Mountain torque and angular momentum in barotropic planetary flows: equilibrium solutions

Mountain torque and angular momentum in barotropic planetary flows: equilibrium solutions
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正压行星流中的山扭矩和角动量：平衡解

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发表时间：
1983
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通讯作者：
J. Frederiksen
J. Frederiksen
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文献类型：
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作者：
B. Sawford;J. Frederiksen

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使用平衡统计力学的方法检查了球体上地形强制无粘正压模型中大气总纬向相对角动量的气候平均值。考虑了包含波浪-波浪相互作用的模型以及仅允许波浪-纬向流相互作用的简化系统。分析表明，对于给定的截断，系统的平衡状态并不依赖于波-波相互作用的存在，尽管其详细的演化却依赖于波-波相互作用的存在。 我们根据非受迫正压流平衡解的性质的概括来解释我们的结果。对于现实的分辨率（截断波数° 15），大多数流向西向角动量的平衡演化，并且解在很大程度上取决于初始条件。一个重要的例外是当流动最初具有向西的角动量时的情况，此时无论分辨率如何，平衡状态都保持接近初始状态。导出了流的固体旋转分量的气候平均值的上限。一般来说，高度截断的系统对初始条件不敏感，并朝着角动量向东且接近上限的状态演化。 所使用的全球地形的合理重新划分对气候平均角动量影响不大，但没有地形的情况代表了角动量守恒的奇异极限。
The climatic-mean-value of the total zonal relative angular momentum of the atmosphere in topographically forced inviscid barotropic models on a sphere is examined using the methods of equilibrium statistical mechanics. Models incorporating wave–wave interactions as well as simplified systems in which only wave–zonal-flow interactions are allowed are considered. It is shown analytically that for a given truncation the equilibrium state of the system does not depend on the presence of wave–wave interactions although the detailed evolution towards it does. We interpret our results in terms of a generalization of the properties of the equilibrium solutions for unforced barotropic flow. For realistic resolution (with truncation wavenumber ° 15) most flows evolve towards an equilibrium with westward angular momentum, and the solutions are strongly dependent on the initial conditions. An important exception is the case when the flow initially has westward angular momentum, when the equilibrium state remains close to the initial state regardless of resolution. An upper bound on the climatic-mean-value of the solid-body rotation component of the flow is derived. In general, highly truncated systems are insensitive to the initial conditions and evolve towards a state in which the angular momentum is eastward and close to the upper bound. Reasonable rescating of the global topography used has little influence on the climatic-mean angular momentum, but the case of no topography represents a singular limit in which angular momentum is conserved.