Numerical Investigation on Roll-Wave Properties: Wave–Wave Interactions, Generality, and Spectrum
AbstractModeling natural roll waves in unstable open channel flows where Froude number F>2 has not been well understood. In this investigation, some evolution properties of natural roll waves are numerically disclosed, with the intention to advance the development of modeling unstable open channel flows. To simulate natural roll waves, the diffusive Saint-Venant equations are solved using a high-resolution scheme based on the finite-volume formulation. The numerical solutions of detailed wave–wave interaction processes, including wave overtaking, absorption, and spawning, are displayed. Wave overtaking and absorption result in the coalescence of multiple waves; wave spawning results in the birth of new waves. The spatial evolution of roll waves always undergoes initial, transition, and final phases. The three phases constitute a generality for roll-wave evolutions. Finally, the spectral analysis along channel reveals that both the wave period and nonperiodicity increase from upstream to downstream channel...