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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 陳發林(Falin Chen) | |
dc.contributor.author | An-Cheng Ruo | en |
dc.contributor.author | 羅安成 | zh_TW |
dc.date.accessioned | 2021-06-13T06:37:38Z | - |
dc.date.available | 2005-10-05 | |
dc.date.copyright | 2005-10-05 | |
dc.date.issued | 2005 | |
dc.date.submitted | 2005-09-25 | |
dc.identifier.citation | Abbott, M. B. (1961) “On the spreading of one fluid over another, Part II: The wave front”. La Houille Blanche 6, 827-836.
Ames, W. F. (1965) “Nonlinear partial differential equations in engineering”, vol 1, Academic Press. Barenblatt, G. I. (1979) “Similarity, self-similarity, and Intermediate asymptotics”. Consultants Bureau. Benjamin, T. B. (1968) “Gravity currents and related phenomena”, J. Fluid Mech. 31, 209-248. Bonnecaze, R. T., Huppert, H. E. and Lister, J. R. (1993) “Particle-driven gravity currents”, J. Fluid Mech. 250, 339. Britter, R. E. (1979) “The spread of a negatively buoyant plume in a calm environment”, Atmos. Enuiron. 13, 1241-1247. Chen, F., (2000) “Smoke propagation in road tunnels”, ASME, Appl Mech Rev, 53, 207-218. Curric, I. G., (1993) “Fundamental mechanics of fluid 2/E”, McGraw-Hill Didden, N. and T. Maxworthy, T. (1982) “The viscous spreading of plane and axisymmetric gravity currents”, J. Fluid Mech. 121, 27-42. Droegemeier, K.K. and Wilhelmson, R.B. (1987) “Numerical simulation of thunderstorm outflow dynamics, part I: outflow sensitivity experiments and turbulence dynamics”, J. Atmos. Sci., 44, 1180-1210. Fannelop, T. K. and Waldman, G. D. (1971) “Dynamics of oil slicks”, AIAA J. 10, 506. Fay, J. A. (1969) “The spread of oil slicks on a calm sea”, In Oil on the sea (ed. D. P. Hoult), 46-63. Gratton, J. and Vigo, C. (1994) “Self-similar gravity currents with variable inflow revisited: plane currents”, J. Fluid Mech. 258, 77-104. Groebelbauer, H. P, Fannelop, T. K. and Britter, R. E. (1993) “The propagation of intrusion fronts of high density ratios”, J. Fluid Mech. 250, 669-687. Grundy, R. E. and Rottman, J. W. (1985) “The approach to self-similarity of the solutions of the shallow-water equations representing gravity-current releases”, J. Fluid Mech. 156, 39-53. Grundy, R. E. and Rottman, J. W. (1986) “Self-similar solutions of the shallow-water equations representing gravity currents with variable inflow”, J. Fluid Mech. 169, 337. Hallworth, M., Huppert, H. and Ungarish, M. (2003) “On inwardly propagating high-Reynolds-number axisymmetric gravity currents”, J. Fluid Mech. 494, 255-274. Hartel, C., Meiburg, E. and Necker, F. (2000) “Analysis and direct numerical simulation of the flow at a gravity-current head. Part 1. Flow topology and front speed for slip and no-slip boundaries”, J. Fluid Mech. 418, 189-212. Hoult, D. P. (1972) “Oil spreading on the sea”, Ann. Rev. Fluid Mech. 4, 341-365. Huppert H. E., (1982) “The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface,” J. Fluid Mech. 121, 43 Hogg, A. J. and Pritchard, D. (2004) “The effects of hydraulic resistance on dam-break and other shallow inertial flows”, J. Fluid Mech. 501, 179-212. Karman, T. von (1940) “The engineer grapples with nonlinear problems”, Bull. Am. Math. Soc. 46, 615. Kevorkian, J. and Cole, J. D. (1981) “Perturbation methods in applied mathematics”, Springer-Verlag . Klemp, J. B., Rotunno, R. and Skamarock, W. C. (1994) “On the dynamics of gravity currents in a channel”, J. Fluid Mech. 269, 169-198. K. K. Droegemeier and R. B. Wilhelmson, (1987) “Numerical simulation of thunderstorm outflow dynamics. Part I: Outflow sensitivity experiments and turbulence dynamics,” J. Atmos. Sci. 44, 1180 –1210. Lamb, H. (1945) “Hydrodynamics”. Dover Mei, C.C., (1995) “Mathematical analysis in engineering : how to use the basic tools”, New York, NY, USA : Cambridge University press. Mei, C.C., (2001) “Advanced fluid dynamics of the environment, Lecture note. chapter 2” (http://web.mit.edu/1.63/www/lecnote.html) Montgomery, P. J., Moodie T. B., (1999) “Two-layer gravity currents with topography”, Stud. App. Math, 102 (3): 221-266. Moodie T. B., (2002) “Gravity currents”. J. Comp. Appl. Math., 144, 49- Rottman, J. W. and Simpson, J. E. (1983) “Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel”, J. Fluid Mech. 135, 95-110. Ruo, A. C. and Chen, F., (2004) “A similarity transformation for inviscid non-Boussinesq gravity currents”, ACTA MECHANICA, 173(1-4), 33-40. Ruo, A. C. and Chen, F., (2005) “On the front condition for compositional gravity currents”, Theoret. Comput. Fluid Dynamics, 18(6), 435-441. Simpson, J. E. (1997) “Gravity currents in the environment and in the laboratory”, 2nd ed. Cambridge University Press (1st edn. 1987, Ellis-Hornwood, Chichester) Simpson, J. E. and Britter, R. E. (1979) “The dynamics of the head of a gravity current advancing over a horizontal surface”, J. Fluid Mech. 94, 477-495. Slim, A. C. and Huppert, H. (2004) “Self-similar solutions of the axisymmetric shallow-water equations governing converging inviscid gravity currents”, J. Fluid Mech. 506, 331-355. Stansby, P. K., Chegini, A. and Barnes, T. C. D. (1998) “The initial stages of dam-break flow”, J. Fluid Mech. 374, 407. Stoker, J. J. (1957) “Water Waves”. Interscience. Zoppou , C. and Roberts, S. (2000) “Numerical solution of the two dimensional unsteady dam break”, Applied Mathematical Modeling, 24, 457-475. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/34959 | - |
dc.description.abstract | 重力流的研究在理論解析方法上,通常是發展一套數學模式(即所謂的淺水方程式shallow-water equation, SWE),並求其解來模擬分析重力流的相關現象。然而這套方程式並沒有考慮任何來自外圍流體的阻力,使得其解與許多實驗觀察結果不符合,無法正確預測重力流之流動行為。為了使這套模型能被應用合宜,先前學者們便在重力流的前緣處套用一個波前條件來解SWE。雖然這個方法已被廣泛並有效地應用在許多重力流的研究上,但由於波前條件僅適用於二維流場,因此使得淺水方程式一直無法用來預測三維流場的行為,此為其一大缺點。另外一方面,雖然波前條件的使用已經導致理論分析上很大成功,但卻沒有人曾解釋過為何會成功的原因。從數學上看來,使用這個波前條件來解一套雙曲線型的方程式是不嚴謹的,所以「使用波前條件」被視為只是一個邏輯性的妥協,並非正規或嚴謹的方法。
本論文的主要目的,是發展一套由基本統御方程式出發的完整數學模型,並把影響重力流動力行為甚鉅的形狀阻力(form drag)包含在方程式中,使得本模型可以不用波前條件便足以適當的描述重力流之動力行為。因此本模型可被擴充和應用至三維流場的分析,這是重力流理論分析的一大進展。更特別的是,我們利用微擾法中一種很有用的方法-貼合漸近展開法,可將重力流分成靠近頭部的內場區域和遠離頭部的外場區域,分別解得各區域的近似解,最後再貼合起來成為全解。結果顯示,我們所獲得的外場方程式便等於SWE,而我們的內場分析竟然可以回復成波前條件。最終我們便可由此結果清楚地解釋為何波前條件解淺水方程的方法可以奏效的原因。 研究結果亦顯示,重力流前緣的阻力主要來自於將外圍流體排開之形狀阻力。但當密度比很小時,形狀阻力式微,此時黏滯阻力才變得重要。因此對密度比不很小的重力流而言,本理論模型可以適當地描述出重力流主要的行為。 | zh_TW |
dc.description.abstract | To analyze the motion of gravity currents, a common approach is to solve the hyperbolic shallow water equations (SWE) together with the boundary conditions at both the current source far upstream and the current front at the downstream margin. The use of the front condition aims to take the resistance from the ambient fluid into account, however, which is absent in the SWE. In the present study, we re-derive the SWE by taking the ambient resistance into account, and end up with the so-called modified shallow water equations (MSWE) in which the ambient resistance is accounted for by a nonlinear term, so that the use of the front condition becomes unnecessary. These highly nonlinear equations are approximated by perturbation expansions to the leading order, and the resultant singular perturbation equations are solved by an inner-outer expansion. For constant-flux and constant-volume gravity currents, the outer solutions turn out to be exactly the same as the previous ones obtained by solving SWE with the front condition. The inner solution gives both the profile and the velocity of the current head and also leads to the recovery of the front condition while is in a more general form. The combination of inner and outer solutions gives a composite solution for the whole current, which was called by Benjamin (1968) a “formidably complicated” task. To take the turbulent drag on the current into account, we introduce the semi-empirical Chezy drag term into the MSWE and end up with a result comparable with experimental data. The result implies that the ambient resistance is contributed mainly by the inviscid form drag, and the viscous drag dominates only when the density ratio is small. Furthermore, the MSWE can be extended for three-dimensional viscous currents, while will become more complicate that present analytical approach may not be feasible. | en |
dc.description.provenance | Made available in DSpace on 2021-06-13T06:37:38Z (GMT). No. of bitstreams: 1 ntu-94-D89543004-1.pdf: 4499222 bytes, checksum: a66e43dd6298e1daaa8cc23ed6ee1ba6 (MD5) Previous issue date: 2005 | en |
dc.description.tableofcontents | 英文摘要 i
中文摘要 ii 致謝 iii 目錄 iv 表目錄 vii 圖目錄 vii 符號對照表 x 第一章 緒 論 1 1.1 基本現象的描述 2 1.2 流場的特徵與研究上的困難 5 1.2.1 實驗室的觀察方法 6 1.2.2 研究上的困難點 7 1.3 文獻回顧 8 1.3.1 自由表面流的潰壩問題 10 1.3.2 海面下的潰壩問題 11 1.3.3 穩態分析方法 14 1.3.4 其它相關重要文獻 17 1.4 研究動機 20 1.4.1 邏輯性的妥協 21 1.4.2 本文的目標 21 1.5 本文架構 22 第二章 重力流理論分析之初探-穩態分析 23 2.1 穩態的重力流模型 23 2.2 二維勢流理論之應用 27 2.2.1 單層重力流 28 2.2.2 雙層重力流 31 2.2.3 考慮外圍流體之流動 33 第三章 淺水方程之修正式 34 3.1 二維淺水方程式之推導 35 3.2 二維淺水方程之修正 40 3.2.1 未知速度 的分解 42 3.2.2 包含速度勢 的微分項之分解 44 3.2.3 二維淺水方程之修正式 46 第四章 固定入流率的重力流分析 48 4.1 外場分析 49 4.1.1 外場方程式與異性微擾 49 4.1.2 相似變換法 51 4.2 內場分析 54 4.3 使用貼合的技巧獲得完整的解 57 4.3.1 外解間的貼合 58 4.3.2 內解與外解的貼合 59 4.3.3 完整的貼合解 62 4.4 解的合理性與細部討論 63 4.4.1 解的合理性和成立條件 63 4.4.2 解的極限與其物理涵義 64 第五章 固定體積的重力流分析 68 5.1 初始潰散期 (initial slumping phase) 69 5.1.1 外場分析 69 5.1.2 內場的獨立性 72 5.1.3 貼合出完整解 72 5.1.4 應用與討論 74 5.2自我相似期 (Self-similar phase) 75 5.2.1 外場方程式 75 5.2.2 相似解 76 5.2.3 貼合的工作 78 5.2.4 乾區解 (dry-zone solutions) 80 第六章 MSWE之衍生式 85 6.1 黏滯阻力項的修正-柯西阻力 85 6.1.1 外場分析 87 6.1.2 內場分析 87 6.2 三維的MSWE 90 第七章 結果討論與展望 95 7.1 本理論方法與結果之總回顧 95 7.2 非線性本質和相似解的真義 98 7.2.1 非線性本質 99 7.2.2 相似解的真義 100 7.3 理論與實驗誤差之來源剖析 101 7.4 其它特別應用與展望 102 7.5 結語 103 參考文獻 104 附錄 A 相似轉換群之推導 108 附錄B 第一階微擾解為零之佐證 113 附錄 C 軸對稱重力內解獨立性之證明 115 附錄 D 不同釋放條件下所有解之總整理 118 附錄 E 用微擾法解MSWE之流程圖 119 作者簡歷 120 | |
dc.language.iso | zh-TW | |
dc.title | 無黏性重力流新解 | zh_TW |
dc.title | The New Approach for Inviscid Gravity Currents | en |
dc.type | Thesis | |
dc.date.schoolyear | 94-1 | |
dc.description.degree | 博士 | |
dc.contributor.oralexamcommittee | 翁政義(Cheng-I Weng),陳朝光(Chao-Kuang Chen),陳文華(Wen-Hwa Chen),葛煥彰(Huan-Jang Keh),曲新生(CHU HSIN-SEN) | |
dc.subject.keyword | 重力流,異重流,淺水波方程式,波前條件,形狀阻力,移動性邊界,潰壩,貼合展開法, | zh_TW |
dc.subject.keyword | gravity current,shallow water equations,front condition,form drag,moving boundary,Dam break,method of matched asymptotic expansion, | en |
dc.relation.page | 119 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2005-09-27 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 應用力學研究所 | zh_TW |
顯示於系所單位: | 應用力學研究所 |
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