On Galerkin Approximations of the Surface Active Quasigeostrophic Equations
On Galerkin Approximations of the Surface Active Quasigeostrophic Equations
复制标题
表面活性准地转方程的伽辽金近似
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
I. Grooms
中科院分区：
文献类型：
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作者：
C. Rocha;W. Young;I. Grooms
摘要本文研究了三维准地转（QG）方程解的表示，采用Galerkin级数和标准垂直模态，特别注意将主动表面浮力动力学。本研究扩展了现有的两种Galerkin方法（A和B），并发展了一种新的Galerkin近似（C）。近似A，由于Flierl，表示流函数作为截断Galerkin级数和定义的位涡（PV），满足反演问题。近似B，由于Tulloch和Smith，代表PV作为截断Galerkin级数和计算流函数，满足反演问题。近似C是QG方程的真正Galerkin近似，它将流函数和PV都表示为截断的Galerkin级数，但并不完全满足反演方程。除非边界是等密度曲面，否则这三种近似是根本不同的。作者们...
AbstractThis study investigates the representation of solutions of the three-dimensional quasigeostrophic (QG) equations using Galerkin series with standard vertical modes, with particular attention to the incorporation of active surface buoyancy dynamics. This study extends two existing Galerkin approaches (A and B) and develops a new Galerkin approximation (C). Approximation A, due to Flierl, represents the streamfunction as a truncated Galerkin series and defines the potential vorticity (PV) that satisfies the inversion problem exactly. Approximation B, due to Tulloch and Smith, represents the PV as a truncated Galerkin series and calculates the streamfunction that satisfies the inversion problem exactly. Approximation C, the true Galerkin approximation for the QG equations, represents both streamfunction and PV as truncated Galerkin series but does not satisfy the inversion equation exactly. The three approximations are fundamentally different unless the boundaries are isopycnal surfaces. The authors ...