Calculation of Entrainment in Density Jumps

The density jump in a two-layer channel flow of miscible fluids, in which one of the layers is infinitely deep and at rest, is analyzed using the momentum flux and mass flux conservation equations. The analysis yields simple equations relating the heights upstream and downstream of the jump with the upstream Froude number and the rate of entrainment into the moving layer, as well as a relation between the maximum possible entrainment and the upstream Froude number. The analysis also shows that when the flow down-stream of the jump is controlled by an obstruction or a contraction, the entrainment rate into the jump depends solely on the dimensionless obstruction height contraction ratio and the upstream Froude number.     

Effect of initial excess density and discharge on constant flux gravity currents propagating on a slope

The effect of the upstream conditions on propagation of gravity current over a slope is investigated using three-dimensional numerical simulations. The current produced by constant buoyancy flux, is simulated using a large eddy simulation solver. The dense saline solution used at the inlet is the driving force of the flow. Higher replenishment of the current is possible either by a high inflow discharge or high initial fractional density excess. In the simulations, it is observed that these two parameters affect the flow in different ways. Results show that the front speed of the descending current is proportional to the cube root of buoyancy flux, $(g_o^{\prime } Q)^{1/3}$ , which agrees with the previous experimental and numerical observations. The height of the tail of the current grows linearly in the streamwise direction. Formation of a strong shear layer at the boundary of mixed upper layer and dense lower layer is observed within the body and the tail of the current. Over the tail of the current far enough from the inlet, the vertical velocity and density profiles are compared to the ones from an experimental study. Distance from the bed to the point of maximum velocity increases with an increase in inflow discharge, while it remains practically unchanged with increasing initial fractional excess density in the simulations. Even though the velocity profiles are in good agreement, some discrepancies are observed in fractional excess density profiles among experimental and numerical results. Possible reasons for these discrepancies are discussed. Generally, gravity current type of flows could be expressed in layer-integrated formulation of governing equations. However, layer integration introduces several constants, commonly known as shape factors, to the equations of motion. The values of these shape factors are calculated based on simulation results and compared to the values from experiments and to the favorably used ‘top hat’ assumption.     

Mass-based depth and velocity scales for gravity currents and related flows

Gravity driven flows on inclines can be caused by cold, saline or turbid inflows into water bodies. Another example are cold downslope winds, which are caused by cooling of the atmosphere at the lower boundary. In a well-known contribution, Ellison and Turner (ET) investigated such flows by making use of earlier work on free shear flows by Morton, Taylor and Turner (MTT). Their entrainment relation is compared here with a spread relation based on a diffusion model for jets by Prandtl. This diffusion approach is suitable for forced plumes on an incline, but only when the channel topography is uniform, and the flow remains supercritical. A second aspect considered here is that the structure of ET’s entrainment relation, and their shallow water equations, agrees with the one for open channel flows, but their depth and velocity scales are those for free shear flows, and derived from the velocity field. Conversely, the depth of an open channel flow is the vertical extent of the excess mass of the liquid phase, and the average velocity is the (known) discharge divided by the depth. As an alternative to ET’s parameterization, two sets of flow scales similar to those of open channel flows are outlined for gravity currents in unstratified environments. The common feature of the two sets is that the velocity scale is derived by dividing the buoyancy flux by the excess pressure at the bottom. The difference between them is the way the volume flux is accounted for, which—unlike in open channel flows—generally increases in the streamwise direction. The relations between the three sets of scales are established here for gravity currents by allowing for a constant co-flow in the upper layer. The actual ratios of the three width, velocity, and buoyancy scales are evaluated from available experimental data on gravity currents, and from field data on katabatic winds. A corresponding study for free shear flows is referred to. Finally, a comparison of mass-based scales with a number of other flow scales is carried out for available data on a two-layer flow over an obstacle. Mass-based flow scales can also be used for other types of flows, such as self-aerated flows on spillways, water jets in air, or bubble plumes.     

Exchange flow between open water and floating vegetation

This study describes the exchange flow between a region with open water and a region with a partial-depth porous obstruction, which represents the thermally-driven exchange that occurs between open water and floating vegetation. The partial-depth porous obstruction represents the root layer, which does not penetrate to the bed. Initially, a vertical wall separates the two regions, with fluid of higher density in the obstructed region and fluid of lower density in the open region. This density difference represents the influence of differential solar heating due to shading by the vegetation. For a range of root density and root depths, the velocity distribution is measured in the lab using PIV. When the vertical wall is removed, the less dense water flows into the obstructed region at the surface. This surface flow bifurcates into two layers, one flowing directly through the root layer and one flowing beneath the root layer. A flow directed out of the vegetated region occurs at the bed. A model is developed that predicts the flow rates within each layer based on energy considerations. The experiments and model together suggest that at time- and length-scales relevant to the field, the flow structure for any root layer porosity approaches that of a fully blocked layer, for which the exchange flow occurs only beneath the root layer.     

Turbulent entrainment into fluid mud gravity currents

The entrainment of ambient water into non-Newtonian fluid mud gravity currents was investigated in this study. Constant volume release gravity currents were generated in a lock-exchange tank for a wide range of experimental conditions. A technique similar to the so-called light attenuation technique was used to find the boundary of the current, allowing for the calculation of both temporal and bulk entrainment parameters (in terms of the temporal and bulk entrainment velocities, respectively). It was found that the temporal entrainment velocity is dependent on different parameters in the different propagation phases. The slumping phase begins with an adjustment zone (henceforth, non-established zone) in which the temporal entrainment velocity is not a function of the current front velocity, followed by the established zone in which the temporal entrainment velocity is a function of the current front velocity. This dependence of the temporal entrainment velocity on the current front velocity carries through to the inertia-buoyancy phase. As expected, temporal entrainment velocity in the viscous-buoyancy phase was negligible in comparison to average entrainment velocity in the other phases. It is observed that the temporal entrainment characteristics in the non-established zone is governed by the competition between the entrainment-inhibiting density stratification effects and the entrainment-favouring effects of the Kelvin–Helmholtz billows that are quantified by the Richardson number and the Reynolds number of the gravity current, respectively. In the established zone, Reynolds number effects were observed to dominate over Richardson number effects in dictating temporal entrainment characteristics. A parameterization for the temporal entrainment velocity for non-Newtonian fluid mud gravity currents is developed based upon the experimental observations. This study also found that the bulk entrainment characteristics for the non-Newtonian fluid mud gravity currents can be parameterized by the Newtonian bulk entrainment parameterizations that rely solely on a bulk Richardson number. Interestingly, it was found that the non-Newtonian characteristics of the gravity current have little to no effect on the entrainment of the Newtonian ambient fluid.     

Buoyancy-Driven Two-Layer Exchange Flows Across a Slowly Submerging Barrier

Results are presented from a combined analytical and laboratory study of unsteady, two-layer, density-driven, sub-maximal exchange over a slowly-descending estuarine barrier located very close to the junction of the river mouth and the near-shore coastal zone. As in the precursor study (Cuthbertson et al. 2004, Environ. Fluid Mech. 4, 127–155) that the present investigation extends, the rate of descent of the barrier is assumed to be sufficiently slow for the unsteady exchange flow to adjust continuously to the appropriate quasi-steady conditions at every stage of the descent. The results demonstrate that the thickness of each layer at the barrier crest can be predicted satisfactorily by a hydraulic analysis that (i) assumes the existence of a single control point at the barrier crest and (ii) incorporates the hydraulic losses arising from the sudden expansion and contraction of the upper and lower layers, respectively, at the channel exit. Predictions of the normalised elevations of the interface at the barrier and exit for the “inviscid” maximal exchange case are shown to coincide with the maximal exchange predictions of Zhu and Lawrence (2000, J. Hydraul. Eng. ASCE 126(12), 921–928).     

Simulation of exchange flow between open water and floating vegetation using a modified RNG <Emphasis Type="Italic">k</Emphasis>-<Emphasis Type="Italic">ε</Emphasis> turbulence model

The paper focuses on the numerical simulation of the exchange flow between open water and floating vegetation, which plays an important role in maintaining the ecological balance by transporting nutrient matter. The simulation was conducted using a new solver developed upon OpenFOAM. A modified RNG k-ε turbulence model, which is expected to model both the high- and low-Reynolds number flows correctly, was used to determine the eddy viscosity. Several particular terms were added into the momentum equations and turbulence model equations to model the effects of vegetation and buoyancy. Among these terms, the term for the effect of vegetation in the ε-equation was re-modelled. The model was validated by properly predicting the profiles of mean velocity and turbulent kinetic energy for flows through suspended canopies. The density flow between open and vegetated water was simulated with the same conditions as those of the experiment conducted by Zhang and Nepf. The predicted results agreed well with the experimental data and provided more detailed information of such exchange flow. The convection between the root layer and the layer beneath the roots, which was not observed in the experiment, was observed in the numerical simulation.     

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.     

Compound channel flow with a longitudinal transition in hydraulic roughness over the floodplains

Flows in a compound open-channel (two-stage geometry with a main channel and adjacent floodplains) with a longitudinal transition in roughness over the floodplains are experimentally investigated in an 18 m long and 3 m wide flume. Transitions from submerged dense vegetation (meadow) to emergent rigid vegetation (wood) and vice versa are modelled using plastic grass and vertical wooden cylinders. For a given roughness transition, the upstream discharge distribution between main channel and floodplain (called subsections) is also varied, keeping the total flow rate constant. The flows with a roughness transition are compared to flows with a uniformly distributed roughness over the whole length of the flume. Besides the influence of the downstream boundary condition, the longitudinal profiles of water depth are controlled by the upstream discharge distribution. The latter also strongly influences the magnitude of the lateral net mass exchanges between subsections, especially upstream from the roughness transition. Irrespective of flow conditions, the inflection point in the mean velocity profile across the mixing layer is always observed at the interface between subsections. The longitudinal velocity at the main channel/floodplain interface, denoted \(U_{int}\), appeared to be a key parameter for characterising the flows. First, the mean velocity profiles across the mixing layer, normalised using \(U_{int}\), are superimposed irrespective of downstream position, flow depth, floodplain roughness type and lateral mass transfers. However, the profiles of turbulence quantities do not coincide, indicating that the flows are not fully self-similar and that the eddy viscosity assumption is not valid in this case. Second, the depth-averaged turbulent intensities and Reynolds stresses, when scaled by the depth-averaged velocity \(U_{d,int}\) exhibit two plateau values, each related to a roughness type, meadow or wood. Lastly, the same results hold when scaling by \(U_{d,int}\) the depth-averaged lateral flux of momentum due to secondary currents. Turbulence production and magnitude of secondary currents are increased by the presence of emergent rigid elements over the floodplains. The autocorrelation functions show that the length of the coherent structures scales with the mixing layer width for all flow cases. It is suggested that coherent structures tend to a state where the magnitude of velocity fluctuations (of both horizontal vortices and secondary currents) and the spatial extension of the structures are in equilibrium.     

Streamwise velocity profiles in coastal currents

The ability to model marine currents can be a powerful device for many planning activities, for which the knowledge of the velocity field is of pivotal importance, such as the evaluation of current-induced loading on maritime structures or the diffusion and dispersion of polluted flow discharges. Observations of time-averaged velocity profiles, taken with a vessel mounted acoustic Doppler current profiler during a monitoring survey program in the seas of Southern Italy, are analysed in this paper. The measurements were taken under non-breaking conditions, offshore the surf zone, with the aim of reproducing the vertical trends of the streamwise velocity by means of standard theoretical laws. To evaluate also the possible influence of stratification on the current velocity profile shape, together with velocity measurements water temperature and salinity were also measured at the same time and locations, by means of a CTD recorder. The examined surveys referred to different time periods and sites, to guarantee a general validity of deductions. On the basis of the experiments, we verified the actual existence of a log-layer and concluded that the upper limit of the region in which the log law is applicable extends well beyond the inner region. Moreover, the deviations of the measured velocity from the logarithmic profiles above the height of the log layer is consistent with the effects of stratification. The parameters of the log law were estimated, depending on both flow dynamics and stratification in the target area. As a second step, in the most superficial and stratified layer, the velocity profiles were modelled by means of a power law, which fitted the measured data well. According to previous studies, the power law parameters result Reynolds number dependent by means of a new proposed formulation. Finally, the bottom stress and the bottom drag coefficient were investigated.     

Gravity currents in two-layer stratified media

An analytical, experimental and numerical study of boundary gravity currents propagating through a two-layer stratified ambient of finite vertical extent is presented. Gravity currents are supposed to originate from a lock-release apparatus; the (heavy) gravity current fluid is assumed to span the entire channel depth, H, at the initial instant. Our theoretical discussion considers slumping, supercritical gravity currents, i.e. those that generate an interfacial disturbance whose speed of propagation matches the front speed, and follows from the classical analysis of Benjamin (J Fluid Mech 31:209?C248, 1968). In contrast to previous investigations, we argue that the interfacial disturbance must be parameterized so that its amplitude can be straightforwardly determined from the ambient layer depths. Our parameterization is based on sensible physical arguments; its accuracy is confirmed by comparison against experimental and numerical data. More generally, measured front speeds show positive agreement with analogue model predictions, which remain strictly single-valued. From experimental and numerical observations of supercritical gravity currents, it is noted that this front speed is essentially independent of the interfacial thickness, ??, even in the limiting case where ?? = H so that the environment is comprised of a uniformly stratified ambient with no readily discernible upper or lower ambient layer. Conversely, when the gravity current is subcritical, there is a mild increase of front speed with ??. Our experiments also consider the horizontal distance, X, at which the front begins to decelerate. The variation of X with the interface thickness and the depths and densities of the ambient layers is discussed. For subcritical gravity currents, X may be as small as three lock lengths whereas with supercritical gravity currents, the gravity current may travel long distances at constant speed, particularly as the lower layer depth diminishes.     

Visualization of the internal flow properties and the material exchange interface in an entraining viscous Newtonian gravity current

In order to simulate a simple entraining geophysical flow, a viscous Newtonian gravity current is released from a reservoir by a dam-break and flows along a rigid horizontal bed until it meets a layer of entrainable material of finite depth, identical to the current. The goal is to examine the entrainment mechanisms by observing the interaction between the incoming flow and the loose bed. The sole parameter varied is the initial volume of the gravity current, thus altering its height and velocity. The gravity current plunges or spills into the entrainable bed and the velocity of the flow front becomes linear with time. The bed material is directly affected: motion is generated in the fluid far downstream of, and in that lying beneath the encroaching front. Shear bands are identified, separating horizontal flow downstream from flow with a strong vertical component close to the step. Downstream of the step the flow is horizontal and stratified, with no slip on the bottom boundary and very low shear near the surface. Between these two regions may lie transitional zones with linear velocity profiles, separated by horizontal bands of high shear; the number of transitional zones in the cross-section varies with the initial volume of the dam-break.     

Study On the Hydraulic Characteristics of Taichung Harbour in Taiwan

For this study, field measurements of current profiles, buoy trajectories and the lag of two tidal stations were performed to explore the flow characteristics of Taichung Harbour. in order to distinguish the effects of wind drift current on circulation inside Taichung Harbour, field surveys during both summer and monsoon (winter) season were completed separately. the speed of the drift current was about 3.5% that of the, wind speed, based on the field data. the horizontal dispersion coefficients were close to Bowden's (1965) formula for the tidal current. the water temperature showed a two-layer profile, with the mixing thickness about 4 to 6 metres for the upper layer. the corresponding Richardson number was about 70. the tidal lag between the two tidal stations was 9.68 minutes. All the results agree well with the theoretical results.     

Nutrients and biomass distribution in the Gulf of Aqaba (Elat), Red Sea

The distribution of phosphate, nitrate and silicate values obtained from 300 samples and of biomass determined by displacement volume in about 1,900 vertical plankton hauls (65, 200 and 330 m) collected from 8 oceanographic station during 1974–1975 in the Gulf of Aqaba (Elat) are summarized and illustrated by crosssections. Generally, the Gulf is poor in nutrients and the data indicate that it is filled with upper (150 m) Red Sea waters, flowing in over the sill of Tiran. Nutrient content of the upper and deep waters immediately outside the sill are well within the known range of those in the northern Red Sea. Biomass values are relatively low in the Gulf are generally similar to those reported from the northern Red Sea. Both nutrients and biomass values display seasonal and bathymetric variations in the Gulf and outside the sill.     

Unusual characteristics in a Meromictic lake in Greece

The studied lake, a meromictic shallow lagoon, in Peloponissos, presents unusual physical and chemical features which derive mainly from its mineral springs, and the sea water that invades into the lake. The form of vegetation and the abundant organic matter of the mud together with the sulfate salts of the water create conditions which are responsible for the production of gases such as H₂S and CH₄. Vertical profiles of temperature, salinity and oxygen show that a large area of the lake is well stratified, at least periodically and no marked mixing occurs, between the upper less saline water and the lower saline water. In the halocline the vertical gradient of salinity is large. Mesothermic and poikilothermic conditions were also observed, whereas large temperature differences were recorded in water column.     

Similarity theory and parameterization of mixing in the upper ocean

Boundary layers with small thermal and mechanical inertia are close to steady-state conditions. This underlies the Monin-Obukhov similarity theory and explains why the surface values of the fluxes can be chosen as external parameters. For fluids with large thermal inertia, such as the ocean, the thermal time scale is relatively large, and the density flux is a complex function of depth; thus, the external thermal forcing is no longer a governing parameter. However, the mechanical inertia of the upper ocean is about three orders of magnitude smaller than the thermal inertia. Consequently, the upper ocean can be considered as steady-state in the dynamic sense, to any dynamic property depends primarily on the depth, the surface momentum flux, and the vertical density structure. This property allows us to suggest an alternative formulation of the similarity theory for the stratified boundary layers through specification of a new stratification parameter which characterizes the internal density structure instead of the external density flux. The turbulent mixing coefficient is derived as dependent on the stratification parameter. The latter includes the surface stress and the integral density deficit for the entire layer above. The general form and the asymptotic behavior of the nondimensional turbulent mixing coefficient as a function of the stratification parameter are obtained using dimensional considerations. Determination of numerical parameters is based on 8 years of temperature profiles acquired at the Ocean Weather Ship (OWS) PAPA. Finally, a method for calculating the profile of the turbulent mixing coefficient is obtained. This approach reproduces the 8-year evolution of the upper ocean with the maximum rms difference of approximately 1C and the bias of 1C over the depth range 0–150 m. Additional 1-year simulation of the upper ocean at OWS CHARLEY and 9-year simulation at OWS NOVEMBER confirms reasonable applicability of this approach. The proposed simple turbulent mixing scheme reproduces the evolution of the upper ocean with accuracies similar to those obtained using much more complicated models.     

Modelling the motion of an internal solitary wave over a bottom ridge in a stratified fluid

A series of laboratory experiments has been carried out to investigate the passage of an internal solitary wave of depression over a bottom ridge, in a two-layer fluid system for which the upper and lower layer is linearly-stratified and homogeneous respectively. Density, velocity and vorticity fields induced by the wave propagation over the ridge have been measured simultaneously at three locations, namely upstream, downstream and over the ridge crest, for a wide range of model parameters. Results are presented to show that wave breaking may occur for a sufficiently large wave amplitude and a strong ridge blockage factor, with accompanying mixing and overturning. Density field data are presented (i) to illustrate the overturning and mixing processes that accompany the wave breaking and (ii) to quantify the degree of mixing in terms of the wave and ridge parameters. For weak encounters, good agreement is obtained between the laboratory experimental results (velocity and vorticity fields induced by the wave propagation) and the predictions of a recently-developed fully nonlinear theory. Discrepancies between theory and experiment are discussed for cases in which breaking and mixing occur.     

Froude scaling limitations in modeling of turbidity currents

The scaling problem associated with the modeling of turbidity currents has been recognized but is yet to be explored systematically. This paper presents an analysis of the dimensionless governing equations of turbidity currents to investigate the scale effect. Three types of flow conditions are considered: (i) conservative density current; (ii) purely depositional turbidity current; and (iii) mixed erosional/depositional turbidity current. Two controlling dimensionless numbers, the Froude number and the Reynolds number, appear in the non-dimensional governing equations. When densimetric Froude similarity is satisfied, the analysis shows that the results would be scale-invariant for conservative density current under the rough turbulent condition. In the case of purely depositional flows, truly scale-invariant results cannot be obtained, as the Reynolds-mediated scale effects appear in the bottom boundary conditions of the flow velocity and sediment fall velocity. However, the scale effect would be relatively modest. The Reynolds effect becomes more significant for erosional or mixed erosional/depositional turbidity currents as Reynolds-mediated scale effects also appear in the sediment entrainment relation. Numerical simulations have been conducted at three different scales by considering densimetric Froude scaling alone as well as combined densimetric Froude and Reynolds similarity. Simulation results confirm that although the scaling of densimetric Froude number alone can produce scale-invariable results for conservative density currents, variations occur in the case of turbidity currents. The results become scale invariant when densimetric Froude and Reynolds similarities are satisfied simultaneously.     

Osmotic adjustment and organic solute accumulation in unicellular cyanobacteria from freshwater and marine habitats

The intracellular concentrations of low-molecular weight carbohydrates and quaternary ammonium compounds present in 26 axenic isolates of unicellular cyanobacteria have been studied over a range of external salinity from freshwater up to 300% seawater (100%=35 S). In all cases, a single carbohydrate, either sucrose or glucosylglycerol, was identified as the principal organic osmoticum, showing major variation in response to the external salt concentration; quaternary ammonium compounds were present in osmotically insignificant amounts. Glucosylglycerol was accumulated as primary osmoticum by nine of the isolates from saline habitats and by five of the freshwater isolates; trace amounts of sucrose were also prsent. The remaining twelve freshwater strains accumulated sucrose as sole osmoticum. Glucosylglycerol-accumulating strains grew over the widest salinity range (up to 200 to 250% seawater), whether isolated from saline or non-saline habitats. Sucrose-accumulating strains were more stenohaline, growing only in up to 50 to 100% seawater and showing no sustained growth in hypersaline media (>100% seawater). The data suggest that (1) glycosylglycerol accumulation is not unique to marine cyanobacteria, and (2) the upper salinity limit for growth may be linked to organic solute accumulation, rather than habitat, with glucosylglycerol-accumulating isolates having a greater potential for growth in salt-stressed conditions than sucrose accumulators.     

Measurements and modeling of open-channel flows with finite semi-rigid vegetation patches

The hydrodynamics of flows through a finite length semi-rigid vegetation patch (VP) were investigated experimentally and numerically. Detailed measurements have been carried out to determine the spatial variation of velocity and turbulence profiles within the VP. The measurement results show that an intrusion region exists in which the peak Reynolds stress remains near the bed. The velocity profile is invariant within the downstream part of the VP while the Reynolds stress profile requires a longer distance to attain the spatially invariant state. Higher vegetation density leads to a shorter adjustment length of the transition region, and a higher turbulence level within the VP. The vegetation density used in the present study permits the passing through of water and causes the peak Reynolds stress and turbulence kinetic energy each the maximum at the downstream end of the patch. A 3D Reynolds-averaged Navier–Stokes model incorporating the Spalart–Allmaras turbulence closure was employed subsequently to replicate the flow development within the VP. The model reproduced transitional flow characteristics well and the results are in good agreement with the experimental data. Additional numerical experiments show that the adjustment length can be scaled by the water depth, mean velocity and maximum shear stress. Empirical equations of the adjustment lengths for mean velocity and Reynolds stress were derived with coefficients quantified from the numerical simulation results.