Fast-Wave Averaging with Phase Changes: Asymptotics and Application to Moist Atmospheric Dynamics
Fast-Wave Averaging with Phase Changes: Asymptotics and Application to Moist Atmospheric Dynamics
复制标题
DOI：
10.1007/s00332-021-09697-2
复制
发表时间：
2021-03
影响因子：
3
通讯作者：
Yeyu Zhang;L. Smith;S. Stechmann
中科院分区：
文献类型：
--
作者：
Yeyu Zhang;L. Smith;S. Stechmann
许多系统涉及慢速和快速分量的耦合非线性演化，例如，快波可能是马赫数较小的声波或弗劳德数和罗斯贝数较小的惯性重力波。过去，对于一些这样的系统，已经显示出一个有趣的特性：在快波振荡的奇异极限中，慢波成分实际上独立于快波而演化。在这里，为潮湿的 Boussinesq 系统开发了一个快波平均框架，其复杂性超出了过去的情况，现在包括水蒸气和液态水之间的相变。主要问题是：相位变化是否会引起慢波和快波之间的耦合？或者根据潮湿的准地转方程，慢分量是否独立演化？与干动力学相比，一个重大挑战是，由于相变，该方法需要适应具有可变系数的分段算子。这里提出了正式的渐近分析。对于没有相变的纯饱和流，研究表明沉淀不会引起耦合，并且慢模态独立演化。由于存在相位变化，极限方程表明相边界可能会引起慢波模式和快波之间的耦合。
Many systems involve the coupled nonlinear evolution of slow and fast components, where, for example, the fast waves might be acoustic (sound) waves with a small Mach number or inertio-gravity waves with small Froude and Rossby numbers. In the past, for some such systems, an interesting property has been shown: the slow component actually evolves independently of the fast waves, in a singular limit of fast wave oscillations. Here, a fast-wave averaging framework is developed for a moist Boussinesq system with additional complexity beyond past cases, now including phase changes between water vapor and liquid water. The main question is: Do phase changes induce coupling between the slow component and fast waves? Or does the slow component evolve independently, according to moist quasi-geostrophic equations? Compared to the dry dynamics, a substantial challenge is that the method needs to be adapted to a piecewise operator with variable coefficients, due to phase changes. A formal asymptotic analysis is presented here. For purely saturated flow without phase changes, it is shown that precipitation does not induce coupling, and the slow modes evolve independently. With phase changes present, the limiting equations show that phase boundaries could possibly induce coupling between the slow modes and fast waves.