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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/6287完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳義裕(Yih-Yuh Chen) | |
| dc.contributor.author | Wei-Ting Lin | en |
| dc.contributor.author | 林蔚廷 | zh_TW |
| dc.date.accessioned | 2021-05-16T16:25:05Z | - |
| dc.date.available | 2013-06-21 | |
| dc.date.available | 2021-05-16T16:25:05Z | - |
| dc.date.copyright | 2013-06-21 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-06-07 | |
| dc.identifier.citation | [1] G. K. Batchelor. Note on a class of solutions of the Navier-Stokes equations
representing steady rotationally-symmetric flow. The Quarterly Journal of Me- chanics and Applied Mathematics, 4(1):29–41, 1951. [2] C. M. Bender and S. A. Orszag. Advanced mathematical methods for scien- tists and engineers I: Asymptotic methods and perturbation theory, volume 1. Springer, 1999. [3] J. J. Boisvert, P. H. Muir, and R. J. Spiteri. BVP_SOLVER-2. http://cs. stmarys.ca/~muir/BVP\_SOLVER\_Webpage.shtml. [4] P. R. N. Childs. Rotating flow. Butterworth-Heinemann, 2010. [5] W. G. Cochran. The flow due to a rotating disc. In Mathematical Proceedings of the Cambridge Philosophical Society, volume 30, pages 365–375. Cambridge Univ Press, 1934. [6] A. Einstein. Die Ursache der Mäanderbildung der Flußläufe und des sogenan- nten Baerschen Gesetzes. Naturwissenschaften, 14(11):223–224, 1926. [7] G. L. Mellor, P. J. Chapple, and V. K. Stokes. On the flow between a rotating and a stationary disk. J. Fluid Mech, 31(1):95–112, 1968. [8] A. H. Nayfeh. Perturbation methods. Wiley-VCH, 2008. [9] K. Stewartson. On the flow between two rotating coaxial disks. In Proc. Camb. Phil. Soc, volume 49, pages 333–341. Cambridge Univ Press, 1953. [10] J. P. Vanyo. Rotating fluids in engineering and science. Dover Publications, 2001. [11] T. von Kármán. Über laminare und turbulente Reibung. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 1(4):233–252, 1921. [12] P. J. Zandbergen and D. Dijkstra. Von Kármán swirling flows. Annual review of fluid mechanics, 19(1):465–491, 1987. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/6287 | - |
| dc.description.abstract | 我們比較了von Kármán方程式的數值解與線性近似的結果,發現某些von Kármán方程式的解的特性,能夠被其線性化方程所表現。為了更進一步驗證這個結果,我們採用amplitude equation。為了解決 damping 項造成的影響,我們提出一個新的方法。此方法雖然amplitude部份近似的很好,但phase部份相當差,有待進一步的研究。 | zh_TW |
| dc.description.abstract | By the comparison between the numerical results and the linearized solution,we show some solutions of von Kármán’s equation have global feature that can becaptured by the linearized solutions, although there are some shifts in amplitudeand phase.
To show the validity of this approach and polish the approximation, we use the amplitude equation approach, which can tune the amplitude and phase of the linearized solutions to make them fit. We encounter difficulty in the course of finding the amplitude equation of damping systems. To solve this problem, we propose an idea to deal with the exponential growth of the zero-th order solution. Although the phase of the approximate solution deviates from the numerical results very much, the amplitude fits well. Further investigation is under way. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-16T16:25:05Z (GMT). No. of bitstreams: 1 ntu-102-R99222027-1.pdf: 847537 bytes, checksum: ae445bbbc830f6a33fbfc5c2623db3ab (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | 1 Introduction
1 2 A review of von Kármán’s swirling solution 5 2.1 von Kármán’s similarity solution . . . . . . . . . . . . . . . . . . . . 5 2.2 Rotating fluid with a stationary disk . . . . . . . . . . . . . . . . . . 10 2.3 The two-disk problem . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3 Linearized Solution 15 3.1 The one-disk problem . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.1.1 Von Kármán’s problem (g∞ = 0, h∞ < 0) . . . . . . . . . . . 17 3.1.2 Rotating fluid with a stationary disk . . . . . . . . . . . . . . 18 3.2 The two-disk problem . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4 The amplitude equation approach 27 4.1 A brief review of the multiple scale analysis . . . . . . . . . . . . . . 28 4.2 Damping and negative damping systems . . . . . . . . . . . . . . . . 31 4.2.1 A possible approach . . . . . . . . . . . . . . . . . . . . . . . 34 5 Conclusion 39 Bibliography 41 | |
| dc.language.iso | en | |
| dc.subject | 多尺度分析 | zh_TW |
| dc.subject | 馮卡門旋轉流 | zh_TW |
| dc.subject | 振幅方程式 | zh_TW |
| dc.subject | multiple-scale analysis | en |
| dc.subject | n swirling flow | en |
| dc.subject | rmá | en |
| dc.subject | von Ká | en |
| dc.subject | amplitude equation | en |
| dc.title | 對von Kármán旋轉流的進一步研究 | zh_TW |
| dc.title | Further Investigation on von Kármán's Swirling Flow | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳明志(Ming-Jyh Chern),蔡日強(Jih-Chiang Tsai) | |
| dc.subject.keyword | 馮卡門旋轉流,振幅方程式,多尺度分析, | zh_TW |
| dc.subject.keyword | von Ká,rmá,n swirling flow,amplitude equation,multiple-scale analysis, | en |
| dc.relation.page | 42 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2013-06-07 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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