Experimental study of recirculating flows generated by lateral shock waves in very large channels

Due to the lack of data on hydraulic-jump dynamics in very large channels, the present paper describes the main characteristics of the velocity field and turbulence in a large rectangular channel with a width of 4 m. Although a hydraulic jump is always treated as a wave that is transversal to the channel wall, in the case of this study it has a trapezoidal front shape, first starting from a point at the sidewalls and then developing downstream in an oblique manner, finally giving rise to a trapezoidal shape. The oblique wave front may be regarded as a lateral shockwave that arises from a perturbation at a certain point of the lateral wall and travels obliquely toward the centreline of the channel. The experimental work was carried out at the Coastal Engineering Laboratory of the Water Engineering and Chemistry Department of the Technical University of Bari (Italy). In addition to the hydraulic jump formation, a large recirculating flow zone starts to develop from the separating point of the lateral shock wave and a separate boundary layer occurs. Intensive measurements of the streamwise and spanwise flow velocity components along one-half width of the channel were taken using a bidimensional Acoustic Doppler Velocimeter (ADV). The water surface elevation was obtained by means of an ultrasonic profiler. Velocity vectors, transversal velocity profiles, turbulence intensities and Reynolds shear stresses were all investigated. The experimental results of the separated boundary layer were compared with numerical predictions and related work presented in literature and showed good agreement. The transversal velocity profiles indicated the presence of adverse pressure gradient zones and the law of the wall appears to govern the region around the separated boundary layer.     

PIV experimental study on the flow characteristics upstream of a floating intake in nonlinear stratified ambient conditions

Selective withdrawal is commonly implemented in nonlinearly stratified ambient, which typically has stratified ambient conditions, for purposes of controlling quality. A floating intake is applied as an effective facility of selective withdrawal. However, the outflow dynamics of a floating intake in a nonlinearly stratified ambient have been disregarded, which has a significant effect on the outflow water quality of a reservoir. Experiments were conducted to investigate the effect of thermal stratification on the flow characteristics using particle image velocimetry at three temperature distributions (no stratification, weak stratification and strong stratification). The flow fields upstream of the floating intake showed that the withdrawal layer was formed inhibited by the thermal stratification. And strong stratification produced the thinner withdrawal layer thickness, leading to a larger nonuniform coefficient of the velocity profile. To quantitatively describe the velocity profiles, formulas of dimensionless velocity profiles were proposed. The flow developments were analysed, and the virtual control points located 0.56d above the floating intake (where d is the straight pipe diameter of the floating intake) were obtained. The positions of virtual control points mainly depended on the withdrawal discharge. The decay rate of the velocity along the horizontal line passing through the virtual control point was inversely proportional to the stratification intensity.

     

Kelvin–Helmholtz instability in the presence of variable viscosity for mudflow resuspension in estuaries

The temporal stability of a parallel shear flow of miscible fluid layers of different density and viscosity is investigated through a linear stability analysis and direct numerical simulations. The geometry and rheology of this Newtonian fluid mixing can be viewed as a simplified model of the behavior of mudflow at the bottom of estuaries for suspension studies. In this study, focus is on the stability and transition to turbulence of an initially laminar configuration. A parametric analysis is performed by varying the values of three control parameters, namely the viscosity ratio, the Richardson and Reynolds numbers, in the case of initially identical thickness of the velocity, density and viscosity profiles. The range of parameters has been chosen so as to mimic a wide variety of real configurations. This study shows that the Kelvin–Helmholtz instability is controlled by the local Reynolds and Richardson numbers of the inflection point. In addition, at moderate Reynolds number, viscosity stratification has a strong influence on the onset of instability, the latter being enhanced at high viscosity ratio, while at high Reynolds number, the influence is less pronounced. In all cases, we show that the thickness of the mixing layer (and thus resuspension) is increased by high viscosity stratification, in particular during the non-linear development of the instability and especially pairing processes. This study suggests that mud viscosity has to be taken into account for resuspension parameterizations because of its impact on the inflection point Reynolds number and the viscosity ratio, which are key parameters for shear instabilities.     

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.     

Some characteristics of the urban boundary layer above Rome, Italy, and applicability of Monin–Obukhov similarity

Air temperature and wind speed profiles measured during one year by means of a SODAR-RASS system located within a large park were examined for the urban boundary layer (UBL) over Rome, Italy. These data, combined with velocity and temperature measurements performed near the ground were used to analyze the vertical structure of the boundary layer and to estimate some turbulence parameters characterizing the surface layer. About 52,000 vertical profiles of wind speed and temperature were used for the analysis, allowing investigation for a large variety of stability conditions. First, friction velocity and Obukhov length were examined, showing clearly their dependence on the time of day and season. Second, the applicability of the Monin–Obukhov (MO) similarity theory—developed over rural terrain—was tested up to 200?m above ground level. For the wind speed profiles, the performance of the MO similarity degrades with both increasing height and stability, with maximum errors that are on the order of 300?% at 200?m for the most stable case. In contrast, for the air temperature the error always remains below 50?%.     

Downward Migration of Dense Bottom Currents

The focus of this paper is on the dynamics of a dense current flowing along the continental slope, and the frictionally induced downward motion it experiences. In particular, the movement of the lateral boundaries where the isopycnals meet the bottom are considered. The current is taken to be wide compared to the Rossby radius, which is in accordance with observations and makes the dynamics quasigeostrophic. The time development of the plume thickness is studied, using three different parameterisations for the bottom friction.Independently of the choice of parameterisation, the following results are obtained: In the central part of the plume friction acts as a diffusive process to minimise the curvature of the upper surface of the plume. At the upper edge the plume quickly approaches a state with small slope, i.e. small geostrophic velocity and small frictionally induced downward flow. At the lower edge a tongue of dense water shoots out creating a widening layer. The thickness of the migrating layer is approximately equal to the boundary layer depth and its downward speed is comparable to the along-slope geostrophic velocity. The downslope end of the migrating layer may form a steep front which requires some precautions in the numerical procedure.     

Blockage of saline intrusions in restricted,two-layer exchange flows across a submerged sill obstruction

Results are presented from a series of large-scale experiments investigating the internal and near-bed dynamics of bi-directional stratified flows with a net-barotropic component across a submerged, trapezoidal, sill obstruction. High-resolution velocity and density profiles are obtained in the vicinity of the obstruction to observe internal-flow dynamics under a range of parametric forcing conditions (i.e. variable saline and fresh water volume fluxes; density differences; sill obstruction submergence depths). Detailed synoptic velocity fields are measured across the sill crest using 2D particle image velocimetry, while the density structure of the two-layer exchange flows is measured using micro-conductivity probes at several sill locations. These measurements are designed to aid qualitative and quantitative interpretation of the internal-flow processes associated with the lower saline intrusion layer blockage conditions, and indicate that the primary mechanism for this blockage is mass exchange from the saline intrusion layer due to significant interfacial mixing and entrainment under dominant, net-barotropic, flow conditions in the upper freshwater layer. This interfacial mixing is quantified by considering both the isopycnal separation of vertically-sorted density profiles across the sill, as well as calculation of corresponding Thorpe overturning length scales. Analysis of the synoptic velocity fields and density profiles also indicates that the net exchange flow conditions remain subcritical (G < 1) across the sill for all parametric conditions tested. An analytical two-layer exchange flow model is then developed to include frictional and entrainment effects, both of which are needed to account for turbulent stresses and saline entrainment into the upper freshwater layer. The experimental results are used to validate two key model parameters: (1) the internal-flow head loss associated with boundary friction and interfacial shear; and (2) the mass exchange from the lower saline layer into the upper fresh layer due to entrainment.     

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.     

Turbulence closure models and their application in RAMS

Turbulence closures are fundamental for modelling the atmospheric diffusion in numerical codes and the resulting eddy diffusivities are key parameters in describing the transport and dispersion in the boundary layer. In this work, four turbulence closure schemes have been applied for reproducing a neutral flow over schematic complex terrain using the meteorological model RAMS. Two of the closures, a one-equation (E-l) and a two-equations (E-) model, have been implemented in RAMS in alternative to the ones originally available. In these cases, an analytical method based on the similarity theory for the atmospheric surface layer and boundary layer is adopted to calculate the empirical constants of the turbulence closures. Some examples of numerical studies performed to simulate the flow and turbulence over a 3-D hill in wind-tunnel experiment in neutral stratification are presented and discussed. An intercomparison of simulations related to different closures is considered by analysing the main features of the flow over the hill and by comparing calculated vertical profiles of turbulent kinetic energy with measured ones.     

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.     

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.     

A modification of the classical Ekman model accounting for the Stokes drift and stratification effects

A modification of the classical Ekman model of oceanic wind-driven currents including the Stokes drift and stratification effects is discussed. The modification is formulated as an application of turbulence mechanics accounting for the curvature effect of velocity fluctuation streamlines. It is shown that similar to the Stokes drift effect, the presence of a density jump layer (pycnocline) decreases the veering of the flow velocity vector at the surface from the direction of the wind stress. It is shown also that in the pycnocline the decrease of the norm of the velocity vector as well as its rotation with depth is smaller than in the regions adjacent to the pycnocline. If the Stokes drift and stratification effects are neglected, the model reduces to the classical Ekman solution with the coefficient of the turbulent shear viscosity replaced by an effective viscosity coefficient. The vertical distributions of velocity predicted by the modified model are compared with the velocity data measured in the Drake Passage and within the Long-Term Upper Ocean Study (LOTUS) in the North Atlantic.     

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.     

Integral Model for Turbulent Buoyant Jets in Unbounded Stratified Flows. Part I: Single Round Jet

The mechanics of buoyant jet flows issuing with a general three-dimensional geometry into an unbounded ambient environment with uniform density or stable density stratification and under stagnant or steady sheared current conditions is investigated. An integral model is formulated for the conservation of mass, momentum, buoyancy and scalar quantities in the turbulent jet flow. The model employs an entrainment closure approach that distinguishes between the separate contributions of transverse shear (leading to jet, plume, or wake internal flow dynamics) and of azimuthal shear mechanisms (leading to advected momentum puff or thermal flow dynamics), respectively. Furthermore, it contains a quadratic law turbulent drag force mechanism as suggested by a number of recent detailed experimental investigations on the dynamics of transverse jets into crossflow. The model is validated in several stages: First, comparison with basic experimental data for the five asymptotic, self-similar stages of buoyant jet flows, i.e., the pure jet, the pure plume, the pure wake, the advected line puff, and the advected line thermal, support the choice and magnitude of the turbulent closure coefficients contained in the entrainment formulation. Second, comparison with many types of non-equilibrium flows support the proposed transition function within the entrainment relationship, and also the role of the drag force in the jet deflection dynamics. Third, a number of spatial limits of applicability have been proposed beyond which the integral model necessarily becomes invalid due to its parabolic formulation. These conditions, often related to the breakdown of the boundary layer nature of the flow, describe features such as terminal layer formation in stratification, upstream penetration in jets opposing a current, or transition to passive diffusion in a turbulent ambient shear flow. Based on all these comparisons, that include parameters such as trajectories, centerline velocities, concentrations and dilutions, the model appears to provide an accurate and reliable representation of buoyant jet physics under highly general flow conditions.     

Experimental Study of the Criteria of Flow Laminarization in Two-Dimensional Dense Gas Plumes

Laminarization of flow in a two-dimensional dense gas plume was experimentally investigated in this study. The plume was created by releasing CO₂ through a ground-level line source into a simulated turbulent boundary layer over an aerodynamically rough surface in a meteorological wind tunnel. The bulk Richardson number (Ri_*), based on negative plume buoyancy, plume thickness, and friction velocity, was varied over a wide range so that the effects of stable stratification on plume laminarization could be observed. A variety of ambient wind speeds as well as three different sizes of roughness arrays were used so that possible effects of roughness Reynolds number (Re_*) on plume laminarization could also be identified. Both flow visualization methods and quantitative measurements of velocity and intermittency of turbulence were used to provide quantitative assessments of plume laminarization.Flow visualization provided an overall picture of how the plume was affected by the negative buoyancy. With increasing Ri_*, both the plume depth and the vertical mixing were significantly suppressed, while upstream propagation of the plume from the source was enhanced. The most important feature of the flow revealed by visualization was the laminarization of flow in the lower part of the plume, which appeared to be closely related to both Ri_* and Re_*.Measurements within the simulated dense gas plumes revealed the influence of the stable stratification on mean velocity and turbulence intensity profiles. Both the mean velocity and turbulence intensity were significantly reduced near the surface; and these reductions systematically depended on Ri_*. The roughness Reynolds number also had considerable influence on the mean flow and turbulence structure of the dense gas plumes.An intermittency analysis technique was developed and applied to the digitized instantaneous velocity signals. It not only confirmed the general flow picture within the dense plume indicated by the flow visualization, but also clearly demonstrated the changes of flow regime with variations in Ri_* and Re_*. Most importantly, based on this intermittency analysis, simple criteria for characterizing different flow regimes are formulated; these may be useful in predicting when plume laminarization might occur.     

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.     

Laboratory-numerical studies of stratified spin-up flows

The stability of stratified rotating flows is investigated by means of laboratory experiments and numerical simulations in axisymmetric cylindrical and annular containers with both horizontal and sloping bottoms. The baroclinic current is initiated via incremental spin-up/down of a linearly stratified fluid by an abrupt change in the rotation rate of the system. Particular attention is given to the non-linear flow regime (finite Rossby numbers). It is found that axisymmetric spin-up current loses its azimuthal symmetry when the Burger number drops below unity, and breaks into a system of large-scale cyclonic and anticyclonic vortices with predominantly vertical axis of rotation. Eddies always develop at the density fronts formed by the corner regions adjacent to the sidewalls of the container. It is shown that the stability of the spin-up flow is largely affected by the bottom slope and the structure of the bottom boundary layer.