Double-average methodology applied to turbulent gravel-bed river flows

For low relative roughness, the flow near the bed is three-dimensional and spatially hetero-geneous, and bed forms play a major role. To incorporate the effects of bed irregularity, upscaling above the dominant wavelength of the bed forms is needed. This can be obtained by applying spatial averaging to the RANS equations resulting in the so-called double-averaged (both in time and space) Navier-Stokes equations. When compared to the RANS equations, these equations provide additional terms, i.e. form-induced stresses. The present work presents and discusses instantaneous velocity measurements made in the Swiss river Venoge, using an Acoustic Velocity Profiler (ADVP). A 3D measuring grid with 15 pro-files was defined. The riverbed, composed of coarse round gravel, presented a relative submergence of 2.94. Double-averaging is applied to velocity and to fluid stresses distributions. Three regions of the flow are identified: surface, intermediate and roughness layers. The roughness layer is below z/ h ≈ 0.40, in which the stresses distribution is determined by local effects of the bed forms. Form-induced and total normal stresses peak within the roughness layer. Form-induced normal stresses within the roughness layer are of the same order of magnitude or higher than Reynolds normal stresses.