The geomagnetic field presents several stationary features that are thought to be linked to inhomogeneities at the core–mantle boundary. Particularly important stationary structures of the geomagnetic field are the flux lobes, which appear in pairs in mid- to high mid- to high latitudes. A recently discovered stratified layer at the top of the Earth’s core poses important constraints on the dynamics at this layer and on the interaction of the core dynamics and the base of the mantle. In this article, we introduce the linear and nonlinear theories of magnetic Rossby waves in a thin shell at the top of the Earth’s core. We study the nonlinear interaction of these waves in the presence of prescribed forcings at the base of the mantle of both a thermal and a topographic nature. We show that the combined effects of forcing and nonlinear interaction can lead the wave phases to be locked around a particular geographical longitude, generating a quasi- stationary flow pattern with a significant meridional component. The solutions of the system are shown to be analogous to atmospheric blocking phenomena. Therefore, we argue that persistent and long-lived structures of the geomagnetic field, such as the geomagnetic lobes, might be associated with a blocking at the top of the Earth’s core due to nonlinear stationary waves.

中文翻译：

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非线性 MHD Rossby 波相互作用和持久地磁场结构

地磁场呈现出几个静止特征，被认为与地核-地幔边界的不均匀性有关。地磁场中特别重要的静止结构是磁通瓣，它们成对出现在中高纬度地区。最近在地核顶部发现的分层层对这一层的动力学以及地核动力学与地幔底部的相互作用构成了重要限制。在本文中，我们将介绍地核顶部薄壳中磁性罗斯贝波的线性和非线性理论。我们研究了在具有热性质和地形性质的地幔底部存在规定强迫的情况下这些波的非线性相互作用。我们表明，强迫和非线性相互作用的组合效应可以导致波相位被锁定在特定的地理经度附近，从而产生具有显着经向分量的准静止流型。该系统的解决方案类似于大气阻塞现象。因此，我们认为地磁场的持久和长寿命结构，例如地磁瓣，可能与由于非线性驻波而导致地核顶部的阻塞有关。