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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.

由于流域致密性和微分旋转的影响，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模式形成现象，并且与地球物理流的基本性质密切相关。在这个项目中，我们主要研究了湍流初始条件下的流型形成，以及流体动力学和数值分析中的相关问题。我们首先研究了旋转球体上圆形域内的二维流体运动，发现在赤道为刚性边界的南半球情况下，会自发形成向东的绕极地流，而在整个球体情况下会出现向西的绕极地喷流。罗斯贝波的动量传递在此过程中非常重要，我们在弱非线性理论的框架下对射流形成进行了理论描述。还以强迫风的强度作为分叉参数，研究了西向强化流的不稳定性。随着强迫风的增加，发现了霍普夫型不稳定性，随后出现超临界分岔，并讨论了不稳定性与环流构型之间的关系。水的相变是地球大气环流的重要因素，我们从热带降雨活跃区的角度研究湿对流产生的流动模式及其与全球环流的关系。数值方法在这些研究中非常重要，我们准备了几种类型的计算机代码进行数值模拟，还提出了一些新的数值方法，用于使用到平面盘的共形投影来求解球体上的流体方程，以及使用雅可比多项式的谱方法来求解有界域上的流体方程。还研究了与湍流动力学相关的流体方程的数学性质。