Two-layer roll waves in rapid gravity currents on mild slopes

The nonlinear development of roll waves in two-layer gravity currents on mild slopes are numerically investigated using an integrated layer model including inertia effect. Periodic roll waves and roll-wave packets initiated by localized disturbance are examined for a realistic range of density and viscosity ratios. When a localized disturbance is introduced initially, the leading wave in the roll-wave packet for both of the layers (referred to as the ”front runner”) could develop exceedingly large peak depth and velocity which increase as the wave packet travels downstream. The upper-layer roll wave and lower-layer roll wave show different characteristics. The amplitude of upper-layer roll wave was found to be significantly larger than that of the lower-layer roll wave. Furthermore, peaks of upper-layer periodic roll waves or front runners always coincide with the shock-like wavefront, while peaks of lower-layer front runners with sufficiently large amplitudes are connected to the shock-like wavefront by a smooth profile. Simulations for three-dimensional two-layer flows using the integrated layer model extended to two dimensions demonstrate similar front-runner existence. However, the three-dimensional front runner has remarkably smaller peak depth and velocity than its unidirectional counterpart due to the transversal spreading of the wavefront.