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Nonhydrostatic Atmospheric Normal Modes on Beta-Planes

机译：Beta平面上的非静压大气正常模式

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—To facilitate the understanding of nonhydrostatic effect in global and regional nonhydrostatic models, the normal modes of a nonhydrostatic, stratified, and compressible atmosphere are studied using Cartesian coordinates on midlatitude and equatorial β-planes. The dynamical equations without forcing and dissipation are linearized around the basic state at rest, and solved by using the method of separation of variables. An eigenvalue-eigenfunction problem is formulated, consisting of the horizontal and vertical structure equations with suitable boundary conditions. The wave frequency and the separation parameter, referred to as “equivalent height,” appear in both the horizontal and vertical characteristic equations as a coupled problem, unlike the hydrostatic case. Therefore, the nonhydrostatic equivalent height depends not only on the vertical modal scale, as in the hydrostatic case, but also on the zonal and meridional modal scales. Numerical resu lts on the dispersion relations are presented for an isothermal atmosphere. Three kinds of normal modes, namely acoustic, gravity, and Rossby modes, are solved and compared with the corresponding global solutions. Nonhydrostatic effects are studied in terms of normal modes in a wide range of wavelengths from small to planetary scales. It is demonstrated that Rossby modes are hardly affected by nonhydrostatic effects regardless of wavelengths. However, nonhydrostatic effects on gravity modes become significant for smaller horizontal and deeper vertical scales of motion. The equivalent height plays a particularly important role in evaluating nonhydrostatic effects of normal modes on the equatorial β-plane, because the equivalent height appears in the scaling of meridional distance variable of the eigenfunctions. The implementation of nonhydrostatic normal mode analysis on high-resolution numerical modeling is also discussed.
机译：－为了促进对整体和区域非静水模型中的非静水作用的理解，使用中纬度和赤道β平面上的笛卡尔坐标研究了非静水，分层和可压缩大气的正常模式。将没有强迫和耗散的动力学方程在静止的基本状态周围线性化，并使用变量分离方法求解。提出了一个特征值-特征函数问题，包括具有适当边界条件的水平和垂直结构方程。与静水压情况不同，在水平和垂直特征方程中，波频率和分离参数（称为“等效高度”）都作为耦合问题出现。因此，非静水当量高度不仅取决于静水压情况下的垂直模态尺度，还取决于纬向和经向模态尺度。给出了等温气氛下弥散关系的数值结果。求解了三种普通模式，即声学，重力和Rossby模式，并与相应的整体解进行了比较。在从小到行星的各种波长范围内，均以正常模式研究了非静水效应。已经证明，不管波长如何，Rossby模几乎不受非静水效应的影响。但是，对于较小的水平和较深的垂直运动比例，对重力模式的非静液压作用变得很重要。当量高度在评估正常模式对赤道β平面的非静水效应方面起着特别重要的作用，因为当量高度出现在本征函数的子午距离变量的缩放比例中。还讨论了在高分辨率数值建模中非静水法模分析的实现。

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