标题： 地转-重力波在地理漩涡中 显示英文标题

标题： Inertia-gravity waves in geophysical vortices

摘要： 类似煎饼的涡旋通常由地理流中的湍流产生。 在这里，我们研究了由于旋转和重力共同作用而存在于这种地理涡旋中的惯性重力振荡。 我们考虑一种被三轴椭球体包围的流体，该流体在密度上是分层的，具有恒定的布伦特-瓦伊萨尔频率（使用 Boussinesq 近似），并且相对于重力沿一个（可能倾斜的）轴均匀旋转。 然后，波问题由速度的混合双曲-椭圆方程控制。 如同 Vantieghem（2014，Proc. R. Soc. A, 470, 20140093, doi:10.1098/rspa.2014.0093）考虑的旋转非分层情况一样，我们发现椭球体内的谱是纯点谱（即仅由特征值组成），并且具有平滑的多项式特征向量。 然后，我们通过数值计算（使用定制的伽辽金方法获得）和渐近谱理论来表征谱。 最后，根据自然应用（例如，地中海涡旋或木星的涡旋）讨论了这些结果。 显示英文摘要

摘要： 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-V\"ais\"al\"a 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 smooth polynomial eigenvectors. Then, we characterise 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).