Mixing layers in open channel flow with abrupt bed roughness changes

Abstract

Hydraulic roughness is a key factor in modeling open channel flow. The frictional effects of roughness elements are generally parameterized by a roughness coefficient, representative for the roughness of a grid cell in a model. Bed roughness can be very heterogeneous in practical situations. Especially in floodplains, the roughness height can differ an order of magnitude over a small distance. This roughness heterogeneity impacts the shear stress distribution and the effective friction exerted on the flow. Previous research showed that the effective friction was 20% more than the theoretically weighted average value (Jarquín, 2007) in a flume with a parallel smooth-to-rough bed. Another calculation showed even 80% additional effective friction (Jarquín, 2007; Vermaas et al., 2007). New measurements and a detailed Large Eddy Simulation model described in this report were used to investigate the underlying mixing layer processes and the corresponding development length scales. This may provide the basis to parameterize roughness heterogeneity. Measurements in a developed flow over a parallel smooth-to-rough bottom show a secondary circulation in vertical planes across the flow. This circulation causes a transverse momentum transport from the smooth to the rough side. The momentum transport by this mechanism has nearly the same order of magnitude as the transverse momentum exchange by turbulent mixing. The transverse momentum exchange enhances the effective friction. An example with a 2D model shows that this can not explain the entire increase in effective friction; additional friction is probably also caused by extra turbulence production near the smooth-to-rough interface, and bed shear stress in the spanwise direction. In the transition from a uniform flow to a compound flow over parallel roughness lanes, transverse volume transport occurs mainly in the first 4 meter (twice the width of the flume), with a maximum velocity at the start of the parallel roughness section. The development length of the velocity profiles can be scaled to the depth of flow. The vertical profiles outside the mixing layer develop in about 25 times the water depth; the mixing layer at mid depth in about 50 water depths. The secondary circulation was estimated to be fully developed after 80 water depths, but has already a significant momentum transport at half of this distance. Furthermore, the depth averaged transverse mass transport causes a gradient in the advected longitudinal momentum and therefore the water level slope is even more increased above the start of a parallel rough bottom. As a typical example of repetitive changing roughness, the flow over a roughness pattern resembling an elongated checkerboard pattern was tested. The flow appeared to develop much slower in each section than over a single parallel (infinitely long) roughness. The maximum velocity remains close to the smooth-to-rough interface and no secondary flow is observed in this configuration. Turbulent mixing is neither very effective since the vortices are changing direction not before 1 meter after a roughness change. Nevertheless, the effective friction is seriously increased by this configuration; about 30% additional friction is observed in comparison with a developed parallel flow without transverse interaction. This can be explained by the large adaptation length of the flow relative to the size of the checkerboard fields. The flow velocity is relatively large over the rough fields, and slow over the smooth fields, causing the additional drag.Hydrology and Quantitative Water ManagementWater ManagementCivil Engineering and Geoscience