Collaborative Research: CMG: Anisotropic Atmospheric Dynamics Across a Wide Range of Scales

我们的重点是温带大气，特别强调在高度各向异性背景下的动力学，例如对流层顶附近的情况。理论上，高度各向异性背景大气的波动动力学研究要比均匀和各向同性背景大气少得多。然而，在大气混合过程中，几乎是逐步形成的环境是固有的。此外，当各向异性处于位涡（PV）时，由于罗斯比波的传播依赖于PV梯度的存在，因此对大尺度波动动力学的影响发生在阶上。本文的工作重点是研究背景各向异性对气旋组织、锋生、重力波发射和大气总能谱的动力学影响。统一的主题是，同时研究整个尺度的频谱是至关重要的，从天气尺度的能量注入到锋面尺度的耗散，因为非线性相互作用影响其间的所有尺度。因此，通过非线性级联，行星尺度的低频变异性和可预测性在很大程度上取决于中尺度和锋面尺度的耗散过程。一类新的动力模式特别利用了对流层顶不连续时位涡度的跃变。精确和高分辨率的解决方案提供了一个测试平台，以评估当前操作模型在解决动态各向异性方面的充分性。认识到对流层动力学的高度各向异性性质，使以前对各向同性和均匀湍流的数学研究转向与大气更相关的各向异性问题。北美的天气在很大程度上受到对流层顶附近风的影响，对流层顶是在大约10公里高空发现的大气条件急剧变化的水平。由于操作天气模式通常没有足够的分辨率来准确描述这些高度的大气运动，因此我们理解并预测整个大气天气和气候的能力减弱了。将要研究的许多问题之一的一个例子是，为什么许多当前的气候模式显示对流层顶附近温度较低的偏差。这项工作的范围旨在统一大气动力学，从最大的大陆尺度（低压）单体，通过它们随后的崩溃到中等尺度的风暴锋，以及更小尺度（重力波）湍流的产生。新的理论进展的主要焦点是解释对流层顶在天气模式演变中的重要贡献。拟议的研究是数学和大气科学的交叉，现在可以通过综合研究人员在对流层顶模拟方面的最新进展和大气湍流统计数值计算方面的新结果来实现。进一步了解低层大气能量如何在数千公里到数十公里的整个范围内演变的预期影响，将有助于阐明目前天气预报和气候模式中尚未解决的特征。

Our focus is on the extratropical atmosphere, with special emphasis on the dynamics in highly anisotropic backgrounds, such as is the case near the tropopause. Theoretically, the wave dynamics for a highly-anisotropic background atmosphere has been much less studied than for the homogeneous and isotropic case. Yet it is intrinsic in the atmospheric mixing process that nearly-stepwise environments form in the atmosphere. Furthermore, when the anisotropy is in potential vorticity (PV), the impact on large-scale wave dynamics occurs at leading order, since Rossby wave propagation depends on the presence of PV gradients. The proposed work focuses on the dynamical impact of background anisotropy on cyclone organization, frontogenesis, gravity wave emission and the overall atmospheric energy spectrum. The unifying theme is that it is crucial to study the whole spectrum of scales simultaneously, from energy injection at synoptic scales down to dissipation at frontal scales, because nonlinear interactions affect all scales in between. Hence, thelow-frequency variability and predictability of the planetary scales depend significantly, through nonlinear cascades, on the dissipative process at the meso- and frontal scales. A new class of dynamical models take specific advantage of jumps in potential vorticity at a tropopause discontinuity. Exact- and high-resolution solutions provide a testbed to assess the adequacy of current operational models in resolving the dynamical anisotropies. Recognition of the highly-anisotropic nature of tropospheric dynamics redirects previous mathematical efforts on isotropic and homogeneous turbulence to atmospherically more relevant anisotropic problems. The weather over North America is greatly influenced by the pattern of winds near the tropopause, a level of sharpchange in the atmospheric conditions found at an altitude ofroughly 10 km. Because operational weather models often do not have sufficient resolution to accurately describe the atmospheric motions at these heights, our ability to understand, and thus forecast, the weather and climate throughout the atmosphere is diminished. An example of one of the many issues which will be investigated is why many of the current climate models show a biased error of colder temperatures near the tropopause. The scope of this work seeks to unify the dynamics of the atmosphere from the largest continental-scale (low pressure) cells, through their subsequent collapse to intermediate-scale storm fronts, and the generation of yet smaller-scale (gravity wave) turbulence. The primary focus of new theoretical progress is to account for the important contributions of the tropopause in the evolution of weather patterns. The proposed research lies at the intersection between mathematics and atmospheric science, which is now possible through the synthesis of the investigators' recent advances in tropopause modeling and new results in the numerical computation of the statistics of atmospheric turbulence. The anticipated impact of further understanding of how energy in the lower atmosphere evolves over the full range of thousands down to tens of kilometers would be the elucidation of currently under-resolved features of weather prediction and climate models.