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.     

Hydrodynamics and turbulence in emergent and sparsely vegetated open channel flow

This present study reports the results of an experimental study characterizing thorough variation of turbulent hydrodynamics and flow distribution in emergent and sparsely vegetated open channel flow. An emergent and rigid sparse vegetation patch with regular spacing between stems along the flow and transverse directions was fixed in the central region of the cross-section of open channel. Experiments were conducted in subcritical flow conditions and velocity measurements were obtained with an acoustic Doppler Velocimetry system. Large variations of the turbulence intensities, Reynolds shear stress, turbulent kinetic energy and vortical motions are found in and around the vegetation patch. At any cross-section through the interior of the vegetation patch, streamwise velocity decreases with increase in streamwise length and the velocity profiles converge from the log-law to a linear profile with increasing slope. Time-averaged lateral and vertical velocities inside the vegetation patch increase with increasing streamwise distance and converge from negative values to positive values. Turbulence intensities interior of the sparse vegetation patch are more than those of without the vegetation patch. Similar to the trend of streamwise velocity profiles inside the vegetation, turbulence intensities and longitudinal-normal Reynolds shear stress profile decreases with streamwise direction. In the interior of the vegetation patch and downstream of the trailing edge, turbulent kinetic energy profiles are exhibiting irregular fluctuations and the maximum values are occurring in the outer layer. Analysis of flow distribution confirms sparse vegetation patch is inducing a serpentine flow pattern in its vicinity. At the leading edge, flow is rushing towards the right hand sidewall, and at the trailing edge, flow is turning to the left hand sidewall. In between the leading and trailing edges, the streamlines are following a zig-zag fashion at varied degree along the streamwise and lateral directions. Immediate upstream of the leading edge and in the interior of the vegetation patch, vortex motion is clearly visible and the vortices are stretched along the width of the channel with streamwise direction.     

Variations of bed elevations due to turbulence around submerged cylinder in sand beds

This paper presents the spatio-temporal variations in bed elevations and the near-bed turbulence statistics over the deformed bed generated around the submerged cylindrical piers embedded vertically on loose sediment bed at a constant flow discharge. Experiments were carried out in a laboratory flume for three blockage ratios in the range of 0.04–0.06 using three different sizes of submerged cylinders individually placed vertically at the centerline of the flume. Clear-water experimental conditions were maintained over the smooth sediment bed surface with a constant flow discharge (\(Q = 0.015\,{\rm m}^3/{\rm sec}\)), thereby giving three different cylinder Reynolds numbers \(Re_{D_c} = \frac{U_mD_c}{\nu }\) (=10200, 12750, 15300) away from the cylinder locations, where \(U_m\) is the maximum mean velocity, \(D_c\) is the cylinder diameter and \(\nu\) is the kinematic viscosity of fluid. Instantaneous sand bed elevations around the cylinders were recorded using a SeaTek 5MHz ultrasonic ranging system of net 24 transducers to estimate bed form migration, and the near-bed velocity data at transducer locations over the stable deformed bed around the pier-like structures were collected using down-looking three-dimensional (3D) Micro-acoustic Doppler velocimeter to estimate the bottom Reynolds shear stresses and the contributions of bursting events to the dominant shear stress component. The flow perturbation generated due to relatively lower flow blockage ratio favored to achieve the stable bed condition more rapidly than the others, and larger upstream scour-depth and deformed areas were noticed for greater flow blockage ratio due to larger cylinder diameter. For larger blockage ratio in the upstream of scour-hole near the bed, occurrences of probabilities of both boundary-ward interactions (Q1 and Q3) were the dominant; whereas in the downstream of the scoured region, occurrences of probabilities of second and third quadrant events (Q2 and Q4) were dominant. On the other hand, for the lower blockage ratio, quadrant (Q2) was dominant over Q4 in the downstream of scour-hole, and in the upstream of scour-hole, quadrant Q4 was the dominant.     

Effect of atmospheric boundary layer stability on the inclination angle of turbulence coherent structures

Coherent structures in the atmospheric boundary layer are fundamental to the transport of momentum and heat as well as to the production of turbulence. The present work attempts to investigate the behavior of the inclination angle of the vortex packet structures (\(\gamma\)) under different stability conditions. The data were collected from the Marine Ecosystem Research Centre (EKOMAR) site at the east coast of Peninsular Malaysia. The main measurements were conducted by placing two hotwires 3 and 12 m above ground. The two-point correlation method was used to calculate the vortex packet structure inclination angle, while the one-point correlation method was employed to calculate its length-scale. The inclination angle was found to increase under both stable and unstable conditions. As the Obukhov stability parameter (\(\zeta\)) approaches 0, the inclination angle ranged between \(\gamma = 15^\circ\) to \(\gamma = 18^\circ\) for the stable and unstable conditions, respectively, which agrees with the findings of previous research. The vertical gradient of velocity is the dominant parameter affecting the inclination angle under different stability conditions.     

Evolution and decay of gravity wavefields in weak-rotating environments: a laboratory study

Gravity waves are prominent physical features that play a fundamental role in transport processes of stratified aquatic ecosystems. In a two-layer stratified basin, the equations of motion for the first vertical mode are equivalent to the linearised shallow water equations for a homogeneous fluid. We adopted this framework to examine the spatiotemporal structure of gravity wavefields weakly affected by the background rotation of a single-layer system of equivalent thickness \(h_{\ell }\), via laboratory experiments performed in a cylindrical basin mounted on a turntable. The wavefield was generated by the release of a diametral linear tilt of the air–water interface, \(\eta _{\ell }\), inducing a basin-scale perturbation that evolved in response to the horizontal pressure gradient and the rotation-induced acceleration. The basin-scale wave response was controlled by an initial perturbation parameter, \({\mathcal{A}}_{*} = \eta _{0}/h_{\ell }\), where \(\eta _{0}\) was the initial displacement of the air–water interface, and by the strength of the background rotation controlled by the Burger number, \({\mathcal{S}}\). We set the experiments to explore a transitional regime from moderate- to weak-rotational environments, \(0.65\le {\mathcal{S}} \le 2\), for a wide range of initial perturbations, \(0.05\le {\mathcal{A}}_{*}\le 1.0\). The evolution of \(\eta _{\ell }\) was registered over a diametral plane by recording a laser-induced optical fluorescence sheet and using a capacitive sensor located near the lateral boundary. The evolution of the gravity wavefields showed substantial variability as a function of the rotational regimes and the radial position. The results demonstrate that the strength of rotation and nonlinearities control the bulk decay rate of the basin-scale gravity waves. The ratio between the experimentally estimated damping timescale, \(T_{d}\), and the seiche period of the basin, \(T_{g}\), has a median value of \(T_{d}/T_{g}\approx 11\), a maximum value of \(T_{d}/T_{g}\approx 10^{3}\) and a minimum value of \(T_{d}/T_{g}\approx 5\). The results of this study are significant for the understanding the dynamics of gravity waves in waterbodies weakly affected by Coriolis acceleration, such as mid- to small-size lakes.     

On the front conditions for gravity currents in channels of general cross-section

We consider the propagation of a high-Reynolds-number gravity current in a horizontal channel with general cross-section whose width is \(f(z), 0 \le z\le H\), and the gravity acceleration g acts in \(-z\) direction. (The classical rectangular cross-section is covered by the particular case \(f(z) =\) const.) We assume a two-layer system of homogeneous fluids of constant densities \(\rho _{c}\) (current, of height \(h < H \)) and smaller \(\rho _{a}\) (ambient, filling the remaining part of the channel). We focus attention on the calculation and assessment of the nose Froude-number condition \(Fr = U/(g' h)^{1/2}\); here U is the speed of propagation of the current and \(g' = (\rho _{c}/\rho _{a}-1) g\) is the reduced gravity. We first revisit the steady-state current, and derive compact insightful expressions of Fr and energy dissipation as a function of \(\varphi \) (\(=\) area fraction occupied by the current in the cross-section). We show that the head loss \(\delta _0\) on the stagnation line is formally a degree of freedom in the determination of \(Fr(\varphi )\), and we clarify the strong connections with the head loss \(\delta \) in the ambient fluid, and with the overall rate of dissipation \(\dot{{\mathcal{D}}}\). We demonstrate that the closure \(\delta _0 = 0\) [suggested by Benjamin (J Fluid Mech 31, 209–248, 1968) for the rectangular cross-section] produces in general the smallest Fr for a given \(\varphi \); the results are valid for a significant range \([0, \varphi _{\max }]\), in which the current is dissipative, except for the point \(\varphi _{\max }\) where \(\delta = \dot{{\mathcal{D}}} = 0\). We show that imposing the closure \(\delta = \dot{{\mathcal{D}}} = 0\), which corresponds to an energy-conserving or non-dissipative current, produces in general unacceptable restrictions of the range of validity, and large values of Fr; in particular, deep currents (\(\varphi < 0.3\) say) must be excluded because they are inherently dissipative. On the other hand, the compromise closure \(\delta (\varphi ) =\delta _0(\varphi )\) produces the simple \(Fr(\varphi ) = \sqrt{2}(1 - \varphi )\) formula whose values and dissipation properties are very close, and the range of validity is identical, to these obtained with Benjamin’s closure (moreover, we show that this corresponds to circulation-conservation solutions). The results are illustrated for practical cross-section geometries (rectangle, \(\Delta \) and \(\nabla \) triangle, circle, and the general power-law \(f(z) = b z ^\alpha \) (\(b>0, \alpha \ge 0, 0< z \le H\)). Next, we investigate the connection of the steady-state results with the time-dependent current, and show that in a lock-released current the rate of dissipation of the system is equal to, or larger than, that obtained for Fr corresponding to the conditions at the nose of the current. The results and insights of this study cover a wide range of cross-section geometry and apply to both Boussinesq and non-Boussinesq systems; they reveal a remarkable robustness of Fr as a function of \(\varphi \).     

Small-scale entrainment in inclined gravity currents

We investigate the effect of buoyancy on the small-scale aspects of turbulent entrainment by performing direct numerical simulation of a gravity current and a wall jet. In both flows, we detect the turbulent/nonturbulent interface separating turbulent from irrotational ambient flow regions using a range of enstrophy iso-levels spanning many orders of magnitude. Conform to expectation, the relative enstrophy isosurface velocity \(v_n\) in the viscous superlayer scales with the Kolmogorov velocity for both flow cases. We connect the integral entrainment coefficient E to the small-scale entrainment and observe excellent agreement between the two estimates throughout the viscous superlayer. The contribution of baroclinic torque to \(v_n\) is negligible, and we show that the primary reason for reduced entrainment in the gravity current as compared to the wall-jet are 1) the reduction of \(v_n\) relative to the integral velocity scale \(u_T\); and 2) the reduction in the surface area of the isosurfaces.     

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.     

Lock-exchange gravity currents over rough bottoms

In nature, density driven currents often flow over or within a bottom roughness: a sea breeze encountering tall buildings, a shallow flow encountering aquatic vegetation, or a dense oceanic current flowing over a rough bottom. Laboratory experiments investigating the mechanisms by which bottom roughness enhances or inhibits entrainment and dilution in a lock-exchange dense gravity current have been conducted. The bottom roughness has been idealized by an array of vertical, rigid cylinders. Both spacing (sparse vs. dense configuration) and height of the roughness elements compared with the height of the current have been varied. Two-dimensional density fields have been obtained. Experimental results suggest that enhancement of the entrainment/dilution of the current can occur due to two different mechanisms. For a sparse configuration, the dense current propagates between the cylinders and the entrainment is enhanced by the vortices generated in the wake of the cylindrical obstacles. For a dense configuration, the dense current rides on top of the cylinders and the dilution is enhanced by the onset of convective instability between the dense current above the cylinders and the ambient lighter water between the cylinders. For low values of the ratio of the cylinder to lock height \(\lambda \) the dense current behavior approaches that of a current over a smooth bottom, while the largest deviations from the smooth bottom case are observed for large values of \(\lambda \).     

Thin-layer models for gravity currents in channels of general cross-section area,a review

We present a brief review of the recent investigations on gravity currents in horizontal channels with non-rectangular cross-section area (such as triangle, \(\bigvee \)-valley, circle/semi-circle, trapezoid) which occur in nature (e.g., rivers) and constructed environment (tunnels, reservoirs, canals). To be specific, we discuss the propagation of a gravity current (GC) in a horizontal channel along the horizontal coordinate x, with gravity g acting in the \(-z\) direction, and y the horizontal–lateral coordinate. The bottom and top of the channel are at \(z=0,H\). The “standard” problem is concerned with 2D flow in a channel with rectangular (or laterally unbounded) cross-section area (CSA). Recent investigations have successfully extended the standard knowledge to the channels of CSA given by the quite general \(-f_1(z)\le y \le f_2(z)\) for \(0 \le z \le H\). This includes the practical \(\bigvee \)-valley, triangle, circle/semi-circle and trapezoid; these geometries may be in “up” or “down” setting with respect to gravity, e.g., \(\bigtriangleup \) and \(\bigtriangledown \). The major objective of the extended theory is to predict the height of the interface \(z=h(x,t)\) and the velocity (averaged over the CSA) u(x, t), where t is time; the prediction includes the speed and position of the nose \(u_N(t), x_N(t)\). We show that the motion is governed by a set of simplified equations, called “model,” that provides versatile and insightful solutions and trends. The emphasis in on a high-Reynolds-number current whose motion is dominated by buoyancy–inertia balance; in particular a GC released from a lock, which also contains general effects such as front and internal jumps (shocks), and reflected bore. We discuss two-layer, one-layer, and box models; Boussinesq and non-Boussinesq systems; compositional and particle-driven cases; and the effect of stratification of the ambient fluid. The models are self-contained, and admit realistic initial and boundary conditions. The governing equations are amenable to analytical solutions in some special circumstances. Some salient features of the buoyancy-viscous regime, and the estimate for the length at which transition to this regime takes place, are also presented. Some experimental support to the theory, and open questions for further investigations, are also mentioned. The major conclusions are (1) The CSA geometry has significant influence on the motion of the GC; and (2) The new theory is a useful, very significant, extension of the standard two-dimensional GC problem. The standard current is just a particular case, \(f_{1,2} =\) constants, among many other covered by the new theory.     

Wind-induced pressure at a tunnel portal

In order to properly size the mechanical ventilation system of a tunnel, it is essential to estimate the wind-driven pressure difference that might rise between its two portals. In this respect, we explore here the pressure distribution over a tunnel portal under the influence of an incident atmospheric boundary layer and, in particular, its dependency on wind direction and on tunnel geometry. Reduced scale models of generic configurations of a tunnel portal are studied in an atmospheric wind tunnel. Pressure distributions over the front section of different open cavities are measured with surface taps, which allows us to infer the influence of the tunnel aspect ratio and wind direction on a pressure coefficient \(C_{P}\), defined as a spatially and time averaged non-dimensional pressure. Experiments reveal that the magnitude of the coefficient \(C_{P}\), as a function of the wind direction, is significantly influenced by the portal height-to-width ratio and almost insensitive to its length. The experimental data set is completed by hot-wire anemometry measurements providing vertical distribution of velocity statistics. The same configurations are simulated by numerically solving the Reynolds-averaged Navier–Stokes equations, adopting the standard \(k - \varepsilon\) turbulence model. Despite some discrepancies between numerical and experimental estimates of some flow parameters (namely the turbulent kinetic energy field), the numerical estimates of the pressure coefficients \(C_{P}\) show very good agreement with experimental data. The latter is also compared to the predictions of an analytical model, based on the estimate of a spatially averaged velocity within an infinitely long street canyon. The results of the model, which takes into account varying canyon aspect ratios, are in reasonable agreement with experimental data for all cases studied. Notably, its predictions are significantly better than those provided by the simple analytical relations usually adopted as a reference in tunnel ventilation studies.     

Spatial evolution of coherent motions in finite-length vegetation patch flow

A number of experimental studies on submerged canopy flows have focused on fully-developed flow and turbulent characteristics. In many natural rivers, however, aquatic vegetation occurs in patches of finite length. In such vegetated flows, the shear layer is not formed at the upstream edge of the vegetation patch and coherent motions develop downstream. Therefore, more work is neededz to reveal the development process for large-scale coherent structures within vegetation patches. For this work, we considered the effect of a limited length vegetation patch. Turbulence measurements were intensively conducted in open-channel flows with submerged vegetation using Particle Image Velocimetry (PIV). To examine the transition from boundary-layer flow upstream of the vegetation patch to a mixing-layer-type flow within the patch, velocity profiles were measured at 33 positions in a longitudinal direction. A phenomenological model for the development process in the vegetation flow was developed. The model decomposed the entire flow region into four zones. The four zones are the following: (i) the smooth bed zone, (ii) the diverging flow zone, (iii) the developing zone and (iv) the fully-developed zone. The PIV data also confirmed the efficiency of the mixing-layer analogy and provided insight into the spatial evolution of coherent motions.     

Fitting the truncated negative binomial distribution to count data

Modeling empirical distributions of repeated counts with parametric probability distributions is a frequent problem when studying species abundance. One must choose a family of distributions which is flexible enough to take into account very diverse patterns and possess parameters with clear biological/ecological interpretations. The negative binomial distribution fulfills these criteria and was selected for modeling counts of marine fish and invertebrates. This distribution depends on a vector \(\left( K,\mathfrak {P}\right) \) of parameters, and ranges from the Poisson distribution (when \(K\rightarrow +\infty \)) to Fisher’s log-series, when \(K\rightarrow 0\). Moreover, these parameters have biological/ecological interpretations which are detailed in the literature and in this study. We compared three estimators of K, \(\mathfrak {P}\) and the parameter \(\alpha \) of Fisher’s log-series, following the work of Rao CR (Statistical ecology. Pennsylvania State University Press, University Park, 1971) on a three-parameter unstandardized variant of the negative binomial distribution. We further investigated the coherence underlying parameter values resulting from the different estimators, using both real count data collected in the Mauritanian Exclusive Economic Zone (MEEZ) during the period 1987–2010 and realistic simulations of these data. In the case of the MEEZ, we first built homogeneous lists of counts (replicates), by gathering observations of each species with respect to “typical environments” obtained by clustering the sampled stations. The best estimation of \(\left( K,\mathfrak {P}\right) \) was generally obtained by penalized minimum Hellinger distance estimation. Interestingly, the parameters of most of the correctly sampled species seem compatible with the classical birth-and-dead model of population growth with immigration by Kendall (Biometrika 35:6–15, 1948).     

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.     

The CPCAT as a novel tool to overcome the shortcomings of NOEC/LOEC statistics in ecotoxicology: a simulation study to evaluate the statistical power

Species reproduction is an important determinant of population dynamics. As such, this is an important parameter in environmental risk assessment. The closure principle computational approach test (CPCAT) was recently proposed as a method to derive a NOEC/LOEC for reproduction count data such as the number of juvenile Daphnia. The Poisson distribution used by CPCAT can be too restrictive as a model of the data-generating process. In practice, the generalized Poisson distribution could be more appropriate, as it allows for inequality of the population mean \(\mu\) and the population variance \(\sigma ^2\). It is of fundamental interest to explore the statistical power of CPCAT and the probability of determining a regulatory relevant effect correctly. Using a simulation, we varied between Poisson distribution (\(\mu =\sigma ^2\)) and generalized Poisson distribution allowing for over-dispersion (\(\mu <\sigma ^2\)) and under-dispersion (\(\mu >\sigma ^2\)). The results indicated that the probability of detecting the LOEC/NOEC correctly was \(\ge 0.8\) provided the effect was at least 20% above or below the mean level of the control group and mean reproduction of the control was at least 50 individuals while over-dispersion was missing. Specifically, under-dispersion increased, whereas over-dispersion reduced the statistical power of the CPCAT. Using the well-known Hampel identifier, we propose a simple and straight forward method to assess whether the data-generating process of real data could be over- or under-dispersed.     

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.     

Double-average mean flow and local turbulence intensity profiles from PIV measurements for an open channel flow with rigid vegetation

This contribution presents particle image velocimetry measurements for an open channel stationary uniform and fully developed flow of water over a horizontal flat bed of uniform glass beads in presence of a staggered array of vertical cylindrical stems. The main objective was to explore and quantify the influence of the stems-to-flow relative submergence, h _v /h, over the mean flow and local turbulence intensities. A comparison with measurements for the non-vegetated flow over the same granular bed is presented. Results indicate a remarkable influence of h _v /h over the whole flow field. The time-average mean flow presents a strong spatial variation in the layer of the flow occupied by the stems. The local velocity fluctuations are strongly affected by the presence of the stems, with regions in between the stems where they reach peaks that are several times larger than those encountered in the flow in absence of vegetation. The turbulence intensity profiles are noticeably different when compared to those measured in the non-vegetated flow conditions. From previous works it was possible to derive an equation for the mean velocity, U _v , of the flow through the vegetated layer of height h _v . The prediction of this equation is in good agreement with the uniform value for the double-average longitudinal velocity profile in this layer. A final brief discussion about the possible impact of these vegetated-flow features on the sediment transport is presented.     

Turbulent flow characteristics and drag over 2-D forward-facing dune shaped structures with two different stoss-side slopes

The present paper explores the characteristics of turbulent flow and drag over two artificial 2-D forward-facing waveform structures with two different stoss side slopes of $50^{\circ }$ and $90^{\circ },$ respectively. Both structures possessed a common slanted lee side slope of $6^{\circ }.$ Flume experiments were conducted at the Fluvial Mechanics Laboratory of Indian Statistical Institute, Kolkata. The velocity data were analyzed to identify the spatial changes in turbulent flow addressing the flow separation region with recirculating eddy, the Reynolds stresses, the turbulent events associated with burst-sweep cycles and the drag over two upstream-facing bedforms for Reynolds number $Re_h=1.44\times 10^5.$ The divergence at the stoss side slope between the two structures revealed significant changes in the mean flow and turbulence. Comparison showed that during the flood-tide condition there was no flow separation region on the gentle lee side of the structure with smaller slope at the stoss side, while for the other structure with vertical stoss side slope a thick flow separation region with recirculating eddy was observed at the gentle lee side just downstream of the crest. The recirculating eddy induced on the lee-side had a strong influence on the resistance that the structure exerts to the flow due to loss of energy through turbulence. In contrast, a great amount of reduction in drag was observed in the case of smaller stoss side sloped structure as there was no flow separation. The quadrant analysis was also used to highlight the turbulent event evolution along the bed form structures under flood-tide conditions.     

The Structure of the Shear Layer in Flows over Rigid and Flexible Canopies

Flume experiments were conducted with rigid and flexible model vegetation to study the structure of coherent vortices (a manifestation of the Kelvin–Helmholtz instability) and vertical transport in shallow vegetated shear flows. The vortex street in a vegetated shear layer creates a pronounced oscillation in the velocity profile, with the velocity near the top of a model canopy varying by a factor of three during vortex passage. In turn, this velocity oscillation drives the coherent waving of flexible canopies. Relative to flows over rigid vegetation, the oscillation in canopy geometry has the effect of decreasing the amount of turbulent vertical momentum transport in the shear layer. Using a waving plant to determine phase in the vortex cycle, each vortex is shown to consist of a strong sweep at its front (during which the canopy is most deflected), followed by a weak ejection at its rear (when the canopy height is at a maximum). Whereas in unobstructed mixing layers the vortices span the entire layer, they encompass only 70% of the flexibly obstructed shear layer studied here.     

Waves and turbulence in katabatic winds

The measurements taken during the Vertical Transport and Mixing Experiment (VTMX, October, 2000) on a northeastern slope of Salt Lake Valley, Utah, were used to calculate the statistics of velocity fluctuations in a katabatic gravity current in the absence of synoptic forcing. The data from ultrasonic anemometer-thermometers placed at elevations 4.5 and 13.9 m were used. The contributions of small-scale turbulence and waves were isolated by applying a high-pass digital (Elliptical) filter, whereupon the filtered quantities were identified as small-scale turbulence and the rest as internal gravity waves. Internal waves were found to play a role not only at canonical large gradient Richardson numbers $(\overline{\hbox {Ri}_\mathrm{g} } >1)$ , but sometimes at smaller values $(0.1 < \overline{\hbox {Ri}_\mathrm{g}}<1)$ , in contrast to typical observations in flat-terrain stable boundary layers. This may be attributed, at least partly, to (critical) internal waves on the slope, identified by Princevac et al. [1], which degenerate into turbulence and help maintain an active internal wave field. The applicability of both Monin-Obukhov (MO) similarity theory and local scaling to filtered and unfiltered data was tested by analyzing rms velocity fluctuations as a function of the stability parameter z/L, where L is the Obukhov length and z the height above the ground. For weaker stabilities, $\hbox {z/L}<1$ , the MO similarity and local scaling were valid for both filtered and unfiltered data. Conversely, when $\hbox {z/L}>1$ , the use of both scaling types is questionable, although filtered data showed a tendency to follow local scaling. A relationship between z/L and $\overline{\hbox {Ri}_\mathrm{g} }$ was identified. Eddy diffusivities of momentum $\hbox {K}_\mathrm{M}$ and heat $\hbox {K}_\mathrm{H}$ were dependent on wave activities, notably when $\overline{\hbox {Ri}_\mathrm{g} } > 1$ . The ratio $\hbox {K}_{\mathrm{H}}/\hbox {K}_{\mathrm{M}}$ dropped well below unity at high $\overline{\hbox {Ri}_\mathrm{g} }$ , in consonance with previous laboratory stratified shear layer measurements as well as other field observations.