A review of open channel turbulence, focusing especially on certain features stemming from the presence of the free surface and the bed of a river. Part one presents the statistical theory of turbulence; Part two addresses the coherent structures in open-channel flows and boundary layers.

Turbulence in Open-Channel Flows

/pdf/current-research-issues-related-to-post-wildfire-runoff-and-337eq10qjd.pdf

Current research issues related to post-wildfire runoff and erosion processes

Data from laboratory flumes and natural streams show that the critical Shields stress for initial sediment motion increases with channel slope, which indicates that particles of the same size are more stable on steeper slopes. This observation is contrary to standard models that predict reduced stability with increasing slope due to the added downstream gravitational force. Processes that might explain this discrepancy are explored using a simple force-balance model, including increased drag from channel walls and bed morphology, variable friction angles, grain emergence, flow aeration, and changes to the local flow velocity and turbulent fluctuations. Surprisingly, increased drag due to changes in bed morphology does not appear to be the cause of the slope dependency because both the magnitude and trend of the critical Shields stress are similar for flume experiments and natural streams, and significant variations in bed morphology in flumes is unlikely. Instead, grain emergence and changes in local flow velocity and turbulent fluctuations seem to be responsible for the slope dependency due to the coincident increase in the ratio of bed-roughness scale to flow depth (i.e., relative roughness). A model for the local velocity within the grain-roughness layer is proposed based on a 1-D eddy viscosity with wake mixing. In addition, the magnitude of near-bed turbulent fluctuations is shown to depend on the depth-averaged flow velocity and the relative roughness. Extension of the model to mixed grain sizes indicates that the coarser fraction becomes increasingly difficult to transport on steeper slopes.

/pdf/is-the-critical-shields-stress-for-incipient-sediment-motion-2at0gou7az.pdf

Is the critical Shields stress for incipient sediment motion dependent on channel‐bed slope?

[1] Alternative general forms are considered for equations to predict mean velocity over the full range of relative submergence experienced in gravel- and boulder-bed streams. A partial unification is suggested for some previous semiempirical models and physical concepts. Two new equations are proposed: a nondimensional hydraulic geometry equation with different parameters for deep and shallow flows, and a variable-power resistance equation that is asymptotic to roughness-layer formulations for shallow flows and to the Manning-Strickler approximation of the logarithmic friction law for deep flows. Predictions by existing and new equations using D84 as roughness scale are compared to a compilation of measured velocities in natural streams at relative submergences from 0.1 to over 30. The variable-power equation performs as well as the best existing approach, which is a logarithmic law with roughness multiplier. For predicting how a known or assumed discharge is partitioned between depth and velocity, a nondimensional hydraulic geometry approach outperforms equations using relative submergence. Factor-of-two prediction errors occur with all approaches because of sensitivity to operational definitions of depth, velocity, and slope, the inadequacy of using a single grain-size length scale, and the complexity of flow physics in steep shallow streams.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2006WR005422

Flow resistance equations for gravel- and boulder-bed streams

The goal of this paper is to discuss the spatial averaging concept in environmental hydraulics and develop it further by considering transport equations for fluid momentum, passive substances, and suspended sediments. The averaging theorems, the double-averaged (in time and in space) fluid momentum equation, and advection-diffusion equations for a passive substance and suspended sediments are introduced and their limitations and applications for modeling rough-bed flows, experimental design, and data interpretation are discussed. The suggested equations differ from those considered in terrestrial canopy aerodynamics and porous media hydrodynamics by accounting for roughness mobility, change in roughness density in space and time, and particle settling effects for the case of suspended sediments. We show that the form of the double-averaged equations may depend on the type of decomposition of flow variables and that this difference may have important implications for modeling. We also show that the suggested methodology offers better definitions for hydraulic characteristics, variables, and parameters such as flow uniformity, flow two dimensionality, and bed shear stress.

Double-Averaging Concept for Rough-Bed Open-Channel and Overland Flows: Theoretical Background

In this paper it is suggested that the double-averaged (in temporal and in spatial domains) momentum equations should be used as a natural basis for the hydraulics of rough-bed open-channel flows, especially with small relative submergence. The relationships for the vertical distribution of the total stress for the simplest case of 2D, steady, uniform, spatially averaged flow over a rough bed with flat free surface are derived. These relationships explicitly include the form-induced stresses and form drag as components of the total stress. Using this approach, we define three types of rough-bed flows: (1) Flow with high relative submergence; (2) flow with small relative submergence; and (3) flow over a partially inundated rough bed. The relationships for the double-averaged velocity distribution and hydraulic resistance for all three flow types are derived and compared with measurements where possible. The double-averaged turbulent and form-induced intensities and stresses for the case of regular spherical-segment-type roughness show the dominant role of the double-averaged turbulence stresses and form drag in momentum transfer in the near-bed region.

Spatially Averaged Open-Channel Flow over Rough Bed

Limitations of access have long restricted exploration and investigation of the cavities beneath ice shelves to a small number of drillholes. Studies of sea-ice underwater morphology are limited largely to scientific utilization of submarines. Remotely operated vehicles, tethered to a mother ship by umbilical cable, have been deployed to investigate tidewater-glacier and ice-shelf margins, but their range is often restricted. The development of free-flying autonomous underwater vehicles (AUVs) with ranges of tens to hundreds of kilometres enables extensive missions to take place beneath sea ice and floating ice shelves. Autosub2 is a 3600 kg, 6.7m long AUV, with a 1600m operating depth and range of 400 km, based on the earlier Autosub1 which had a 500m depth limit. A single direct-drive d.c. motor and five-bladed propeller produce speeds of 1–2m s. Rear-mounted rudder and stern-plane control yaw, pitch and depth. The vehicle has three sections. The front and rear sections are freeflooding, built around aluminium extrusion space-frames covered with glass-fibre reinforced plastic panels. The central section has a set of carbon-fibre reinforced plastic pressure vessels. Four tubes contain batteries powering the vehicle. The other three house vehicle-control systems and sensors. The rear section houses subsystems for navigation, control actuation and propulsion and scientific sensors (e.g. digital camera, upward-looking 300 kHz acoustic Doppler current profiler, 200 kHz multibeam receiver). The front section contains forward-looking collision sensor, emergency abort, the homing systems, Argos satellite data and location transmitters and flashing lights for relocation as well as science sensors (e.g. twin conductivity–temperature–depth instruments, multibeam transmitter, subbottom profiler, AquaLab water sampler). Payload restrictions mean that a subset of scientific instruments is actually in place on any given dive. The scientific instruments carried on Autosub are described and examples of observational data collected from each sensor in Arctic or Antarctic waters are given (e.g. of roughness at the underside of floating ice shelves and sea ice).

Autonomous underwater vehicles (AUVs) and investigations of the ice-ocean interface: deploying the Autosub AUV in Antarctic and Arctic waters

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Spatially Averaged Open-Channel Flow over Rough Bed

Autonomous underwater vehicles (AUVs) and investigations of the ice-ocean interface: deploying the Autosub AUV in Antarctic and Arctic waters