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.