Vortex Structure, Inverse Cascades, and Turbulent Bursts in Rotating, Stratified Flows

旋转和分层流动中流体湍流的三维模拟将使用新的有效基函数的谱方法进行。这些计算将增加我们对地球物理和天体物理流动中常见的各向异性和非均匀环境中湍流的建模和计算的理解和能力，并在许多工程应用中得到应用。旋转和分层倾向于使流体在某些位置、某些长度尺度和/或某些时间间隔上接近二维（2D）。人们通常认为，当气流表现为完全三维时，能量从大尺度转移到小尺度（“正向级联”），小规模湍流主要充当被动的“海绵”消散能量。当流动表现为二维时，能量逆级联从小尺度到大尺度。在这些情况下，小尺度湍流更加复杂和难以模拟，其对大尺度的影响更为深远。将建立一个反级联的数学模型，并将建立行星喷射流强度和宽度的标度定律，并与模拟、实验和观测结果进行比较。湍流的渐近性和数学模型将允许构建新的亚网格尺度湍流模型，用于大涡数值模拟。模拟将与实验室实验和观测以及对地球物理和天体物理流的观测进行比较。这项研究的具体特点使它超出了大多数湍流/涡旋运动研究的标准。期望得到的不同结果不仅有助于阐明“二维”湍流问题，而且通过注意两者之间的异同，有助于阐明更一般的湍流过程。

Three-dimensional simulations of fluid turbulence in rotating and stratified flows will be carried out using spectral methods using new efficient basis functions. The calculations will increase our understanding and ability to model and calculate turbulence in anisotropy and inhomogeneous settings that are commonly found in geophysical and astrophysical flows and is many engineering applications. Rotation and stratification tend to make the fluid act nearly 2-dimensional (2D) at some locations, at some length scales, and/or for some intervals of time. It is commonly thought that when and where the flows behave as if they were fully 3D, energy is transferred ("forward cascades") from large to small scales, and small-scale turbulence acts primarily as a passive "sponge" dissipating energy. When and where the flows behave as if it were 2D, energy inverse cascades from small to large scales. In these cases the small-scale turbulence is much more complex and difficult to model, and its effects on the large-scales are more profound. A mathematical model of the inverse cascade will be developed and scaling laws for the strengths and widths of planetary jet streams will be developed and compared against simulations, experiments and observations. Asymptotics, and mathematical models for the turbulence will permit construction of new sub-grid-scale turbulence models to be used in large-eddy numerical simulations. The simulations will be compared to laboratory experiments and observations and observations of geophysical and astrophysical flows.The specific features of this investigation place it outside of the norm for most studies of turbulent/vortical motions. It is expected that the distinct results to be obtained will not only serve to illuminate the "2-D" turbulence problem but also the more general turbulent flow processes by noting the similarities/differences between the two.