Surface reactions such as the adsorption and desorption at boundaries are very common for solute dispersion in many applications of chemistry, biology, hydraulics, etc. To study how reversible adsorption affects the transient dispersion, Zhang, Hesse & Wang (J. Fluid Mech., vol. 828, 2017, pp. 733–752) have investigated the temporal evolution of moments using the Laplace transform method. Owing to difficulties introduced by the adsorption–desorption boundary condition, great challenges arise from the inverse Laplace transform: dealing with the singularities by the residue theorem can tremendously increase complexities. This work provides a much simpler analytical method to derive solutions in a more compact form that is valid for the entire range of the reactive transport process. Such a progress demonstrates that the classic framework of separation of variables can be extended and applied to this more general adsorption–desorption condition, based on which higher-order statistics including skewness and kurtosis can be explicitly explored in practice. Also extended is Gill's generalised dispersion model for solute concentration distributions, which can now address the entire transient dispersion characteristics, instead of just applied for the long-time asymptotic reactive process as done previously. Regarding the most classic Taylor dispersion problem, we investigate the influence of the reversible adsorption–desorption on the solute cloud in a tube flow. Not only the transient dispersion characteristics of transverse-average concentration distribution but also those of the bulk, surface and total-average distributions are discussed. We further investigate the influence of initial conditions on the non-uniformity of the transient dispersion over the cross-section.

River dams provide many benefits, including flood control. However, due to constantly evolving channel morphology, downstream conveyance of floodwaters following dam closure is difficult to predict. Here, we test the hypothesis that the incised, enlarged channel downstream of dams provides enhanced water conveyance, using a case study from the lower Yellow River, China. We find that, although flood stage is lowered for small floods, counterintuitively, flood stage downstream of a dam can be amplified for moderate and large floods. This arises because bed incision is accompanied by sediment coarsening, which facilitates development of large dunes that increase flow resistance and reduce velocity relative to pre-dam conditions. Our findings indicate the underlying mechanism for such flood amplification may occur in >80% of fine-grained rivers, and suggest the need to reconsider flood control strategies in such rivers worldwide.

Through using a kinetic model for particles in turbulent solid–liquid flows, underlying mechanisms of sediment vertical dispersion as well as sediment diffusion coefficient are investigated. Four hydrodynamic mechanisms, namely gravitational settling, turbulent diffusion, effect of lift force, and that of sediment stress gradient, coexist in two-dimensional (2D) uniform and steady open-channel flows. The sediment diffusion coefficient consists of two independent components: one accounts for the advective transport of sediment probability density distribution function due to sediment velocity fluctuations, and the other results from sediment–eddy interactions. Predictions of the kinetic model are in good agreement with experimental data of 2D open-channel flows. In such flows, it is shown that: (1) the parameter γ (i.e., the inverse of the turbulent Schmidt number) may be greater than unity and increases toward the bed, being close to unity for fine sediments and considerably large for coarse ones; (2) eff...

The rich and complex phenomena of the transport of active particles like microorganisms in shear flows are of great significance to various biological and environmental applications. Recent studies have shown that the motility and gyrotaxis of algae could greatly influence their transport in waters. However, little attention has been paid to the initial and transient transport regime when the classical Taylor dispersion model is not applicable. To tackle this problem, we resort to Gill's generalized dispersion model for passive particles like solute, which has the potential for accurately describing the entire transport process. For the first time, we extend Gill's model to the active particles, and the effects of swimming, gyrotaxis, and flow shear on the microorganism dispersion in an open‐channel flow have been thoroughly investigated. We first theoretically solve the transient drift and dispersion coefficients, based on which we obtain analytical solutions for concentration distributions of microorganisms, and further validate these results by numerically solving the governing equation. We find that when there is no flow, the longitudinal dispersion of microorganisms can be weakened by the gravitactic accumulation in the vicinity of water surface, while enhanced by a stronger swimming ability of the microorganisms. The effect of the flow shear does not affect the form of the asymptotic concentration distribution, but can greatly enhance the transient drift velocity and the dispersivity. We further analyze the effect of turbulence on microorganisms' dispersion by combing the direct numerical simulation and the random walk simulation. The increase of turbulence is shown to decrease the vertical non‐uniformity of the concentration distribution, as well as the relative contribution of active behavior to both the drift and Taylor dispersivity during transport.

Bedload particle hops are defined as successive motions of a particle from start to stop, characterizing one of the most fundamental processes of bedload sediment transport in rivers. Although two transport regimes have been recently identified for short and long hops, respectively, there is still the lack of a theory explaining the mean hop distance–travel time scaling for particles performing short hops, which dominate the transport and may cover over 80 % of the total hop events. In this paper, we propose a velocity-variation-based formulation, the governing equation of which is intrinsically identical to that of Taylor dispersion for solute transport within shear flows. The key parameter, namely the diffusion coefficient, can be determined by hop distances and travel times, which are easier to measure and more accurate than particle accelerations. For the first time, we obtain an analytical solution for the mean hop distance–travel time relation valid for the entire range of travel times, which agrees well with the measured data. Regarding travel times, we identify three distinct regimes in terms of different scaling exponents: respectively, 5/3 for the transition regime, which define the short hops, and 1 for the Taylor dispersion regime defining long hops. The corresponding distribution of the hop distance is analytically obtained and experimentally verified. We also show that the conventionally used exponential distribution, as proposed by Einstein, is solely for long hops. Further validation of the present formulation is provided by comparing the simulated accelerations with measurements.