Convergence to precipitating quasi-geostrophic equations with phase changes: asymptotics and numerical assessment
Convergence to precipitating quasi-geostrophic equations with phase changes: asymptotics and numerical assessment
复制标题
DOI：
10.1098/rsta.2021.0030
复制
发表时间：
2022-06-27
期刊：
影响因子：
5
通讯作者：
Stechmann, Samuel N.
中科院分区：
文献类型：
--
作者：
Zhang, Yeyu;Smith, Leslie M.;Stechmann, Samuel N.
准地转(QG)方程在我们理解大气和海洋流体动力学中起着至关重要的作用。然而，传统的QG方程描述的是没有考虑湿度和云层的“干”动力学。为了走出干燥的环境，最近利用形式渐近法推导了降水QG(PQG)方程。在这里，我们研究带有相变的湿Boussinesq方程是否会收敛到PQG方程。先验地，相界面(云边缘)的非线性可能会使收敛复杂化。文中给出了收敛或不收敛的数值研究。数值模拟考虑了epsilon=0.10.01和0.001的情况，其中epsilon与Rossby数和Froude数成正比。在数值模拟中，垂直速度w的大小(或其他不平衡和惯性重力波的量度)随着epsilon的减小而与epsilon近似成正比，这表明收敛到PQG动力学。这些度量在固定的时间T被量化，即O(1)，并且数值数据也表明在以后的时间收敛的可能性。本文是《物理流体动力学中的数学问题(第二部分)》主题的一部分。
The quasi-geostrophic (QG) equations play a crucial role in our understanding of atmospheric and oceanic fluid dynamics. Nevertheless, the traditional QG equations describe 'dry' dynamics that do not account for moisture and clouds. To move beyond the dry setting, precipitating QG (PQG) equations have been derived recently using formal asymptotics. Here, we investigate whether the moist Boussinesq equations with phase changes will converge to the PQG equations. A priori, it is possible that the nonlinearity at the phase interface (cloud edge) may complicate convergence. A numerical investigation of convergence or non-convergence is presented here. The numerical simulations consider cases of epsilon = 0.1, 0.01 and 0.001, where epsilon is proportional to the Rossby and Froude numbers. In the numerical simulations, the magnitude of vertical velocity w (or other measures of imbalance and inertio-gravity waves) is seen to be approximately proportional to epsilon as epsilon decreases, which suggests convergence to PQG dynamics. These measures are quantified at a fixed time T that is O(1), and the numerical data also suggests the possibility of convergence at later times. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.