A Simple Model for Nonlinear Critical Layers in an Unstable Baroclinic Wave
A Simple Model for Nonlinear Critical Layers in an Unstable Baroclinic Wave
复制标题
不稳定斜压波中非线性临界层的简单模型
DOI：
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发表时间：
1982
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通讯作者：
J. Pedlosky
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文献类型：
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作者：
J. Pedlosky
本文发展了β平面两层模式中微耗散斜压波在最小临界切变点的有限振幅动力学的弱非线性理论。在此参数设置下，非线性理论提供了临界层动态的简单表现，因为多普勒频移在两层中的一层中消失。计算表明，当耗散与位涡成正比且较弱时，新的平衡定态在临界层中具有均匀的位涡，尽管这对波的稳定性并不要求。基波的空间谐波在瞬态和终态都起着重要的作用。对于弱耗散流动，由于谐波引起的位涡沿基波的流线是沿着守恒的。本文在临界层内均匀位涡假设的基础上，给出了平衡波振幅的解析理论，并与实验结果进行了比较。
Abstract Weakly nonlinear theory is developed for finite-amplitude dynamics of a slightly dissipative baroclinic wave at the point of minimum critical shear in the β-plane two-layer model. At this parameter setting the nonlinear theory provides a simple manifestation of critical layer dynamics since the Doppler-shifted frequency vanishes in one of the two layers. Calculations show that when the dissipation is proportional to the potential vorticity and is weak, the new equilibrium steady state has uniform potential vorticity in the critical layer although this is not required for wave stabilization. The spatial harmonics of the fundamental play an important role in both the transient and final state. For a weakly dissipative flow, the potential vorticity due to the harmonics is conserved along streamlines of the fundamental wave. An analytical theory is given for the equilibrated wave amplitude based on the assumption of uniform potential vorticity in the critical layer, and this prediction agrees well wi...