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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 黃美嬌 | |
| dc.contributor.author | Su-Yang Shieh | en |
| dc.contributor.author | 謝曙陽 | zh_TW |
| dc.date.accessioned | 2021-06-15T01:31:47Z | - |
| dc.date.available | 2009-07-27 | |
| dc.date.copyright | 2009-07-27 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-07-20 | |
| dc.identifier.citation | [1] K. Alvelius, ”Random forcing of three-dimensional homogeneous turbulence,” Physics of Fluids, 11, n 7, 1880 (1999).
[2] A. Basdevant, B. Legras, B. Sadourny, and M. Beland, “A study of barotropic model flows : intermittency, waves and predictability.” Journal of the Atmospheric Sciences, 38, 2305 (1981). [3] G. K. Batchelor, “Computation of the energy spectrum in two-dimensional turbulence,” Physics of Fluids, 12, 233 (1967). [4] V. Borue, “Inverse energy cascade in stationary two-dimensional homogeneous turbulence,” Physics Review Letter, 72, 1475 (1994). [5] A. Chekhlov, S. A. Orszag, S. Sukoriansky, B. Galperin, and I. Staroselsky, “Direct numerical simulation tests of eddy viscosity in two dimensions,” Physics of Fluids, 6, 2548 (1994). [6] A. Chekhlov, S. A. Orszag, S. Sukoriansky, B. Galperin, and I. Staroselsky, “The effect of small-scale forcing on large-scale structures in two-dimensional flows,” Physica D, 98, 321 (1996). [7] I. M. Cohen, P. K. Kundu, “Fluid Mechanics,” 3rd edition, Academic Press (2004) [8] S. Danilov and D. Gurarie, “Nonuniversal features of forced two-dimensional turbulence in the energy range,” Physics Review E, 63, 020203 (2001). [9] S. Danilov and D. Gurarie, “Forced two-dimensional turbulence in spectral and physical space,” Physics Review E, 63, 061208 (2001). [10] S. Danilov and D. Gurarie, “Rhines scale and spectra of the β-plane turbulence with bottom drag,” Physics Review E, 65, 067301 (2002). [11] S. Danilov and D. Gurarie, “Scaling, spectra and zonal jets in beta-plane turbulence,” Physics of Fluids, v 16, n 7, July, 2592 (2004). [12] B. Fornberg, “A numerical study of 2D turbulence.” Journal of Computational Physics, 25, 1 (1977). [13] B. Galperin, S. Sukoriansky, and H.-P. Huang, “Universal n-5 spectrum of zonal flows on giant planets,” Physics of Fluids, 13, 1545 (2001). [14] H. L. Grant, R.W. Stewart and Moilleta, “Turbulence spectra from a tidal channel.” Journal of Fluid Mechanics, 12, 241 (1962). [15] G. Holloway and M. Hendershott, “Stochastic closure for nonlinear Rossby waves,” Journal of Fluid Mechanics, 747 (1977). [16] H.-P. Huang and W. A. Robinson, “Two-dimensional turbulence and persistent zonal jets in a global barotropic model,” Journal of the Atmospheric Sciences, 55, 611 (1998). [17] H.-P. Huang, B. Galperin, and S. Sukoriansky, “Anisotropic spectra in two dimensional turbulence on the surface of a rotating sphere,” Physics of Fluids, 13, 225 (2001). [18] M.-J. Huang,“Enstrophy Cascade and Smagorinsky Model of 2D Turbulent flow.” The Chinese Journal of Mechanics, vol.17 ,No.3 (2001). [19] T. Ishihara and Y. Kaneda, “Frequency shifts of Rossby waves in the inertial subranges of β-plane turbulence,” Physics of Fluids, v 13, n 8, August, 2338 (2001). [20] Y. Kaneda and G. Holloway, “Frequency shifts of Rossby waves in Geostrophic Turbulence,” Journal of Physical Society of Japan, 63, 2974 (1994). [21] R. H. Kraichnan, “Inertial ranges in two-dimensional turbulence.” Physics of Fluids, 10, 1417 (1967). [22] R. H. Kraichnan, “Inertial-range transfer in two- and three-dimensional turbulence.” Journal of Fluid Mechanics, 47, 525 (1971). [23] R. H. Kraichnan, “Eddy viscosity in two and three dimensions,” Journal of the Atmospheric Sciences, 33, 1521 (1976). [24] A. N. Kolmogorov, “The local structure of turbulence in incompressible fluid at very high Reynolds number.” Doklady of the Academy of Sciences of the USSR, 30, 299. (1949). [25] H. L. Kuo, “Dynamic instabilty of two-dimensional nondivergent flow in a barotropic atmosphere.” Journal of Meteorology 6, 105 (1949). [26] B. Legras, “Turbulent phase shift of Rossby wave.” Geophysical and Astrophysical Fluid Dynamics, 15, 253 (1980). [27] B. Legras, P. Santangelo, and R. Benzi, “High resolution numerical experiments for forced two-dimensional turbulence.” Europhysics Letter, 5, 37.(1988). [28] M. E. Maltrud and G. K. Vallis, “Energy spectra and coherent structures in forced two-dimensional and beta-plane turbulence,” Journal of Fluid Mechanics, 228,321 (1991). [29] P. S. Marcus, “Jupiter’s Great Red Spot and other vortices,” Annual Review of Astronomy and Astrophysics, 31, 523 (1993). [30] P. S. Marcus and C. Lee, “A model for eastward and westward jets in laboratory experiments and planetary atmospheres,” Physics of Fluids, 10, 1474(1998). [31] P. S. Marcus, T. Kundu, and C. Lee, “Vortex dynamics and zonal flows,”Physics of Plasmas 7, 1630 (2000). [32] J. C. McWilliams, “The emergence of isolated coherent vortices in turbulent flow,” Journal of Fluid Mechanics, 146, 21 (1984). [33] J. C. McWilliams, “The Vortices of Two-dimensional Turbulence.” Journal of Fluid Mechanics,Vol.219.361(1990). [34] G. D. Nastrom and K. S. Gage, “A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft,” Journal of the Atmospheric Sciences, 42, 95CC960 (1985). [35] T. Nozawa and S. Yoden, “Formation of zonal band structure in force two-dimensional turbulence on a rotating sphere,” Physics of Fluids, 9, 2081(1997). [36] T. Nozawa and S. Yoden, “Spectral anisotropy in forced two-dimensiona turbulence on a rotating sphere,” Physics of Fluids, 9, 2081(1997). [37] R. Panetta, “Zonal jets in wide baroclinically unstable regions: Persistence and scale selection.” Journal of the Atmospheric Sciences, 50, 2073 (1993). [38] J. Paret and P. Tabeling, “Experimental Observation of the Two-Dimensional Inverse Energy Cascade,” Physics Review Letter, 79, 4162 (1997). [39] P. B. Rhines, “Waves and turbulence on a beta-plane,” Journal of Fluid Mechanics, 69, 417 (1975). [40] T. G.. Shepherd, “Rossby waves and two-dimensional turbulence in a large-scale zonal jet.” Journal of Fluid Mechanics, 183, 467 (1987). [41] L. M. Smith and V. Yakhot, “Bose condensation and small-scale structure generation in a random force driven 2D turbulence,” Physics Review Letter, 71,352 (1993). [42] L. M. Smith and V. Yakhot, “Finite-size effects in forced two dimensional turbulence,” Journal of Fluid Mechanics, 274, 115 (1994). [43] L. M. Smith and F. Waleffe, “Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence” Physics of Fluids, 11, 1608 (1999). [44] J. Sommeria, “Experimental study of the two-dimensional inverse energy cascade in a square box.” Journal of Fluid Mechanics, 170, 139 (1986). [45] S. Sukoriansky, B. Galperin, and A. Chekhlov, “Large scale drag representation in simulations of two-dimensional turbulence,” Physics of Fluids, 11, 3043 (1999). [46] S. Sukoriansky, B. Galperin, and N. Dikovskaya, “Universal spectrum of two-dimensional turbulence on a rotating sphere and some basic features of atmospheric circulation on giant planets,” Physics Review Letter, 89, 124501 (2002). [47] G. K. Vallis and M. E. Maltrud, “Generation of mean flows and jets on a beta plane and over topography,” Journal of Physical Oceanography, 23, 1346 (1993). [48] O. U. Velasco Fuentes, and F. A. Velázquez Muñoz, “Interaction of two equal vortices on a β plane” Physics of Fluids, Volume 15, Issue 4, 1021 (2003). [49] G. P. Williams, “Planetary circulations. 1. Barotropic representation of Jovian and terrestrial turbulence.” Journal of the Atmospheric Sciences, 35,1399 (1978). | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/42990 | - |
| dc.description.abstract | 本論文以直接數值模擬(Direct Numerical Simulation，DNS)的方法研究在柯氏力影響下的二維均質(homogeneous)正壓(barotropic)紊流場。在物理空間中，我們觀察到在柯氏力影響下，流場會逐漸發展出東西向的帶狀流(zonal flow)，變成非等向性流場；然而穩態時的穩定解並非唯一，這些穩定解對應到數個穩定的帶狀流，而這些帶狀流的波數又與其流場總線性動能之間約呈線性正相關的關係。模擬發現如果初始流場就呈現帶狀流狀態，且其對應波數是穩定解中的其中ㄧ個，則流場會維持這個波數直到穩態；反之，流場會重新調整到某一個穩定的帶狀流。
在波空間中，研究發現柯氏力使得線性動能逐漸集中到ky軸上，穩態時ky軸的線性動能頻譜會生成一連串的峰值，峰點的連線接近Rhines(1975)提出的-5次方；然而在其他大部分的區域，線性動能頻譜仍然維持Kolmogorov紊流理論的-5/3次方，因此可將流場看成是非等向性的帶狀流與等向性二維紊流場的合成體。最後，我們嘗試提出一個機制來解釋在柯氏力影響下動能在不同尺度之間如何傳遞：當三角交互作用中三個波向量受羅士比波頻率而非紊流頻率主宰的時候，動能傳遞會變得沒有效率；反之，動能可以保有原本紊流的非線性傳遞機制。這使得逆向傳遞的線性動能會累積在羅士比波頻率大於紊流頻率的啞鈴形波向量部分空間的外圍。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2021-06-15T01:31:47Z (GMT). No. of bitstreams: 1 ntu-98-R96522103-1.pdf: 3030035 bytes, checksum: 9d0ee933d65f67dca92ada1c354b99d0 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | 口試委員審定書 i
誌謝 ii 中文摘要 iii 英文摘要 iv 目錄 v 表目錄 viii 圖目錄 ix 符號說明 xii 第一章 緒論 1 1-1研究背景 1 1-2研究動機與目的 6 1-3論文架構 6 第二章 基礎理論 7 2-1 慣性座標下的渦度方程式 7 2-2 旋轉座標下的渦度方程式 8 2-3 beta平面近似 9 2-4 無beta效應之二維紊流理論 9 2-4-1動能傳遞現象 9 2-4-2線性動能頻譜 13 2-4-3特徵尺度與雷諾數 14 2-5 beta效應下之二維紊流場 15 2-5-1 beta效應 15 2-5-2過渡尺度與啞鈴型動能屏障 17 2-5-3 beta效應下的流場結構 19 2-5-4帶狀流的穩定分析(Rayleigh-Kuo準則) 19 第三章 數值方法 22 3-1空間離散 22 3-2去除失真誤差 24 3-2-1截斷頻譜法 24 3-2-2網格錯位法 24 3-2-3合成法 25 3-3時間離散 26 3-4 起始條件與邊界條件 27 3-5 消散運算子 27 3-6 外力項 28 3-7 數值方法應用 28 3-8 離散頻譜分析 30 第四章 二維紊流流場 32 4-1 無beta效應之二維紊流場 32 4-1-1線性動能逆傳現象 32 4-1-2轉動動能正傳現象 35 4-2 beta效應下之二維紊流流場 37 第五章 帶狀紊流場研究 42 5-1大尺度消散 42 5-1-1 線性動能分佈 43 5-1-2 過渡尺度 45 5-1-3 帶狀流結構 46 5-1-4 動能傳遞機制 47 5-2記憶效應 52 5-2-1 初始帶狀流波數的影響 52 5-2-2 外力亂數的影響 53 5-2-3 初始線性動能的影響 54 第六章 結論與未來展望 56 6-1結論 56 6-2未來展望 59 參考文獻 60 附錄A 63 附錄B 65 圖表 67 | |
| dc.language.iso | zh-TW | |
| dc.subject | 三角交互作用 | zh_TW |
| dc.subject | 二維均質正壓紊流場 | zh_TW |
| dc.subject | 柯氏力 | zh_TW |
| dc.subject | DNS | zh_TW |
| dc.subject | Kolmogorov紊流理論 | zh_TW |
| dc.subject | DNS | en |
| dc.subject | triad-interaction | en |
| dc.subject | Rossby wave | en |
| dc.subject | 2D homogeneous barotropic turbulent flow | en |
| dc.subject | Coriolis force | en |
| dc.title | Beta平面紊流特性之研究 | zh_TW |
| dc.title | A Study of Turbulent Flows on the Beta-Plane | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 李石頓,顏瑞和,楊照彥 | |
| dc.subject.keyword | 二維均質正壓紊流場,柯氏力,DNS,Kolmogorov紊流理論,三角交互作用, | zh_TW |
| dc.subject.keyword | 2D homogeneous barotropic turbulent flow,Coriolis force,DNS,Rossby wave,triad-interaction, | en |
| dc.relation.page | 108 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-07-20 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 機械工程學研究所 | zh_TW |
| 顯示於系所單位： | 機械工程學系 | |
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