Improved prediction of the front runner in roll waves produced by localized disturbance

Abstract

The roll-wave packet produced by localized disturbance in turbulent clear water is studied in this paper. A recently proposed depth-averaged model with improved turbulence modelling and energy balance is used for numerical simulation compared with the classical shallow water equations. The leading wave of the wave packet, the front runner, increases in depth, velocity and celerity when propagating downstream. The front runner develops to a solitary bore with exceedingly large peak depth and velocity after travelling sufficiently long distance. Shallow water equations are found to significantly underestimate the peak depth and velocity of the front runner. The wavefront smoothly connects the wave peak to the steady-uniform flow with finite shock thickness, as opposed to the simple depth-and-velocity discontinuity predicted by shallow water equations. The bottom friction coefficient is remarkably reduced at the wavefront of the roll wave, especially at the front-runner wavefront, while shallow water equations cannot give such information. The bottom shear stress at the front runner is significantly increased, which explains the observed severe erosion in floods and debris flows.