NUMERICAL STUDY OF COALESCENCE IN ROLL WAVE DEVELOPMENT
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摘要: 滚波是一种重力作用下自由液面失稳诱发的水面波动现象, 通常可分为具有相对稳定波形和波速的周期性滚波与波形和波速不断变化的不规则滚波(自然滚波). 不规则滚波的相互作用和发展演化过程十分复杂, 至今对其认识尚不成熟. 本文采用基于雷诺平均Navier-Stokes方程的立面二维数值模型, 对不规则滚波发展过程中的吸收聚合和追赶聚合现象进行了数值模拟研究. 分析了两种聚合模式的演化过程, 给出了滚波聚合过程中完整的波形、波速、速度剖面以及湍流黏性等重要信息. 结果表明滚波的聚合过程是不规则滚波演化和增长的重要机制, 在特定条件下滚波增长由自然增长模式转变为以吸收聚合和追赶聚合为主的增长模式. 滚波聚合过程中, 依次经历后波追赶、爬升、与前波合并、内部流场调制等多个步骤, 最终形成一个具有更大波长和波高的滚波. 本文发现了在3个滚波间距较近的情况下, 会发生二重聚合现象, 即后两个滚波首先聚合, 然后与前波进一步聚合形成一个新的滚波.Abstract: Roll wave is a kind of unstable gravity driven free surface fluctuation in inclined open channel, which could be classified into two types: periodic roll wave with relatively stable waveform and wave speeds, and irregular roll wave with constantly changing waveform and wave speeds (natural roll wave). The development of irregular roll wave is a complicated process, which is studied however far from enough as compared with the regular roll waves. In this study, a numerical model based on the two-dimensional Reynolds averaged Navier-Stokes equation and the renormalization group $k$-$\varepsilon$ turbulence model was adopted. A large number of numerical simulations and statistical analyses were conducted to provide more dynamical and turbulence information about coalescence processes in irregular roll waves. The evolution processes of both absorption and overtake modes of coalescence were systematically studied to obtain the waveform, wave speeds, velocity profile and turbulence viscosity etc. Results imply that coalescence plays an important role on natural roll wave development, where under certain conditions, roll wave growth changes from regular natural growth mode to irregular mode dominated by coalescence, during which a following wave chases, climbs, and merges with the leading wave successively, along with adjustments of internal flow fields, to finally produce a new combined roll wave with larger wave length and wave height. Furthermore, it is found for the first time that when three roll waves were located closely enough, double coalescences would take place. The two tailing roll waves first coalesce to form a new following wave, which then interacts with the leading wave to produce another stronger roll wave propagating downstream.
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Keywords:
- natural roll wave /
- overtake /
- absorption /
- two-dimensional model
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[1] Cornish V. Ocean Waves and Kindred Geophysical Phenomena. Cambridge: Cambridge University Press, 1934 [2] Dressler RF. Mathematical solution of the problem of roll-waves in inclined open channels. Communications on Pure and Applied Mathematics, 1949,2:149-194 [3] Brooke TB. Wave formation in laminar flow down an inclined plane. Journal of Fluid Mechanics, 1957,2:554-573 [4] Needham DJ, Merkin JH. On roll waves down an open inclined channel. Proceedings of the Royal Society of London A, 1984,394:259-278 [5] Richard GL, Gavrilyuk SL. A new model of roll waves: comparison with Brock's experiments. Journal of Fluid Mechanics, 2012,698:374-405 [6] Hanratty TJ, Hershman A. Initiation of roll waves. AICHE Journal, 1961,7(3):488-497 [7] Balmforth NJ, Mandre S. Dynamics of roll waves. Journal of Fluid Mechanics, 2004,514:1-33 [8] Cristo CD, Lervolino M, Vacca A, et al. Influence of relative roughness and Reynolds number on the roll-waves spatial evolution. Journal of Hydraulic Engineering, 2010,136(1):24-33 [9] 王玉海, 喻国华, 胡彦君. 明渠水流自由面失稳与滚波发育研究. 水科学进展, 2006,6:881-886 (Wang Yuhai, Yu Guohua, Hu Yanjun. Instabilities of free surface in open-channel flows and development of roll waves. Advances in Water Science, 2006,6:881-886 (in Chinese))
[10] 张敏, 周吉军. 泄水陡槽中滚波的危害及预防. 中国农村水利水电, 2001(S1):109-110 (Zhang Min, Zhou Jijun. The hazards and prevention of roll waves in the drain chute. China Rural Water and Hydropower, 2001(S1):109-110 (in Chinese))
[11] Liu QQ, Chen L, Li JC, et al. Roll waves in overland flow. Journal of Hydrologic Engineering, 2005,10(2):110-117 [12] 李侃禹, 曹志先, 谈广鸣. 可冲刷坡面滚波影响因素的数值模拟研究. 应用基础与工程科学学报, 2012,20(6):987-993 (Li Kanyu, Cao Zhixian, Tan Guangming. Factors influenced on the morphology and hydrodynamics of roll waves in overland flow over mobile bed. Journal of Basic Science and Engineering, 2012,20(6):987-993 (in Chinese))
[13] 张宽地, 王光谦, 王占礼 等. 人工加糙床面薄层滚波流水力学特性试验. 农业工程学报, 2011,27(4):28-34 (Zhang Kuandi, Wang Guangqian, Wang Zhanli, et al. Experiments on hydraulic characteristics of roll wave for sheet flow with artificial rough bed. Transactions of the CSAE, 2011,27(4):28-34 (in Chinese))
[14] 黄子一. 用一种新TVD有限体积格式模拟间断行进滚波的演化. 水动力学研究与进展A辑, 2015,30(3):251-258 (Huang Ziyi. Modeling evolution of discontinuous progressing roll waves using a novel TVD finite volume scheme. Chinese Journal of Hydrodynamics, 2015,30(3):251-258 (in Chinese))
[15] Cao Z, Hu P, Hu K, et al. Modelling roll waves with shallow water equations and turbulent closure. Journal of Hydraulic Research, 2015,53(2):161-177 [16] 杨苗. 坡面薄层水流滚波演变规律试验研究. [博士论文]. 咸阳: 西北农林科技大学, 2017 (Yang Miao. Experimental study on evolution law of thin layer rolling wave flow on slope surface. [PhD Thesis]. Xianyang: Northwest Agriculture and Forestry University, 2017 (in Chinese))
[17] 孟鹤, 张宽地, 王静雯. 坡面薄层水流滚波水力参数影响因素. 水科学进展, 2020,31(1):102-111 (Meng He, Zhang KuanDi, Wang JingWen. Influence factors of hydraulic parameters of roll waves in overland flow. Advances in Water Science, 31(1):102-111 (in Chinese))
[18] 詹杰民, 李熠华. 波浪破碎的一种混合湍流模拟模式. 力学学报, 2019,51(6):1712-1719 (Zhan Jiemin, Li Yihua. A hybrid turbulence model for wave breaking simulation. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(6):1712-1719 (in Chinese))
[19] 徐海珏, 吴金森, 白玉川. 波浪扰动下河口幂律异重流的动力场分布特性. 力学学报, 2019,51(6):1699-1711 (Xu Haijue, Wu Jinsen, Bai Yuchuan. Dynamic distribution of power-law density current in estuary under wave. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(6):1699-1711 (in Chinese))
[20] 王展, 朱玉可. 非线性海洋内波的理论、模型与计算. 力学学报, 2019,51(6):1589-1604 (Wang Zhan, Zhu Yuke. Theory, modelling and computation of nonlinear ocean internal waves. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(6):1589-1604 (in Chinese))
[21] 邓斌, 王孟飞, 黄宗伟 等. 波浪作用下直立结构物附近强湍动掺气流体运动的数值模拟. 力学学报, 2020,52(2):408-419 (Deng Bin, Wang Mengfei, Huang Zongwei, et al. Numerical simulation of the hydrodynamic characteristics of violent aerated flows near vertical structure under wave action. Chinese Journal of Theoretical and Applied Mechanics, 2020,52(2):408-419 (in Chinese))
[22] Brock RR. Development of roll waves in open channels. [PhD Thesis]. Pasadena: California Institute of Technology, 1967 [23] Huang Z. Open channel flow instabilities: Modeling the spatial evolution of roll waves. [PhD Thesis]. Los Angles: University of Southern California, 2013 [24] Kranenburg C. On the evolution of roll waves. Journal of Fluid Mechanics, 1992,245:249-261 [25] Jeffreys HJ. The flow of water in an inclined channel of rectangular section. Philosophical Magazine, 1925,6(49):793-807 [26] Razis D, Edwards AN, Gray JMNT, et al. Arrested coarsening of granular roll waves. Physics of Fluids, 2014,26:123305 [27] Yu J, Kevorkian J. Nonlinear evolution of small disturbances into roll waves in an inclined open channel. Journal of Fluid Mechanics, 1992,243:575-594 [28] Ng CO, Mei CC. Roll waves on a shallow layer of mud modelled as a power-law fluid. Journal of Fluid Mechanics, 1994,263:151-183 [29] Brook BS, Falle SAEG, Pedley TJ. Numerical solutions for unsteady gravity-driven flows in collapsible tubes: Evolution and roll-wave instability of a steady state. Journal of Fluid Mechanics, 1999,396:223-256 [30] Chang HC, Demekhin EA, Kalaidin E. Coherent structures, self-similarity, and universal roll wave coarsening dynamics. Physics of Fluids, 2000,12(9):2268-2278 [31] Zanuttigh B, Lamberti A. Roll waves simulation using shallow water equations and Weighted Average Flux method. Journal of Hydraulic Research, 2002,40(5):610-622 [32] Barker B. Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flow. Journal of Differential Equations, 2014,257(8):2950-2983 [33] 黄灿, 刘青泉, 王晓亮. 梯级溃坝洪水洪峰增强机制. 力学学报, 2020,52(3):645-655 (Huang Can, Liu Qingquan, Wang Xiaoliang. Mechanism of peak discharge enhancement of cascade dam break floods. Chinese Journal of Theoretical and Applied Mechanics, 2020,52(3):645-655 (in Chinese))
[34] Chen XY, Wang XL, Liu QQ. Numerical study of roll wave development based on Navier-Stokes equations: A two-dimensional simulation. Journal of Engineering Mechanics, 2021,147(2):0402149 -
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