Numerical modelling of horizontal sediment-laden jets

Sediment-laden turbulent flows are commonly encountered in natural and engineered environments. It is well known that turbulence generates fluctuations to the particle motion, resulting in modulation of the particle settling velocity. A novel stochastic particle tracking model is developed to predict the particle settling out and deposition from a sediment-laden jet. Particle velocity fluctuations in the jet flow are modelled from a Lagrangian velocity autocorrelation function that incorporates the physical mechanism leading to a reduction of settling velocity. The model is first applied to study the settling velocity modulation in a homogeneous turbulence field. Consistent with basic experiments using grid-generated turbulence and computational fluid dynamics (CFD) calculations, the model predicts that the apparent settling velocity can be reduced by as much as 30 % of the stillwater settling velocity. Using analytical solution for the jet mean flow and semi-empirical RMS turbulent velocity fluctuation and dissipation rate profiles derived from CFD predictions, model predictions of the sediment deposition and cross-sectional concentration profiles of horizontal sediment-laden jets are in excellent agreement with data. Unlike CFD calculations of sediment fall out and deposition from a jet flow, the present method does not require any a priori adjustment of particle settling velocity.     

Mixing at a sediment concentration interface in turbulent open channel flow

In this work we address the role of turbulence on mixing of clear layer of fluid with sediment-laden layer of fluid at a sediment concentration interface. This process can be conceived as the entrainment of sediment-free fluid into the sediment-laden layer, or alternatively, as the transport of sediment into the top sediment-free flow. This process is governed by four parameters—Reynolds number of the flow \(Re_\tau\), non-dimensional settling velocity of the sediment (proxy for sediment size) \(\tilde{V}\), Richardson number \(Ri_\tau\) and Schmidt number Sc. For this work we have performed direct numerical simulations for fixed Reynolds and Schmidt numbers while varying the values of Richardson number and particle settling velocity. In the simple model considered here, the flow’s momentum and turbulence pre-exists over the entire layer of fluid, while the sediment is initially confined to a layer close to the bed. Mixing of sediment-free fluid with the sediment-laden layer is associated primarily with upward transport of sediment and buoyancy. There is no simultaneous upward transport of fluid momentum and turbulence into the sediment-free fluid layer, which is already in motion and turbulent. The analysis performed shows that the ability of the flow to transport a given sediment size decreases with the distance from the bottom, and thus only fine enough sediment particles are transported across the sediment concentration interface. For these cases, the concentration profiles evolve to a final steady state in good agreement with the well-known Rouse profile. The approach towards the Rouse profile happens through a transient self-similar state. This behavior of the flow is not seen for larger particles. Detailed analysis of the three dimensional structure of the sediment concentration interface shows the mechanisms by which sediment particles are lifted up by tongues of sediment-laden fluid with positive correlation between vertical velocity and sediment concentration. Finally, the mixing ability of the flow is addressed by monitoring the time evolution of the center of mass of the sediment-laden layer and the vertical location of the sediment-free/sediment-laden interface.     

Improved formulae of velocity distributions along the vertical and transverse directions in natural rivers with the sidewall effect

The distribution of flow velocity is a basis for the research into the transport of flow and sediment in natural rivers. Characteristics of velocity distribution in narrow-deep natural rivers are different from those in wide-shallow open channels, and the effect of sidewalls on the distribution of flow velocity is considerable, which leads to a large transverse gradient of the depth-averaged velocity, with the maximum velocity occurring below the water surface. Based on the Reynolds equation of turbulence flow and the analysis of the features of velocity distribution in natural rivers, improved formulae with two empirical parameters α and β have been proposed for the velocity distributions along the vertical and transverse directions, with the effect of sidewalls being considered, through solving the definite solution problem by the method of variable separation. The proposed formulae were validated fully through comparisons between the calculated and measured velocity profiles and depth-averaged velocities at several sections in the Yangtze and Baitarani Rivers, with close agreement between them being obtained. The formula of velocity distribution along the transverse direction in natural rivers with the sidewall effect was also compared with previous studies, and the calculation accuracy of this formula at a section with a narrow-deep geometry was higher than the accuracy of the previous equations. It is confirmed that the proposed formulae can reproduce well the distribution characteristics of flow velocity along the vertical and transverse directions in narrow-deep natural rivers, with a more wide application in practice.     

Study on the concentration distribution in a trapezoidal open-channel flow with a side discharge

The number and distribution of pollutant concentration in a trapezoidal open channel flow with a side discharge is calculated and effects of the bank gradient are investigated in this paper. A sigma-coordinate water quality numerical model is used to simulate the process of both water and pollutant transportation in the trapezoidal channel open flow. The diffusion coefficient used in the prediction is determined by two methods including constant coefficient and the depth-averaged k-epsilon turbulence closure model. The change of the concentration with the bank gradient is acquired based on the simulation of cases with different bank gradients. An analytical formula is derived by using the mirror image method and related diffusion theories, ignoring the discharge momentum and the influence of the opposite bank. The formula can predict the number and distribution of pollutant concentration with some acceptable errors. The results demonstrate that the bank gradient has great influence on the concentration distribution which will decrease with the increase of the bank gradient approximately following a hyperbolic law.     

Steady Shallow-Water Current and Solute Transport around a Semi-Conical Headland

Laboratory experiments have been carried out to investigate the effects of a sloping wall headland on the flow characteristics and the associated concentration distributions from a point source around the headland. A semi-conical headland with a slope of 1:2 was set up in a flow basin, 4.8 m long and 3.8 m wide. In this paper, the experimental results of a steady shallow-water current are reported. Three dimensional flow velocities in the basin were measured using Sontek-ADV instrument. The dye concentration levels in the basin were measured by two fluorometers. The experimental results showed a large-scale re-circulation region behind the semi-conical headland. The peak turbulence energy, at about 53% of the local kinetic flow energy, coincides with the region of high velocity gradient. Significant vertical flows were observed around the area near the downhill slope of the headland, with a maximum ratio of vertical to horizontal velocities being about 22%. Such relatively significant vertical scouring velocities, coupled with strong turbulence energy and high horizontal velocity gradients in the same region, could cause severe bed erosion. The experimental results have also been compared with the predicted results of a depth-averaged numerical model. The predicted eddy structure and the concentration distribution in the re-circulation area were found to compare favourably with the experimental results. However, the discrepancies in the flow velocities and the concentration levels near the headland were apparent. It was observed that the dye concentration continued to spread in the cross-stream direction after passing the headland, whereas only a limited extent of the lateral spreading was predicted by the numerical model further downstream of the headland.     

Model of turbulence penetration into a suspension layer on a sediment bed and effect on vertical solute transfer

The vertical diffusional mass (solute) transfer through a suspended sediment layer, e.g. at the bottom of a lake, reservoir or estuary, by the propagation of velocity fluctuations from above was investigated. The attenuation of the velocity fluctuations in the suspension layer and the associated effect on solute transfer through the suspension layer was simulated. To represent large eddies traveling downstream in water over a high-concentration suspended sediment layer, a streamwise velocity fluctuation moving in downstream direction was imposed along the upper boundary of the suspension layer. Velocity fluctuations and downstream velocity were normalized by the shearvelocity (U_*) at the top of the suspension layer. Streamwise and vertical velocity components inside the suspension layer, were obtained from the 2-D continuity and the Navier–Stokes equations. The persistence of turbulence with depth—as it penetrates from the overlying water into the suspension layer—was found to depend on its amplitude, its period, and on the apparent viscosity of the suspension. The turbulence was found to propagate efficiently into the suspension layer when its frequency is low, and the apparent viscosity of the suspension is high. Effects on vertical mass transfer were parameterized by penetration depth and effective diffusion coefficient, and related to apparent viscosity of the suspension, Schmidt number and shear velocity on top of the suspension layer. The enhancement of turbulence penetration by viscosity is similar to the flow near an oscillating flat plate (Stokes’ second problem), but is opposite to turbulence penetration into a stationary porous and permeable sediment bed. The information is applicable to water quality modeling mear the sediment/water interface of lakes, river impoundments and estuaries.     

Analytical expression for predicting the reduced settling velocity of small particles in turbulence

The influence of turbulence on the settling velocity of small particles remains an inconclusive research subject. Both enhanced and retarded particle settling compared to quiescent settling have been reported in previous literature, and several theories have been proposed. Among the mechanisms that account for reduced settling velocities in turbulence, the loitering effect is an important one that generally exists in various conditions. This study focuses on an analytical prediction of reduced particle settling velocities due to the loitering effect. By considering the velocity autocorrelation function as a step function analogous to the free path theory, and using a modified integral time scale to capture the essence of the loitering effect, an analytical expression is derived for predicting the reduction in particle settling velocities in turbulent flows. Calculation results of the expression are then examined by comparing with the results of a random walk model, direct numerical simulations that conditionally captured the reduction of particle settling velocities due to the loitering effect, and several representative experiments. Major possible influencing factors on the prediction of the analytical expression and applicable conditions of the expression are then further discussed. The proposed analytical expression is shown to be suitable for predicting the reduced settling velocities of small particles with relatively weak inertia in turbulent flows and could provide a reasonable explanation for reported cases in which small to moderate reductions in particle settling velocities were observed.

     

Buoyancy measurements and vertical distribution of eggs of sardine (<Emphasis Type="Italic">Sardina pilchardus</Emphasis>) and anchovy (<Emphasis Type="Italic">Engraulis encrasicolus</Emphasis>)

Measurements were made of the density and settling velocity of eggs of sardine (Sardina pilchardus) and anchovy (Engraulis encrasicolus), using a density-gradient column. These results were related to observed vertical distributions of eggs obtained from stratified vertical distribution sampling in the Bay of Biscay. Eggs of both species had slightly positive buoyancy in local seawater throughout most of their development until near hatching, when there was a marked increase in density and they became negatively buoyant. The settling velocity of anchovy eggs, which are shaped as prolate ellipsoids, was close to predictions for spherical particles of equivalent volume. An improved model was developed for prediction of the settling velocity of sardine eggs, which are spherical with a relatively large perivitelline volume; this incorporated permeability of the chorion and adjustment of the density of the perivitelline fluid to ambient seawater. Eggs of both species were located mostly in the top 20 m of the water column, in increasing abundance towards the surface. A sub-surface peak of egg abundance was sometimes observed at the pycnocline, particularly where this was pronounced and associated with a low-salinity surface layer. There was a progressive deepening of the depth distributions for successive stages of egg development. Results from this study can be applied for improved plankton sampling of sardine and anchovy eggs and in modelling studies of their vertical distribution.Communicated by J.P. Thorpe, Port Erin     

Characteristics of flow structure of free-surface flow in a partly obstructed open channel with vegetation patch

Free-surface flows over patchy vegetation are common in aquatic environments. In this study, the hydrodynamics of free-surface flow in a rectangular channel with a bed of rigid vegetation-like cylinders occupying half of the channel bed was investigated and interpreted by means of laboratory experiments and numerical simulations. The channel configurations have low width-to-depth aspect ratio (1.235 and 2.153). Experimental results show that the adjustment length for the flow to be fully developed through the vegetation patch in the present study is shorter than observed for large-aspect-ratio channels in other studies. Outside the lateral edge of the vegetation patch, negative velocity gradient (\(\partial \overline{u}/\partial z < 0\)) and a local velocity maximum are observed in the vertical profile of the longitudinal velocity in the near-bed region, corresponding to the negative Reynolds stress (\(- \overline{{u^{\prime}w^{\prime}}} < 0\)) at the same location. Assuming coherent vortices to be the dominant factor influencing the mean flow field, an improved Spalart–Allmaras turbulence model is developed. The model improvement is based on an enhanced turbulence length scale accounting for coherent vortices due to the effect of the porous vegetation canopy and channel bed. This particular flow characteristic is more profound in the case of high vegetation density due to the stronger momentum exchange of horizontal coherent vortices. Numerical simulations confirmed the local maximum velocity and negative gradient in the velocity profile due to the presence of vegetation and bed friction. This in turn supports the physical interpretation of the flow processes in the partly obstructed channel with vegetation patch. In addition, the vertical profile of the longitudinal velocity can also be explained by the vertical behavior of the horizontal coherent vortices based on a theoretical argument.     

Analytical model for vertical velocity profiles in flows with submerged shrub-like vegetation

An analytical solution for the vertical profiles of the horizontal velocity of channel flow with submerged shrub-like vegetation is investigated in this paper. At first, a shape function is proposed to fit the diameter change of different types of shrub-like vegetation. Using the momentum theorem and the mixing-length turbulence model, an analytical solution for the vertical profile of the horizontal velocity within the vegetation is obtained. The velocity distribution of the whole column is determined in tandem with the logarithmic velocity profile above the vegetation. The solution is compared with experimental data in excellent agreement. The results show that the flow above the vegetation has a logarithmic velocity profile while the flow within the vegetation is impacted greatly by the shape and density of vegetation. The flows within shrub-like vegetations are non-uniform and vary inversely with the shrub diameter.     

Turbulent velocity profile in fully-developed open channel flows

The determination of velocity profile in turbulent narrow open channels is a difficult task due to the significant effects of the anisotropic turbulence that involve the Prandtl’s second type of secondary flow occurring in the cross section. With these currents the maximum velocity appears below the free surface that is called dip phenomenon. The well-known logarithmic law describes the velocity distribution in the inner region of the turbulent boundary layer but it is not adapted to define the velocity profile in the outer region of narrow channels. This paper relies on an analysis of the Navier–Stokes equations and yields a new formulation of the vertical velocity profile in the center region of steady, fully developed turbulent flows in open channels. This formulation is able to predict time averaged primary velocity in the outer region of the turbulent boundary layer for both narrow and wide open channels. The proposed law is based on the knowledge of the aspect ratio and involves a parameter C_Ar depending on the position of the maximum velocity (ξ_dip). ξ_dip may be derived, either from measurements or from an empirical equation given in this paper. A wide range of longitudinal velocity profile data for narrow open channels has been used for validating the model. The agreement between the measured and the computed velocities is rather good, despite the simplification used.     

水动力条件对藻类影响的研究进展

水动力过程是影响水体富营养化状态和水华爆发的重要因素,水动力因素对藻类影响的研究对于富营养化水体藻类控制具有重要意义。归纳分析近年来关于流速、流态对藻类生长和种类变化的研究报道;就水动力条件对藻类的影响及其作用机理等详细地进行了文献综述。水动力条件对藻类生长的影响分为流速和流态两个方面,不论是单一藻种还是混合藻类,低流速、小扰动有利于藻类的生长和聚集,流速增大则导致Chla浓度先递增后递减,不同藻类的临界流速并不相同;藻类生长随着湍流程度的增加而逐渐受到抑制,抑制作用与水流流态（层流、过渡流、湍流）无明显相关关系,水体流态的变化造成水流剪应力的变化,藻类种类的差异导致其对水流剪应力的响应变化。水动力条件变化引起的藻类种群结构变化,主要表现为水体混合加剧导致优势种群的转换。水动力条件对藻类影响的作用原理主要是引起了光强的改变、细胞长度的变化、营养盐运送及捕食行为变化等。综观当前的研究成果,水动力能否真正阻止藻类细胞的生长或聚集,影响藻类生长或种类变化的扰动的最低水平以及水动力对藻类影响的作用机理是这一领域未来研究的重点所在。     

A Computational Fluid Dynamics Approach for Urban Area Transport and Dispersion Modeling

A simulation tool has been developed to model the wind fields, turbulence fields, and the dispersion of Chemical, Biological, Radiological and Nuclear (CBRN) substances in urban areas on the building to city blocks scale. A Computational Fluid Dynamics (CFD) approach has been taken that naturally accounts for critical flow and dispersion processes in urban areas, such as channeling, lofting, vertical mixing and turbulence, by solving the steady-state, Reynolds-Averaged Navier–Stokes (RANS) equations. Rapid generation of high quality cityscape volume meshes is attained by a unique voxel-based model generator that directly interfaces with common Geographic Information Systems (GIS) file formats. The flow and turbulence fields are obtained by solving the steady-state RANS equations using a collocated, pressure-based approach formulated for unstructured and polyhedral mesh elements. Turbulence modeling is based upon the Renormalization Group variant of the k–ε model (k–ε RNG). Neutrally buoyant simulations are made by prescribing velocity boundary condition profiles found by a power–law relationship, while turbulence quantities boundary conditions are defined by a prescribed mixing length in conjunction with the assumption of turbulence equilibrium. Dispersion fields are computed by solving an unsteady transport equation of a dilute gas, formulated in a Eulerian framework, using the velocity and turbulence fields found from the steady-state RANS solution. In this paper the model is explained and detailed comparisons of predicted to experimentally obtained velocity, turbulence and dispersion fields are made to neutrally stable wind tunnel and hydraulic flume experiments.     

A Parameterization of the Roughness Length for the Air-Sea Interface in Free Convection

The response of the upper ocean to the parameterization of the roughness length z ₀ on the air side of the air-sea interface is studied using a one-dimensional mixed-layer model. In particular, it is shown that in the free convection limit when both the wind speed and the friction velocity approach zero, the familiar Charnock formula for the momentum roughness, which relies solely on wind generation, can be modified to account for contributions arising from the thermally generated turbulence. Therefore, a new parameterization is proposed for the momentum roughness length which extends the Charnock formula down to zero friction velocity. The value of a parameter which enters in the new formulation is determined by making use of exsisting free convection surface flux parameterizations. The effect of the new parameterization on the model performance is tested using data from the ocean weathership station Papa (OWS P), and data from the Long-Term Upper-Ocean Study (LOTUS) experiment. Simulations were carried out using a recently developed one-dimensional, second-order, turbulence closure scheme over diurnal as well as seasonal time scales. The findings suggest that the new momentum roughness parameterization improves the overall agreement between the observed and simulated sea-surface temperature (SST).     

Modelling hydraulic jump using the bubbly two-phase flow method

Hydraulic jumps have complex flow structures, characterised by strong turbulence and large air contents. It is difficult to numerically predict the flows. It is necessary to bolster the existing computer models to emphasise the gas phase in hydraulic jumps, and avoid the pitfall of treating the phenomenon as a single-phase water flow. This paper aims to improve predictions of hydraulic jumps as bubbly two-phase flow. We allow for airflow above the free surface and air mass entrained across it. We use the Reynolds-averaged Navier–Stokes equations to describe fluid motion, the volume of fluid method to track the interface, and the k–ε model for turbulence closure. A shear layer is shown to form between the bottom jet flow and the upper recirculation flow. The key to success in predicting the jet flow lies in formulating appropriate bottom boundary conditions. The majority of entrained air bubbles are advected downstream through the shear layer. Predictions of the recirculation region’s length and air volume fraction within the layer are validated by available measurements. The predictions show a linear growth of the shear layer. There is strong turbulence at the impingement, and the bulk of the turbulence kinetic energy is advected to the recirculation region via the shear layer. The predicted bottom-shear-stress distribution, with a peak value upstream of the toe of the jump and a decaying trend downstream, is realistic. This paper reveals a significant transient bottom shear stress associated with temporal fluctuations of mainly flow velocity in the jump. The prediction method discussed is useful for modelling hydraulic jumps and advancing the understanding of the complex flow phenomenon.     

A mathematical model for type II profile of concentration distribution in turbulent flows

This paper presents a mathematical model to investigate type II profile of suspension concentration distribution (i.e., the concentration profile where the maximum concentration appears at some distance above the bed surface) in a steady, uniform turbulent flow through open-channels. Starting from the mass and momentum conservation equations of two-phase flow, a theoretical model has been derived. The distribution equation is derived considering the effects of fluid lift force, drag force, particle inertia, particle–particle interactions, particle velocity fluctuations and drift diffusion. The equation is solved numerically and is compared with available experimental data as well as with other models existing in the literature. Good agreement between the observed value and computed result, and minimum error in comparison to other models indicate that the present model can be applied in predicting particle concentration distribution for type II profile for a wide range of flow conditions. The proposed model is also able to show the transition from type I profile to type II profile.     

自然粒度下渤海沉积物中有机碳的地球化学特征

对渤海三个典型海域6个站位柱状沉积物自然粒度下的有机碳（OC）进行了研究，探讨了有机碳的垂直分布特征及其氧化还原环境（Eh^0,Es^0,Fe^3 /Fe^2 比值）因素对渤海沉积物中有机碳的影响，渤海自然粒度沉积物中的有机碳含量在0.39-0.86%之间，一般在表层-次表层含量变化较剧烈，在下层变化较缓，相关分析说明，在中层，一般沉积物的还原性相比表层有增强，氧化环境与还原环境共存，有机质被氧化，OC浓度变得趋于减小，Fe^3 /Fe^2 也趋于减小，二者有明显的正相关；在下层，还原环境占据了主导地位，导致大量OC不能被氧化，就被保存了下来，而Fe^3 /Fe^2 却明显减小，所以在下层OC-Fe^3 /Fe^2 呈较强的负相关；在表层又掺杂了生物化学与物理扰动等因素，使OC-Fe^3 /Fe^2 的相关性变得复杂，且不规律，表层-次表层OC主要取决于物质来源和物理搅动，变化较复杂；中，下层主要受氧化还原环境影响，矿化作用明显，有机碳含量逐渐降低；下层除C3区和A区外，有机碳含量也逐步降低。有机碳含量不同层次受不同的物质来源，沉积环境，氧化还原进程与不同的生物化学过程共同影响，从C区的断面分布看，表层-次表层呈垂直叠层分布，主要是逐步垂直沉降沉积的结果。25cm以下呈水平推进式梯度分布，可能由于特殊的沉积事件如大洪水冲刷沉积而致。     

Living in the front: Neomysis americana (Mysidacea) in the Río de la Plata estuary, Argentina-Uruguay

The Río de la Plata is one of the main estuarine systems of South America. It is characterized by a salt wedge regime, a well-developed bottom salinity front, and a maximum turbidity zone associated with it. We described, for the first time, the spatial distributional patterns of Neomysis americana, the most abundant mysid and the main food item for juvenile fishes in this estuary. We analyzed the link between mysid distribution and abundance and the bottom salinity gradient. A total of 242 plankton samples were taken from the Río de la Plata estuary in spring and fall between 1991 and 2001. Bottom salinity gradient was quantified from grids created on the basis of 348 oceanographic stations. The N. americana population was characterized by high abundances (up to 2500 ind. m⁻³), with juveniles, males, gravid and non-gravid females present in both spring and fall of different years. N. americana distribution followed the position of the bottom salinity front in different years and seasons. Pearson’s correlation analysis between mysid abundance and bottom salinity gradient confirmed the association of mysids with the bottom salinity front (maximum salinity gradient). No correlation was detected between mysid abundance and salinity per se or temperature (neither in spring nor in fall). We speculate that mysids concentrated at the front could take advantage of the high concentration of detrital material for feeding. The results of our work highlight the importance of the magnitude of salinity gradient for the ecological processes of a salt-wedge estuary like the Río de la Plata. The analysis of the spatial distribution of gradient values presented in this work also constitutes a useful tool to locate key ecological areas such as fronts.     

Occurance and control of manganese in a large scale water treatment plant

The continuous variations of dissolved oxygen (DO), manganese (Mn), pH, and their effect on manganese removal by different water treatment processes are investigated. The results show that the declined DO concentration and pH value in the bottom of reservoir results in the increasing release of Mn from sediment to source water. Manganese concentration increased from 0.1 to 0.4 mg·L^-1 under the condition that DO concentration decreased from 12.0 to 2.0 mg·L^-1 in raw water. The different water treatment processes exhibited different efficiency on manganese removal. The processes with recycling of the suspended sludge, low elevation velocity in settling tank and slow filter rate, will benefit the manganese removal. During a high release of manganese in raw water, traditional coagulation-sedimentation and filtration could not completely remove Mn, although granular activated carbon filtration (GAC) had been applied. At that case, preoxidation with chlorine or potassium permanganate (KMnO₄) was necessary to address the high manganese concentration.     

A simplified approach to address turbulence modulation in turbidity currents as a response to slope breaks and loss of lateral confinement

Turbidity currents traversing canyon-fan systems flow over bed slopes that decrease in the downstream direction. This slope decrease eventually causes turbidity currents to decelerate and enter a net-depositional mode. When the slope decrease is relatively rapid in the downstream direction, the turbidity current undergoes a concomitantly rapid and substantial transition. Similar conditions are found when turbidity currents debouch to fan systems with loss of lateral confinement. In this work a simplified approach to perform direct numerical simulation of continuous turbidity currents undergoing slope breaks and loss of lateral confinement is presented and applied to study turbulence modulation in the flow. The presence of settling sediment particles breaks the top–bottom symmetry of the flow, with a tendency to self-stratify. This self-stratification damps turbulence, particularly near the bottom wall, affecting substantially the flow’s ability to transport sediment in suspension. This work reports results on two different situations: turbidity currents driven by fine and coarser sediment flowing through a decreasing slope. In the case of fine sediment, after the reduction in the slope of the channel, the flow remains turbulent with only a modest influence on turbulence statistics. In the case of coarse sediments, after the change in slope, turbulence is totally suppressed.