滚波演化中聚合过程的数值模拟研究

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. 

NUMERICAL STUDY OF COALESCENCE IN ROLL WAVE DEVELOPMENT

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.