Study of fluid motions based on the Riemannian geometry on the group of diffeomorphisms 微分同相写像上のリーマン幾何学に基づく流体運動の考察
Access this Article
Search this Article
Author
Bibliographic Information
- Title
-
Study of fluid motions based on the Riemannian geometry on the group of diffeomorphisms
- Other Title
-
微分同相写像上のリーマン幾何学に基づく流体運動の考察
- Author
-
中村, 英史
- Author(Another name)
-
ナカムラ, フサシ
- University
-
東京大学
- Types of degree
-
博士 (理学)
- Grant ID
-
甲第9341号
- Degree year
-
1992-03-30
Note and Description
博士論文
Table of Contents
- Contents / p1 (0003.jp2)
- 1 Introduction / p2 (0004.jp2)
- 2 The fluid motion as a geodesic on Dυ / p4 (0006.jp2)
- 2.1 The fluid motion from the lagrangian point of view / p4 (0006.jp2)
- 2.2 Riemannian structure of Dυ / p4 (0006.jp2)
- 2.3 Geodesics and fluid motion / p6 (0008.jp2)
- 3 The analysis of fluid motion by Jacobi field / p8 (0010.jp2)
- 3.1 Jacobi field along a geodesic / p8 (0010.jp2)
- 3.2 Fluid motions of different velocity fields / p8 (0010.jp2)
- 3.3 Stretching effect and left translated Jacobi field / p8 (0010.jp2)
- 3.4 Gauss formula and the stretching strength / p10 (0012.jp2)
- 3.5 General properties of Jacobi field / p13 (0015.jp2)
- 4 Fluid motion on flat torus / p15 (0017.jp2)
- 4.1 Geometry of flat torus / p15 (0017.jp2)
- 4.2 Fourier expression of Dυ / p15 (0017.jp2)
- 4.3 Beltrami flow / p17 (0019.jp2)
- 5 Stability of fluid motion on T³ / p19 (0021.jp2)
- 6 Stretching effect and Jacobi field on T² / p21 (0023.jp2)
- 6.1 Jacobi field and passive scalar on T² / p21 (0023.jp2)
- 6.2 Exact solution and numerical simulations / p23 (0025.jp2)
- 7 Concluding remark / p27 (0029.jp2)
- references / p28 (0030.jp2)