球壳中的孤立磁旋Rossby波
Solitary magnetostrophic Rossby waves in spherical shells
摘要：
本文研究了磁转区的磁流体Rossby波。我们考虑慢模式，它在相反的方向上的流体动力学或快速模式，在存在的环形磁场和纬向流的厚球壳的准地转模型。弱非线性，长波导出渐近使用约化摄动方法。在一阶的问题被发现服从二阶常微分方程，导致一个超几何方程的Malkus场和合流Heun方程的电线场，并且是非奇异的，当波的速度接近平均流。研究其中性、非奇异的本征解，发现其演化可用Korteweg-de Vries方程描述。这意味着非线性慢波形成孤子和孤波。它们可能以相干涡旋的形式出现，例如单个反气旋。我们推测反气旋的关系，在地球的流体核心，并在国家的最先进的发电机DNS的不对称的环流。
英文摘要：
Finite-amplitude hydromagnetic Rossby waves in the magnetostrophic regime are studied. We consider the slow mode, which travels in the opposite direction to the hydrodynamic or fast mode, in the presence of a toroidal magnetic field and zonal flow by means of quasi-geostrophic models for thick spherical shells. The weakly-nonlinear, long waves are derived asymptotically using a reductive perturbation method. The problem at the first order is found to obey a second-order ODE, leading to a hypergeometric equation for a Malkus field and a confluent Heun equation for an electrical-wire field, and is nonsingular when the wave speed approaches the mean flow. Investigating its neutral, nonsingular eigensolutions for different basic states, we find the evolution is described by the Korteweg-de Vries equation. This implies that the nonlinear slow wave forms solitons and solitary waves. These may take the form of a coherent eddy, such as a single anticyclone. We speculate on the relation of the anti-cyclone to the asymmetric gyre seen in Earth's fluid core, and in state-of-the-art dynamo DNS.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
