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Flow Pattern Formation in Turbulence on a Rotating Sphere.

旋转球体上湍流中流型的形成。

基本信息

批准号：
13440121
负责人：
YAMADA Michio
金额：
$ 8.58万
依托单位：
KYOTO UNIVERSITY (2003)The University of Tokyo (2001-2002)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2003
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13440121/
关键词：
rotating fluid geophysical fluid dynamics circumpolar flow Rossby wave wave-mean flow interaction rotating turbulence westward intensification moist convection 流体方程式地球流体 barotropic流回転球面ベータ効果 barotroic流 Rosbby波球面 2次元乱流 /

项目摘要

Fluid motion on a rotating sphere often shows pattern formation phenomena never observed in a planer motion because of the influence of the compactness of the flow domain and the differential rotation, and is strongly related to fundamental properties of geophysical flows. Mainly in this project, we studied flow pattern formation arising from turbulent initial conditions, and related problems in fluid dynamics and numerical analysis. We first studied 2D fluid motion in a circular domain on a rotating sphere, and found that in the case of southern hemisphere with the rigid boundary at the equator, eastward circumpolar flow is spontaneously formed, in contrast with the whole sphere case where westward circumpolar jets emerge. The momentum transfer by the Rossby wave is important in this process, and we gave a theoretical description for the jet formation in the frame of weakly nonlinear theory. Instability of westward intensified flows were also studied with the strength of the forcing wind being a bifurcation parameter. A Hopf-type instatility followed by a supercritical bifurcation, is found as the forcing wind increases, and a relation between the instability and configuration of gyres is discussed. Phase change of water is an important factor of general circulation on the earth, and we study flow patterns generated by moist convection and its relation to global circulation from a view point of active rainfall area in tropical zone. Numerical methods are quite important in these studies, and we prepared several types of computer codes for numerical simulation, and also proposed some new numerical methods for a fluid equation on a sphere using a conformal projection to a planer disk, and also for fluid equation on a bounded domain by using a, spectral method with Jacobi polynomials. Mathematical properties of fluid equation related to turbulence dynamics are also studied.

由于流动域的致密性和差异旋转的影响，旋转球体上的流体运动常常表现出平面运动中从未观察到的图案形成现象，并且与地球物理流动的基本性质密切相关。本计画主要研究由紊流初始条件所引起的流态形成，以及相关的流体力学与数值分析问题。我们首先研究了旋转球体上圆形区域内的二维流体运动，发现在南半球赤道刚性边界的情况下，向东的绕极流是自发形成的，而在整个球体的情况下，向西的绕极喷流则是自发形成的。在这一过程中，Rossby波的动量传递是重要的，我们在弱非线性理论框架下对射流的形成进行了理论描述。以强迫风强度为分岔参数，研究了向西向增强气流的不稳定性。随着强迫风的增加，出现了一个Hopf型不稳定性，随后出现了一个超临界分岔，并讨论了不稳定性与涡旋结构之间的关系。水的相变是地球大气环流的一个重要因素，本文从热带地区降水活跃区的角度研究了湿对流产生的流型及其与全球环流的关系。数值方法在这些研究中是非常重要的，我们编写了几种类型的计算机程序进行数值模拟，并提出了一些新的数值方法，对球上的流体方程使用共形投影到平面圆盘上，以及对有界区域上的流体方程使用Jacobi多项式的谱方法。研究了与湍流动力学有关的流体方程的数学性质。