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A Comparative Analysis of Logarithmic Law, Reynolds Stress, and Turbulence Kinetic Energy Methods for Bed Shear Stress Estimation in Complex Open‐Channel Flow
Numerous indirect methods for estimating the bed shear stress using velocity or turbulent stress profiles have been suggested in previous research. Although these methods have proven effective for simple boundary‐layer‐type flows, their efficacy in complex flow scenarios remains largely unexplored. This study aimed to evaluate the predictive capabilities of three popular indirect bed‐shear‐stress estimation methods—the logarithmic law, Reynolds shear stress (RSS), and turbulence kinetic energy (TKE) techniques—in a complex flow environment involving an obstacle in an open channel, producing massive flow separation and unsteady vortex shedding. To circumvent the difficulties of direct bed shear‐stress measurements, the reference bed shear stress was obtained from a high‐resolution wall‐resolving large‐eddy simulation (LES) data set. The key findings of this study are as follows: First, the logarithmic law and TKE methods were effective only in regions where the streamlines were almost parallel to the primary flow direction. Second, the ratio of the bed shear stress to TKE varied significantly in space in complex‐flow regions, rendering TKE methods virtually ineffective in these areas. Third, the RSS methods successfully reproduced the LES‐computed bed shear stress distributions, both qualitatively and quantitatively. Fourth, the accuracy of the RSS methods was influenced by two critical factors: (a) the incorporation of the transverse RSS component in the RSS extrapolation and (b) the selection of extrapolation techniques. Finally, this study recommends the use of RSS methods employing two‐point extrapolation for bed shear‐stress estimation in complex flows. Key Points Indirect methods were tested to estimate bed shear stress in a complex flow setting using high‐resolution large‐eddy simulation data Log‐law and turbulence kinetic energy methods were effective for straight flow regions but unsuitable for regions with complex flows The Reynolds shear stress method using two‐point extrapolation with a lower point close to the bed was the most effective
Journal Article
Onset for Active Swimming of Microorganisms to Shape Their Transport in Turbulent Open Channel Flows
Research on active particles has primarily focused on transport in relatively weak flows, during which their active swimming plays a significant role. However, in natural or manmade waterways, the ambient flow velocity and water depth can be on the order of approximately 1 m/s and 1 m, respectively, generating turbulent diffusion that may be strong enough to potentially dominate the transport process, so that the active swimming might be negligible. In this paper, we propose a theoretical framework aiming at identifying the threshold at which the effects of active swimming become significant, under conditions of insufficient data for motion statistics of swimmers. While deriving the governing equation, we find that only the vertical component of the mean swimming has the potential to significantly influence the transport process. This manifests as the characteristic of inducing a non‐uniform vertical concentration distribution, in competition with the mechanism of turbulent diffusion, which leads to a uniform distribution. We obtain the analytical solution for the vertical concentration distribution, with the key dimensionless parameter α representing the interplay between the active swimming and turbulent diffusion. The threshold is found to be approximately at the order of magnitude of α ∼ 0.1, below which active swimming is considered negligible. The theoretical predictions are validated by numerical simulations employing Direct Numerical Simulation and particle tracking methods. Applying the theory to two types of microorganisms transported under different flow conditions suggests that there are typical scenarios where the active swimming is negligible, and the swimmers can be treated as passive particles. Key Points Only the vertical component of the mean swimming velocity has the potential to significantly influence the transport of active swimmers Threshold for observable active behavior in transport reveals competition between active swimming and turbulent diffusion There are typical scenarios where active swimming is negligible, and the swimmers can be treated as passive particles
Journal Article
Homotopy-based methods in water engineering
\"Exploring the concept of homotopy from topology, different kinds of homotopy-based methods have been proposed for analytically solving nonlinear differential equations, given by approximate series solutions. Homotopy-Based Methods in Water Engineering attempts to present the wide applicability of these methods to water engineering problems. It solves all kinds of nonlinear equations, namely algebraic/transcendental equations, ordinary differential equations (ODEs), systems of ODEs, partial differential equations (PDEs), system of PDEs, and integro-differential equations using the homotopy-based methods\"-- Provided by publisher.
BOOK
Direct numerical simulation of turbulent open channel flows at moderately high Reynolds numbers
Well-resolved direct numerical simulations of turbulent open channel flows (OCFs) are performed for friction Reynolds numbers up to $Re_\\tau =2000$. Various turbulent statistics are documented and compared with the closed channel flows (CCFs). As expected, the mean velocity profiles of the OCFs match well with the CCFs in the near-wall region but diverge notably in the outer region. Interestingly, a logarithmic layer with Kárman constant $\\kappa =0.363$ occurs for OCF at $Re_\\tau =2000$, distinctly different from CCF. Except for a very thin layer near the free surface, most of the velocity and vorticity variances match between OCFs and CCFs. The one-dimensional energy spectra reveal that the very-large-scale motions (VLSMs) with streamwise wavelength $\\lambda _x>3 h$ or spanwise wavelength $\\lambda _z>0.5 h$ contribute the most to turbulence intensity and Reynolds shear stress in the overlap and outer layers (where h is the water depth). Furthermore, the VLSMs in OCFs are stronger than those in CCFs, resulting in a slightly higher streamwise velocity variance in the former. Due to the footprint effect, these structures also have significant contributions to the mean wall shear stress, and the difference between OCF and CCF enlarges with increasing $Re_\\tau$. In summary, the free surface in OCFs plays an essential role in various flow phenomena, including the formation of stronger VLSMs and turbulent kinetic energy redistribution.
Journal Article
Secondary currents and very-large-scale motions in open-channel flow over streamwise ridges
It is widely acknowledged that streamwise ridges on the bed of open-channel flows generate secondary currents (SCs). A recent discovery of meandering long streamwise counter-rotating vortices in open-channel flows, known as very-large-scale motions (VLSMs), raises a question regarding the interrelations between VLSMs and SCs in flows over ridge-covered fully rough beds. To address it, we conducted long-duration experiments using stereoscopic particle image velocimetry, covering a range of ridge spacings ($s$) from${\\approx}0.4$to${\\approx}4$flow depths ($H$). For a benchmark no-ridge case, the flow is quasi-two-dimensional in the central part of the channel, exhibiting a strong spectral signature of VLSMs, as expected. With ridges on the bed at$s\\lessapprox 2H$, two SC cells are formed between neighbouring ridges and VLSMs are entirely suppressed, suggesting that ridge-induced SCs prevent the formation of VLSMs by absorbing their energy or overpowering their formation. At the same time, velocity auto- and cross-spectra reveal a new feature that can be explained by low-amplitude meandering of the alternating low- and high-momentum flow regions associated with instantaneous manifestations of SCs. Two-point velocity correlations and smooth velocity field reconstructions using proper orthogonal decomposition further support the validity of this effect. Its origin is probably due to the instability related to the presence of inflection points in the spanwise distribution of the streamwise velocity within the SC cells. These results have implications for bed friction in open channels, where the friction factor may increase if depth-scale SCs are present, or decrease under conditions of sub-depth-scale SCs and suppressed VLSMs.
Journal Article
An Improved Physical Model for Open Channel Confluences: Bridging the Gap Between Laboratory and Field Observations
Despite decades of research on hydro‐morphodynamic processes at open‐channel confluences, significant discrepancies persist between flume experiments and field observations. This study investigated the underlying causes by compiling and comparing geometric and hydraulic parameters from both natural confluences and laboratory setups. The analysis suggested that these discrepancies largely stem from unrealistic boundary conditions commonly used in experimental designs. To address this issue, this study developed an improved physical model of concordant confluences that more accurately replicated the morpho‐hydraulic characteristics of natural confluences. Key features included a smooth downstream junction, a large post‐confluence width‐to‐depth ratio, downstream channel widening, representative junction angle and discharge ratio. This experiment avoided the unrealistic large separation zone and scour holes near the downstream junction corner caused by sharp‐angled junction. Large Reynolds stresses and turbulent kinetic energy within the shear layer primarily drove scour hole formation, while streamwise‐oriented vortical cells offered additional contributions. In contrast, flow acceleration along the main channel promoted scour step development through low‐intensity sediment redistribution. This study presented a more realistic and representative physical model for simulating hydro‐morphodynamics at confluences with concordant beds and helped bridge the gap between laboratory findings and field‐scale dynamics.
Journal Article
On the role of turbulent large-scale streaks in generating sediment ridges
The role of turbulent large-scale streaks or large-scale motions in forming subaqueous sediment ridges on an initially flat sediment bed is investigated with the aid of particle resolved direct numerical simulations of open channel flow at bulk Reynolds numbers up to 9500. The regular arrangement of quasi-streamwise ridges and troughs at a characteristic spanwise spacing between 1 and 1.5 times the mean fluid height is found to be a consequence of the spanwise organisation of turbulence in large-scale streamwise velocity streaks. Ridges predominantly appear in regions of weaker erosion below large-scale low-speed streaks and vice versa for troughs. The interaction between the dynamics of the large-scale streaks in the bulk flow and the evolution of sediment ridges on the sediment bed is best described as ‘top-down’ process, as the arrangement of the sediment bedforms is seen to adapt to changes in the outer flow with a time delay of several bulk time units. The observed ‘top-down’ interaction between the outer flow and the bed agrees fairly well with the conceptual model on causality in canonical channel flows proposed by Jiménez (J. Fluid Mech., vol. 842, 2018, P1, § 5.6). Mean secondary currents of Prandtl's second kind of comparable intensity and lateral spacing are found over developed sediment ridges and in single-phase smooth-wall channels alike in averages over ${O}(10)$ bulk time units. This indicates that the secondary flow commonly observed together with sediment ridges is the statistical footprint of the regularly organised large-scale streaks.
Journal Article
Contributions of very large-scale motions to turbulence statistics in open channel flows
Time-resolved particle image velocimetry measurements were performed in smooth-walled open channels to investigate the contributions of very large-scale motions (VLSMs) to the turbulence characteristics in open channel flows. The focal point is to clarify the free surface effects on the characteristics of VLSMs and the contributions of VLSMs to the unique statistical features in open channel flows (i.e., the turbulent kinetic energy (TKE) redistribution and smaller wake strength of the mean velocity profile). The resulting wavelength of VLSMs in present smooth-walled open channels is approximately$20h$($h$is water depth), which is comparable to that in pipe and closed channels while smaller than that in rough-walled open channels, and they are shown to make a great contribution to turbulence statistics with over 50 % of streamwise turbulence intensity, Reynolds shear stress and negative net force coming from VLSMs in the outer layer. Compared with other wall-bounded flows, VLSMs maintain higher strength in the outer layer of open channel flows with non-negligible strength even in the near surface region ($y\\sim >0.8h$), indicating that the free surface seems to sustain/promote VLSMs. This strength difference of VLSMs closely relates to the TKE redistribution and smaller wake strength of the mean velocity in the outer layer of open channel flows. The higher streamwise turbulence intensity is mainly contributed from the higher strength of VLSMs therein. The decelerating role of VLSMs combining with their higher strength is vital for shaping the mean velocity profile, which therefore is speculated to make a great contribution to the smaller wake strength phenomenon.
Journal Article