Momentum and energy dynamics across scales in the flow over a rough bed with an array of boulders

Abstract

Turbulent flows over rough beds with macroroughness elements of low relative submergence are characteristic of natural river systems. These flows exhibit highly three-dimensional structures, including large-scale coherent patterns, complex nonlinear interactions and significant drag induced by immobile boulders. In this study, large-eddy simulations are conducted of the flow through an array of boulders on a rough bed, based on experiments by Papanicolaou et al. (2012) Acta Geophys. 60 (6), 1502-1546. The analysis includes the instantaneous flow dynamics, the parameterisation of hydrodynamic roughness on the averaged velocity profile and the application of the double-averaged methodology. These upscaling approaches reveal the combined influence of wake turbulence and secondary currents (SCs), and provide insights into momentum and energy conservation mechanisms, which are critical for transport processes in fluvial environments. Results indicate that the boulder array reduces total fluid stress at the rough bed surface to $0.5 rho u_*2$ , which can have important implications for sediment transport. Form-induced stresses, primarily originating in the boulder wakes, reach up to 37 % of total fluid stress, with peak values comparable to turbulent stresses at mid-boulder elevation. Form-induced kinetic energy (DKE) is shown to have the same magnitude as the turbulent kinetic energy (TKE), highlighting energy transfers from mean flow drag to DKE, then to TKE, before final dissipation. This study underscores the critical role of macroroughness in stress distribution, and the importance of the joint action of SCs and wake turbulence in driving form-induced stresses, which partially counterbalance drag dissipation.