair is proved to depend on the depth function and the Coriolis parameter, and it is independent on the geometry of the lake domain. We apply our result to construct a singular rotating vortex pair in a rotation invariant lake.

中文翻译：

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Lake方程中涡旋对的反奇异化

我们构造了一个湖模型的稳定解决方案族，该解决方案受到一些小科里奥利力的干扰，收敛到一个奇异的涡流对。通过在符号改变函数的一类重排上最大化动能来获得去奇异解。渐近奇异涡对的精确定位被证明取决于深度函数和科里奥利参数，并且与湖域的几何形状无关。我们将我们的结果应用于在旋转不变湖中构造奇异的旋转涡对。