Numerical Studies of Three-Dimensional Turbulence in Small Aspect Ratio Domains

这是对小纵横比（SAR）域中的三维湍流的研究，其中垂直高度H与水平方向上的长度L相比较小。目的是解决不可压缩的纳维尔斯托克斯方程使用伪谱码在周期域为不同的分辨率。这项研究将旨在弥合湍流研究与地球物理应用之间的差距。特别感兴趣的是从二维到三维湍流的过渡和相关的基本问题，如能量级联的变化。二维湍流的特征是能量向大尺度的逆级联，而三维湍流的能量流方向是小尺度的。尽管SAR领域与地球物理现象（如大气湍流）相关，但显然缺乏详细的研究。本研究的一个独特之处在于考虑了SAR湍流，其中垂直速度与小尺度的水平湍流相比并不小。这将允许模拟准地转模式无法模拟的现象，例如部分由相对小尺度的垂直对流驱动的大气大尺度运动。相干结构与背景强迫在SAR域中的相互作用是研究的目标之一。该研究解决了湍流动力学的一个重要方面，在过去没有得到足够的重视。这项研究的结果将对我们预测地球物理流的能力产生重要影响。

CTS-9528491 Smith This is a study of three dimensional turbulence in small aspect ratio (SAR) domains, where the vertical height, H, is small compared to the length, L, in the horizontal direction. The objective is to solve the incompressible Navier Stokes equations using a pseudo-spectral code in a periodic domain for varying resolutions. The study will be aimed at bridging the gap between turbulence research and geophysical applications. Of special interest is the transition from two dimensional to three dimensional turbulence and related fundamental issues such as the change in the energy cascade. Two-dimensional turbulence is characterized by an inverse cascade of energy to large scales whereas the direction of the energy flux in three-dimensional turbulence is in the direction of smaller scales. The interest in the SAR domain is the apparent lack of detailed study in spite of the relevance to geophysical phenomena such as atmospheric turbulence. One of the unique features of this study is to consider SAR turbulence where the vertical velocity is not small in comparison to the horizontal turbulence at small scales. this would allow the modeling of phenomena that are inaccessible to quasi-geostrophic models, such as atmospheric large scale motions that are partially driven by vertical convection at relatively small scales. The interaction of coherent structures with background forcing in SAR domains is one of the objectives of the research. The research addresses an important aspect of turbulence dynamics that has not received adequate attention in the past. The results of this research will have an important impact on our ability to predict geophysical flows.