论文标题
球体中的陀螺多项式基础
A gyroscopic polynomial basis in the sphere
论文作者
论文摘要
全球动力学的标准光谱代码利用了球形谐波和适合核心基础的组合来表示流体变量。这些基础函数具有不存在的旋转不变性。陀螺比对 - 沿旋转轴的动力学对齐 - 是快速旋转状态中地球物理流体的Ahallmark。泰勒苏格拉德人定理从科里奥利力和压力梯度力的主要平衡中产生的，沿着轴向方向产生几乎不变的流动。在本文中，我们将坐标系统定制到旋转球体中的圆柱体结构。垂直方向，在整个球中常规。我们使用此基础扩展流体变量，并利用稀疏的jacobi多项式代数来实现球形环境中偏微分方程的所有操作员。我们在三个特征值问题中证明了基础的表示能力。
Standard spectral codes for full sphere dynamics utilize a combination of spherical harmonics and a suitableradial basis to represent fluid variables. These basis functions have a rotational invariance not present ingeophysical flows. Gyroscopic alignment - alignment of dynamics along the axis of rotation - is ahallmark of geophysical fluids in the rapidly rotating regime. The Taylor-Proudman theorem, resultingfrom a dominant balance of the Coriolis force and the pressure gradient force, yields nearly invariant flows along this axial direction.In this paper we tailor a coordinate system to the cylindrical structures found in rotating spherical flows.This "spherindrical" coordinate system yields a natural hierarchy of basis functions, composed of Jacobi polynomialsin the radial and vertical direction, regular throughout the ball.We expand fluid variables using this basis and utilize sparse Jacobi polynomial algebra to implement all operatorsrelevant for partial differential equations in the spherical setting. We demonstrate the representation power ofthe basis in three eigenvalue problems for rotating fluids.
