The structure of gravel‐bed flow with intermediate submergence: A laboratory study

Abstract

The paper reports an experimental study of the flow structure over an immobile gravel bed in open channel at intermediate submergence, with particular focus on the near‐bed region. The experiments consisted of velocity measurements using three‐component (stereoscopic) Particle Image Velocimetry (PIV) in near‐bed horizontal plane and two‐component PIV in three vertical planes that covered three distinctly different hydraulic scenarios where the ratio of flow depth to roughness height (i.e., relative submergence) changes from 7.5 to 10.8. Detailed velocity measurements were supplemented with fine‐scale bed elevation data obtained with a laser scanner. The data revealed longitudinal low‐momentum and high‐momentum “strips” in the time‐averaged velocity field, likely induced by secondary currents. This depth‐scale pattern was superimposed with particle‐scale patches of flow heterogeneity induced by gravel particle protrusions. A similar picture emerged when considering second‐order velocity moments. The interaction between the flow field and gravel‐bed protrusions is assessed using cross correlations of velocity components and bed elevations in a horizontal plane just above gravel particle crests. The cross correlations suggest that upward and downward fluid motions are mainly associated with upstream‐facing and lee sides of particles, respectively. Results also show that the relative submergence affects the turbulence intensity profiles for vertical velocity over the whole flow depth, while only a weak effect, limited to the near‐bed region, is noticed for streamwise velocity component. The approximation of mean velocity profiles with a logarithmic formula reveals that log‐profile parameters depend on relative submergence, highlighting inapplicability of a conventional “universal” logarithmic law for gravel‐bed flows with intermediate submergence.

Sampling variability in estimates of flow characteristics in coarse‐bed channels: Effects of sample size

“…where j is von K arm an constant (j % 0.4), <u * > is spatially averaged shear velocity, <z 0 > is spatially averaged roughness height, and b 0 and b 1 are, respectively, the intercept and slope of a regression line. Although we adopted a commonly used value of von K arm an constant, it is worth noting that recent work indicates that it may also take different values [Franca et al, 2008;Ferreira, 2014;Mohajeri et al, 2015].…”

Low relative-submergence effects in a rough-bed open-channel flow

“…The roughness sublayer structure is presented and discussed in Section 4. In Section 5, the logarithmic and outer laws and its parameters will be sought by different methods, including the Clauser method with a fixed K = 0.41 and a free-K method based on the indicator function (Mohajeri et al, 2015 ;Segalini et al, 2013;Spalart, 1988). The existence and universality ofthese laws will also be discussed in Section 5 using evaluations of the mixing length and turbulence statistics.…”

Direct numerical simulation of turbulent channel flow over a surrogate for Nikuradse-type roughness

“…The friction Reynolds number, Re τ = δu τ /ν, where δ is the mean channel half-height, varies in the range 180 Re τ 720, whereas the roughness Reynolds number, k + = ku τ /ν = (k/δ)Re τ , varies in the range 3.75 k + 120 (where k is the mean peak-to-valley height and a '+' superscript indicates wall units), as shown in table 1. All cases for k + 30 are scaled to a roughness height of k/δ = 1/6, which has been previously shown to be small enough to collapse the mean flow in the outer layer (Busse et al 2015), as well as being directly relevant to flow over gravel beds (Mohajeri et al 2015) and urban environments (Orlandi & Leonardi 2006). The computational domain size scales with the roughness height, and k/δ = 1/6 leads to streamwise, L x , and spanwise, L y , domain extents of 5.63δ and 2.815δ respectively, where L y = L x /2.…”