Vortices, waves, and energy cascades in atmospheric turbulence

大气流体力学跨越了广泛的长度尺度，从行星尺度到毫米尺度。中尺度是从公里到数百公里的中间尺度；它支持各种令人惊叹的现象，包括涡旋、重力波、对流风暴和湍流。中尺度动力学在大气能量收支中起着关键作用。动能主要储存在大尺度涡旋中，并被极小尺度的涡旋耗散；要达到耗散尺度，能量必须通过中尺度。能量在中尺度不同尺度之间的传递称为中尺度级联。尽管这一过程很重要，但数值天气预报模式并没有完全理解和捕捉到这一过程。这项研究计划旨在通过对这一过程的基本了解来改进大气模式中的中尺度级联的表示。该项目有三个主要目标：了解非线性波动和涡旋在中尺度级联中的作用；量化不同过程在不同尺度上的能量交换；改进小尺度湍流在数值模式中的表现，特别是局部化的高尺度能量传递。这里提出的工作将加深对大气动力学的基本理解，提高数值天气模式预测小尺度现象的能力，并培训学生在大气/海洋/气候动力学和建模方面以及在计算建模和数据分析方面的各种职业。

Atmospheric fluid mechanics spans a wide range of length scale, from planetary scales down to millimetre scales. The mesoscale is an intermediate range of scales from kilometres to hundreds of kilometres; it supports an amazing variety of phenomena, including vortices, gravity waves, convective storms, and turbulence. Mesoscale dynamics play a key role in the energy budget of the atmosphere. Kinetic energy is primarily stored in large-scale vortices, and dissipated by very small-scale vortices; to reach the dissipation scales, energy must pass through the mesoscale. The transfers of energy between different scales in the mesoscale is called the mesoscale cascade. Despite its importance, this process is not completely understood and not fully captured by numerical weather prediction models. This research program aims to improve the representation of the mesoscale cascade in atmospheric models by gaining fundamental understanding of this process. There are three main objectives of this program: to understand the role of nonlinear waves and vortices in the mesoscale cascade; to quantify the exchanges of energy by different processes at different scales; and to improve the representation of small-scale turbulence in numerical models, especially localized upscale energy transfer. The work proposed here will deepen the fundamental understanding of atmospheric dynamics, improve the ability of numerical weather models to predict small-scale phenomena, and train students in atmosphere/ocean/climate dynamics and modelling, as well as for a variety of careers in computational modelling and data analysis.