請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/69887完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 蔡武廷 | |
| dc.contributor.author | Chia-I Hu | en |
| dc.contributor.author | 胡家宜 | zh_TW |
| dc.date.accessioned | 2021-06-17T03:32:30Z | - |
| dc.date.available | 2020-03-01 | |
| dc.date.copyright | 2018-03-01 | |
| dc.date.issued | 2018 | |
| dc.date.submitted | 2018-02-13 | |
| dc.identifier.citation | Boomkamp, P. A. M., Boersma, B. J., Miesen, R. H. M., & Beijnon, G. V. (1997). A Chebyshev collocation method for solving two-phase flow stability problems. Journal of Computational Physics, 132(2), 191-200.
Craik, A. D. D. (1982). The drift velocity of water waves. Journal of Fluid Mechanics, 116, 187-205. Craik, A. D., & Leibovich, S. (1976). A rational model for Langmuir circulations. Journal of Fluid Mechanics, 73(3), 401-426. Drazin, P. G., & Reid, W. H. (1981). Hydrodynamic Stability. Cambridge university press. Langmuir, I. (1938). Surface motion of water induced by wind. Science, 87(2250), 119-123. Leibovich, S. (1977a). On the evolution of the system of wind drift currents and Langmuir circulations in the ocean. Part 1. Theory and averaged current. Journal of Fluid Mechanics, 79(4), 715-743. Leibovich, S. (1977b). Convective instability of stably stratified water in the ocean. Journal of Fluid Mechanics, 82(3), 561-581. Leibovich, S. (1983). The form and dynamics of Langmuir circulations. Annual Review of Fluid Mechanics, 15(1), 391-427. Leibovich, S., & Paolucci, S. (1981). The instability of the ocean to Langmuir circulations. Journal of Fluid Mechanics, 102, 141-167. Lele, S. K. (1985). Some problems of hydrodynamic stability arising in geophysical fluid dynamics. Longuet-Higgins, M. S. (1953). Mass transport in water waves. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 245(903), 535-581. Orszag, S. A. (1971). Accurate solution of the Orr–Sommerfeld stability equation. Journal of Fluid Mechanics, 50(4), 689-703. Phillips, W. R. C. (2001). On an instability to Langmuir circulations and the role of Prandtl and Richardson numbers. Journal of Fluid Mechanics, 442, 335-358. Phillips, W. R. C., & Dai, A. (2014). On Langmuir circulation in shallow waters. Journal of Fluid Mechanics, 743, 141-169. Savelyev, I. B., Maxeiner, E., & Chalikov, D. (2012). Turbulence production by nonbreaking waves: Laboratory and numerical simulations. Journal of Geophysical Research: Oceans, 117(C11). Tsai, W. T., Chen, S. M., & Lu, G. H. (2015). Numerical evidence of turbulence generated by nonbreaking surface waves. Journal of Physical Oceanography, 45(1), 174-180. Tsai, W. T., Lu, G. H., Chen, J. R., Dai, A., & Phillips, W. R. (2017). On the Formation of Coherent Vortices beneath Nonbreaking Free-Propagating Surface Waves. Journal of Physical Oceanography, 47(3), 533-543. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/69887 | - |
| dc.description.abstract | 朗謬爾環流(Langmuir Circulation)係因海面波浪與風成流之交互作用形成，然於自由傳播波浪之數值模擬結果中，亦發現類似於朗謬爾環流之渦旋。本研究以Craik-Leibovich equation之線性穩定性分析，判斷Craik-Leibovich type 2 (CL2)不穩定性能否解釋此現象。此穩定性分析以正規模態展開線性擾動方程式，並以契比雪夫配置法(Chebyshev Collocation Method)求解；契比雪夫配置法乃基於契比雪夫多項式、點配置法之擴展，及衍伸出的廣義特徵值之解。研究發現最不穩定模態與於數值模擬及實驗觀察之主要渦旋對間距相近；因此，被觀察到之條痕有很高可能性為CL2不穩定性所造成。 | zh_TW |
| dc.description.abstract | Langmuir circulations are formed from the interaction between surface waves and wind driven currents, however in the numerical simulations of free-propagating surface waves, streaks resembling the Langmuir circulation exists. Linear stability analysis of the Craik-Leibovich equation is conducted to determine if the Craik-Leibovich type 2 (CL2) instability can explain the similarities. The analysis is done by representing the perturbations by normal-mode expansion, and solved using Chebyshev collocation method; this method is based on expansions in terms of Chebyshev polynomials, point collocation, and subsequent solution of the generalized eigenvalue problem. The most unstable mode is found to be close to the spacing of predominant vortex pairs observed in numerical simulations and laboratory experiments; hence, it is highly probable that the elongated streaks observed on the surfaces are excited by the CL2 instability. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T03:32:30Z (GMT). No. of bitstreams: 1 ntu-107-R04525009-1.pdf: 2117109 bytes, checksum: 26d7e5a2a30ba5579449dcb5e37702f1 (MD5) Previous issue date: 2018 | en |
| dc.description.tableofcontents | 中文摘要 i
Abstract ii Contents iii List of Figures v List of Tables vii List of Symbols ix Chapter 1. Introduction 1 1.1 Langmuir Circulation beneath Wind Waves 1 1.2 Vortical Flow beneath Free-Propagating Waves 2 1.3 Outline of this Thesis 3 Chapter 2. Problem Formulation 4 2.1 Governing Equations 4 2.2 Nondimensional Governing Equations 6 2.3 Linearized Perturbed Equation 9 Chapter 3. Numerical Procedure of Linear Stability Analysis 12 3.1 Normal Mode Expansion 12 3.2 Chebyshev Collocation Method 15 3.3 Convergence Test of the Eigensystem 18 Chapter 4. Results and Discussion 22 4.1 Marginal Stability Curve & Stability Diagram 22 4.2 Eigenvalue Spectrum in Complex Plane 26 4.3 Growth Rate of Most Unstable Mode / Second Mode 33 4.4 Velocity Profiles of the Unstable Mode 35 Chapter 5. Conclusion 39 References 40 Appendix A. Viscous Stability Analysis – Plane Poiseuille Flow 42 A.1 Problem Formulation 42 A.2 Normal Mode Expansion 44 A.3 The Orr-Sommerfeld Equation 46 A.4 Chebyshev Collocation Method 47 A.5 Marginal Stability Curve 49 A.6 Matrix 50 Appendix B. Matrix Arising from Collocation Method 51 B.1 Matrix Arising from Collocation Method 51 B.2 Additional notes on solving the generalized eigenvalue problem 53 Appendix C. Comparing with Galerkin Method 54 C.1 Eigenvalue Convergence Comparison 54 C.2 Stability Curve Comparison 56 C.3 Growth Rate Comparison 57 | |
| dc.language.iso | en | |
| dc.title | 應用契比雪夫配置法探討自由傳播波浪下黏性流之穩定性分析 | zh_TW |
| dc.title | Stability Analysis of Viscous Flow beneath a Free-Propagating Surface Wave Using Chebyshev Collocation Method | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 106-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 戴璽恆,陳世楠 | |
| dc.subject.keyword | 自由傳播波浪,朗謬爾環流,Craik-Leibovich equation,契比雪夫配置法,不穩定性, | zh_TW |
| dc.subject.keyword | free-propagating wave,Langmuir circulation,Craik-Leibovich equation,Chebyshev collocation method,instability, | en |
| dc.relation.page | 58 | |
| dc.identifier.doi | 10.6342/NTU201800558 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2018-02-15 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 工程科學及海洋工程學研究所 | zh_TW |
| 顯示於系所單位： | 工程科學及海洋工程學系 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-107-1.pdf 目前未授權公開取用 | 2.07 MB | Adobe PDF |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。