Instability Associated with the Continuous Spectrum in a Baroclinic Flow
Instability Associated with the Continuous Spectrum in a Baroclinic Flow
复制标题
斜压流中与连续谱相关的不稳定性
DOI：
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发表时间：
1966
期刊：
影响因子：
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通讯作者：
A. Burger
中科院分区：
文献类型：
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作者：
A. Burger
摘要 利用无摩擦、静水、绝热和地转理论以及 β 平面动力学，解决了具有恒定垂直剪切和消失温度递减率的纬向大气流上小振幅波扰动的一般初值问题。对于每个东西向波长，解决方案被视为由有限数量的离散光谱模式和连续光谱贡献组成。 （与许多其他流体动力学问题一样，L−λM=0 形式的相关算子是奇异的，微分算子 L 和 M 具有相同的阶数。）如前所述，对于几乎所有波长，特征值模式之一是不稳定的。目前的分析表明，对于不存在这种不稳定简正模的特殊波长，连续光谱的贡献是不稳定的。
Abstract A general initial value problem is solved for wave perturbations of small amplitude on a zonal atmospheric flow with constant vertical shear and vanishing temperature lapse rate, using frictionless, hydrostatic, adiabatic and geostrophic theory and beta-plane dynamics. For every west-east wavelength, the solution is seen to be constituted of a finite number of discrete spectrum modes and a continuous spectrum contribution. (As in many other hydrodynamical problems, the relevant operator of the form L−λM=0 is singular and the differential operators L and M are of equal order.) As was previously demonstrated, for almost all wavelengths one of the eigenvalue modes is unstable. The present analysis shows that, for the exceptional wavelengths for which no such unstable normal mode exists, the continuous spectrum contribution is unstable.