地球物理旋涡中的惯性重力波

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-03-13 DOI:10.1098/rspa.2023.0789
Jérémie Vidal, Yves Colin de Verdière
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引用次数: 0

摘要

地球物理流中的湍流经常会产生盘状漩涡。在此,我们将研究在旋转和重力的共同作用下,此类地球物理漩涡中可能存在的惯性-重力振荡。我们考虑了封闭在三轴椭球体中的流体,该椭球体以恒定的布伦特-韦赛莱频率(使用布西内斯克近似)进行密度分层,并沿着(可能)相对于重力的倾斜轴均匀旋转。然后,波问题由速度的双曲-椭圆混合方程控制。正如 Vantieghem(2014,Proc.R.Soc.A,470,20140093。(doi:10.1098/rspa.2014.0093))一样,我们发现频谱是椭圆体中的纯点(即只由特征值组成),具有多项式特征向量。然后,我们利用数值计算(通过定制的 Galerkin 方法获得)和渐近光谱理论描述了频谱的特征。最后,我们结合自然应用(如地中海漩涡或木星旋涡)对结果进行了讨论。
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Inertia-gravity waves in geophysical vortices

Pancake-like vortices are often generated by turbulence in geophysical flows. Here, we study the inertia-gravity oscillations that can exist within such geophysical vortices, due to the combined action of rotation and gravity. We consider a fluid enclosed within a triaxial ellipsoid, which is stratified in density with a constant Brunt–Väisälä frequency (using the Boussinesq approximation) and uniformly rotating along a (possibly) tilted axis with respect to gravity. The wave problem is then governed by a mixed hyperbolic-elliptic equation for the velocity. As in the rotating non-stratified case considered by Vantieghem (2014, Proc. R. Soc. A, 470, 20140093. (doi:10.1098/rspa.2014.0093)), we find that the spectrum is pure point in ellipsoids (i.e. only consists of eigenvalues) with polynomial eigenvectors. Then, we characterize the spectrum using numerical computations (obtained with a bespoke Galerkin method) and asymptotic spectral theory. Finally, the results are discussed in light of natural applications (e.g. for Mediterranean eddies or Jupiter’s vortices).

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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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