A Barotropic Model of the Angular Momentum–Conserving Potential Vorticity Staircase in Spherical Geometry
A Barotropic Model of the Angular Momentum–Conserving Potential Vorticity Staircase in Spherical Geometry
复制标题
球几何中角动量守恒势涡阶梯的正压模型
DOI：
10.1175/2007jas2223.1
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发表时间：
2008
影响因子：
3.1
通讯作者：
R. K. Scott
中科院分区：
文献类型：
--
作者：
T. Dunkerton;R. K. Scott
在满足绝对角动量守恒、西风急流混合区位涡均匀化和正压稳定性要求的条件下，建立了一个正压位涡阶梯的理想解析模式。强加的函数关系也假设喷气速度和纬度分离使用多个“动态Rossby波”莱茵河尺度推断西风急流的强度。正压系统的相对简单性提供了绝对角动量和PV（或绝对涡度）之间的简单关系。一个家庭的解决方案，包括一个任意数量的射流构造和用于说明的限制射流的间距和强度所施加的全球角动量守恒和正压稳定性的约束。理论解的渐近分析表明，射流间距的动态莱茵尺度等于6的平方根的限制比，这意味着西风射流的间隔比预测的动态莱茵尺度。据推断，另一种“几何”莱茵尺度射流间距可以从绝对角动量守恒的球体上，如果纬向射流的强度是已知的从其他方面考虑。完整的（非轴对称）方程的数值模拟揭示了一种模式的纬向喷流的演变，这是符合我们的建设理想的PV楼梯在球形几何形状（可以被认为是限制的情况下），以及与几何莱茵尺度的渐近分析。因此，从正压模型中的能量的高档级联起源的PV阶梯的演变被认为取决于能量守恒（射流的强度）和绝对角动量守恒（射流的间距和数量）。对数值结果的进一步分析证实了涡动位涡通量与平均流加速度之间的泰勒恒等式。涡动通量是负责偶尔之间的模式数的转换，以及为维持尖锐的西风急流对小尺度耗散。建议扩展的理论模型PV楼梯是不对称的半球之间或与纬度变化的幅度，模拟浅水系统。
An idealized analytical model of the barotropic potential vorticity (PV) staircase is constructed, constrained by global conservation of absolute angular momentum, perfect homogenization of PV in mixing zones between (prograde) westerly jets, and the requirement of barotropic stability. An imposed functional relationship is also assumed between jet speed and latitudinal separation using a multiple of the “dynamical Rossby wave” Rhines scale inferred from the strength of westerly jets. The relative simplicity of the barotropic system provides a simple relation between absolute angular momentum and PV (or absolute vorticity). A family of solutions comprising an arbitrary number of jets is constructed and is used to illustrate the restriction of jet spacing and strength imposed by the constraints of global conservation of angular momentum and barotropic stability. Asymptotic analysis of the theoretical solution indicates a limiting ratio of jet spacing to the dynamical Rhines scale equal to the square root of 6, meaning that westerly jets are spaced farther apart than predicted by the dynamical Rhines scale. It is inferred that an alternative “geometrical” Rhines scale for jet spacing can be obtained from conservation of absolute angular momentum on the sphere if the strength of zonal jets is known from other considerations. Numerical simulations of the full (nonaxisymmetric) equations reveal a pattern of zonal jet evolution that is consistent with our construction of ideal PV staircases in spherical geometry (which can be considered as limiting cases), as well as with the asymptotic analysis of a geometrical Rhines scale. The evolution of the PV staircase originating from an upscale cascade of energy in the barotropic model is therefore seen to depend on conservation of energy (for the strength of jets) and conservation of absolute angular momentum (for the spacing and number of jets). Further analysis of the numerical results confirms a “Taylor identity” relating the flux of eddy potential vorticity to mean-flow acceleration. Eddy fluxes are responsible for the occasional transitions between mode number as well as for maintaining the sharp westerly jets against small-scale dissipation. Suggestions are made for extending the theoretical model to PV staircases that are asymmetric between hemispheres or with latitudinal variation of amplitude, as modeled in the shallow-water system.