Stratified flow interactions with a suspended canopy

Field observations of the interactions between a stratified flow and a canopy suspended from the free surface above a solid boundary are described and analysed. Data were recorded in and around the canopy formed by a large long-line mussel farm. The canopy causes a partial blockage of the water flow, reducing velocities in the upper water column. Deceleration of the approaching flow results in a deepening of isopycnals upstream of the canopy. Energy considerations show that the potential for an approaching stratified flow to be diverted beneath a porous canopy is indicated by a densimetric Froude number. Strong stratification or low-velocities inhibit vertical diversion beneath the canopy, instead favouring a horizontal diversion around the sides. The effect on vertical mixing is also considered with a shear layer generated beneath the canopy and turbulence generated from drag within the canopy. In the observations, stratification is shown to be of sufficient strength to limit the effectiveness of the first mixing process, while the turbulence within the canopy is likely to enhance vertical exchange. Velocity and temperature microstructure measurements are used to investigate the effect of the canopy on turbulent dissipation and show that dissipation is enhanced within the canopy.     

Dissipation of Tidal Energy and Associated Mixing in a Wide Fjord

This paper sets out to test the hypothesis that vertical mixing due to the dissipation of the internal tide accounts for a significant proportion of the total vertical mixing in a fjordic basin during a period of deep water isolation. During July and August 1999 two locations in the Clyde Sea were instrumented with moored RD Instruments Acoustic Doppler Current Profilers (ADCPs) and conductivity-temperature-pressure chains: Station C2, near the shallow entrance sill (55 m water depth), and station C1 in the deep basin (155 m water depth). A bottom pressure recorder was also deployed at station C3 by the seaward entrance to the Clyde Sea in the North Channel of the Irish Sea. A Free-falling Light Yo-yo shear microstructure profiler (FLY) was used to measure the dissipation rate of turbulent kinetic energy (TKE) throughout the water column over 25 h at both C1 and C2. These were interspersed with two-hourly conductivity-temperature-depth casts at both sites. The observations show agreement between the dissipation rate of TKE estimated by using a microstructure profiler and that estimated from the decay of the internal tide as measured by the two ADCPs. However, to account for all the implied mixing it is necessary to invoke an additional source of buoyancy flux, the most probable candidate mechanism is enhanced internal wave breaking near the sill and at the sloping boundaries of the deep basin. In addition, the vertical eddy diffusivity estimated from the micro-structure profiler (O(0.5 cm² s^–1) indicates that internal tide induced mixing away from any boundaries contributed significantly to the overall level of mixing which is required to account for the observed evolution of the deep basin water properties.     

The similarity solution for turbulent mixing of two-layer stratified fluid

Experiments are reviewed in which a two-layer salt-stratified tank of water was mixed by turbulence. The density profile began as a single step and evolved to a smooth mixed profile. The turbulence was generated by many excursions of a horizontally moving vertical rod with Richardson number Ri >  0.9 and Reynolds Number Re  >  600. There was almost perfect collapse of all the profiles to one universal profile as a function of a similarity variable. We develop a theoretical model for a simple mixing law with a buoyancy flux that is a function of internal Richardson number Rii. A similarity equation is found. A flux law that increases with small Rii and decreases with large Rii is considered next. Since no analytical solution is known, the similarity concept is tested by numerically integrating the equations in space and time. With buoyancy flux monotonically increasing with internal Richardson number, the similarity approach is valid for a profile starting from a slightly smoothed step. However, a shock forms for a mixing law with higher initial Rii (so that buoyancy flux decreases with Richardson number) and the similarity approach is invalid for those initial conditions.     

Experimental investigation of bubbly flow and turbulence in hydraulic jumps

Many environmental problems are linked to multiphase flows encompassing ecological issues, chemical processes and mixing or diffusion, with applications in different engineering fields. The transition from a supercritical flow to a subcritical motion constitutes a hydraulic jump. This flow regime is characterised by strong interactions between turbulence, free surface and air–water mixing. Although a hydraulic jump contributes to some dissipation of the flow kinetic energy, it is also associated with increases of turbulent shear stresses and the development of turbulent eddies with implications in terms of scour, erosion and sediment transport. Despite a number of experimental, theoretical and numerical studies, there is a lack of knowledge concerning the physical mechanisms involved in the diffusion and air–water mixing processes within hydraulic jumps, as well as on the interaction between the free-surface and turbulence. New experimental investigations were undertaken in hydraulic jumps with Froude numbers up to Fr = 8.3. Two-phase flow measurements were performed with phase-detection conductivity probes. Basic results related to the distributions of void fraction, bubble frequency and mean bubble chord length are presented. New developments are discussed for the interfacial bubble velocities and their fluctuations, characterizing the turbulence level and integral time scales of turbulence representing a “lifetime” of the longitudinal bubbly flow structures. The analyses show good agreement with previous studies in terms of the vertical profiles of void fraction, bubble frequency and mean bubble chord length. The dimensionless distributions of interfacial velocities compared favourably with wall-jet equations. Measurements showed high turbulence levels. Turbulence time scales were found to be dependent on the distance downstream of the toe as well as on the distance to the bottom showing the importance of the lower (channel bed) and upper (free surface) boundary conditions on the turbulence structure.     

Spatial–temporal structure of mixing interface turbulence at two large river confluences

Converging flows at stream confluences often produce highly turbulent conditions. The shear layer/mixing interface that develops within the confluence hydrodynamic zone (CHZ) is characterized by complex patterns of three-dimensional flow that vary both spatially and temporally. Previous research has examined in detail characteristics of mean flow and turbulence along mixing interfaces at small stream confluences and laboratory junctions; however few, if any, studies have examined these characteristics within mixing interfaces at large river confluences. This study investigates the structure of mean velocity profiles as well as spatial and temporal variations in velocity, backscatter intensity, and temperature within the mixing interfaces of two large river confluences. Velocity, temperature, and backscatter intensity data were obtained at stationary locations within the mixing interfaces and at several cross sections within the CHZ using acoustic Doppler current profilers. Results show that mean flow within the mixing interfaces accelerates over distance from the junction apex. Turbulent kinetic energy initially increases rapidly over distance, but the rate of increase diminishes downstream. Hilbert–Huang transform analysis of time series data at the stationary locations shows that multiple dominant modes of fluctuations exist within the original signals of velocity, backscatter intensity, and temperature. Frequencies of the largest dominant modes correspond well with predicted frequencies for shallow wake flows, suggesting that mixing-interface dynamics include wake vortex shedding—a finding consistent with spatial patterns of depth-averaged velocities at measured cross sections. Spatial patterns of temperature and backscatter intensity show that the converging flows at both confluences do not mix substantially, indicating that turbulent structures within the mixing interfaces are relatively ineffective at producing mixing of the flows in the CHZ.     

A model of vertical distribution of suspended matter in an open channel flow

A quasi-stationary model of vertical distribution of concentration of suspended particular matter in the bottom layer of 1D open channel with a sloped bottom and varying free surface slope is discussed. The model proceeds from the balance between the turbulent diffusion and settling with the buoyancy flux effects on the medium turbulence neglected. The model outcome is formulated in the form of an analytic formula for the vertical distribution of concentration. It is shown that the derived formula embraces two basic types of vertical distribution of concentration, one with a monotonic decrease of concentration gradient and the other with a gradient maximum (lutocline) located at some distance from the bottom. The first distribution type realizes for a relatively large settling velocity or low intensity of turbulence and the second type for a small settling velocity or high intensity of turbulence. The skill of the model to mimic realistic situations is demonstrated on data measured in the Jiaojiang Estuary (China).     

RANS-based simulation of transverse turbulent mixing in a 2D geometry

Although transverse mixing is a significant process in river engineering when dealing with the discharge of pollutants from point sources or the mixing of tributary inflows, no theoretical basis exists for the prediction of its rate, which is indeed based upon the results of experimental works carried on in laboratory channels or in streams and rivers. The paper presents the preliminary results of a numerical study undertaken to simulate the transverse mixing of a steady-state point source of a tracer in a two-dimensional rectangular geometry, which is expected to reproduce a shallow flow. This geometry is that of Lau and Krishnappan (J Hydraul Div 13(HY10):1173–1189, 1977), who collected turbulent mixing data for a shallow flow. In the numerical study an approach based on the Reynolds Averaged Navier–Stokes (RANS) equations was applied, where the closure problem was solved by using turbulent viscosity concept. Particularly, the classical two-equations k–? model was used. Two methods were applied to the model results to evaluate the turbulent transverse mixing coefficient. The effect on transverse mixing of a grid located upstream the tracer source was also studied. Numerical results were generally higher than the experimental data. This overestimation could be explained considering the hypothesis of isotropic turbulence underlying the k–? model, which can lead to large turbulent viscosities and rate of mixing. However, RANS-based results may still be considered acceptable also providing the large uncertainties associated with literature predictive equations.     

A numerical (LES) investigation of a shallow-water, mid-latitude, tidally-driven boundary layer

We investigate turbulent mixing in a tidally driven, mid-latitude, shallow-water basin. The study is carried out numerically at a laboratory-scale, using large-eddy simulation. We compared the results of the simulation with those of a correspondent purely oscillatory flow (Stokes boundary layer). The effect of rotation on the flow dynamics is twofold. First, rotation gives rise to a mean spanwise flow that concurs to redistribute the turbulent energy among the Reynolds stresses, in particular between the horizontal directions, thus increasing the mixing across the water column and thickening the layer where developed turbulence is observable. Second, the presence of the horizontal component of the background vorticity (latitude effect) breaks the symmetry between the two semi-cycles of the oscillation, since turbulence results suppressed/enhanced during the first/second semi-cycle. These two effects significantly modify the turbulent characteristics with respect to the purely oscillating flow, although the mechanisms that generates turbulence present similar features. The qualitative agreement between our results and some measurements carried out in two sites with characteristics similar to the case analyzed suggests that the outcomes here provided may be of general use for the analysis of mid-latitude, neutrally stratified, shallow-water basins mainly driven by semi-diurnal tidal currents.     

Eddy covariance CO2 flux measurements in nocturnal conditions: an analysis of the problem

A detailed analysis of the various processes at work in stable boundary layers was made. It pointed out that two main mechanisms may affect eddy covariance measurements in stable conditions and that their impacts were different. On one hand, intermittent turbulence produces strongly nonstationary events during which the validity of turbulent transport and storage measurements is uncertain. On the other hand, during breeze and drainage flow events, significant advection takes place and competes with turbulent flux and storage. Intermittent turbulence questions both the ability of eddy covariance systems to adequately capture turbulent flux and storage and the representativeness of the measurements. Ability of the systems to capture the fluxes could be improved by adapting the averaging time period or the high pass filtering characteristics. However, beyond this, the question of representativeness of the flux remains open as the flux measured during an intermittent turbulence event represents not only the source term, but also the removal of CO2 that built up in the control volume and that cannot be simply related to the source term. In these conditions, the u* discrimination is likely to be insufficient and should be completed with a stationarity criterion. Further research should allow determining better selection criteria. Advection occurs mainly in presence of flows associated with topographical slopes (drainage flows) or with land use changes (breezes). Direct advection measurements were performed at several sites, but the results were shown to be strongly site dependent. A classification based on the general flow pattern and on the source intensity evolution along streamlines was proposed here. Five different patterns were identified that helped to classify the different observations. The classification was found to be a fairly good fit for the observations. This could serve as a tool to better understand and quantify the fluxes at sites subjected to repeatable patterns.     

Generation of internal waves by sheared turbulence: experiments

A series of experiments is presented that model the generation of internal gravity waves in the ocean by the forcing of turbulent eddies in the surface mixed layer.The experimental setup consists of a shallow mixed upper layer and a deep continuously stratified lower layer. A source of turbulence is dragged through the upper layer. Internal waves can freely propagate in the lower layer. The internal waves are measured using synthetic schlieren to determine the frequencies of the generated waves. Consistent with other studies, it is found that the characteristic frequencies of internal waves generated by turbulence are an approximate constant fraction of the buoyancy frequency.     

A closure approach with multi-scale mixing length,and its application to wind and shear stress profiles within the atmospheric boundary layer

A method to determine flow specific first-order closure for the turbulent flux of momentum in the atmospheric boundary layer (ABL) is presented. This is based on the premise that eddy viscosity is a flow rather than a fluid property, and the physically more realistic assumption that the transfer of momentum and other scalar quantities in a turbulent flow takes place by a large, but finite number of length scales, than the often used single length scale, the ‘mixing length’. The resulting eddy viscosity is flow specific and when applied to the study of the ABL, yields the vertical profiles of shear stress and mean wind velocity in good agreement with observations. The method may be extended to other types of turbulent flows, however it should be recognized that each type of flow may yield a different eddy viscosity profile. Using the derived eddy viscosity the paper presents simple analytical solutions of the ABL equations to determine observationally consistent wind speed and shear stress profiles in the ABL for a variety of practical applications including air pollution modelling.     

Dynamics of Turbulence in Low-Speed Oscillating Bottom-Boundary Layers of Stratified Basins

This paper focuses on the impact of an oscillating low-speed current on the structure and dynamics of the bottom-boundary layer (BBL) in a small stratified basin. A set of high-resolution current profile measurements in combination with temperature-microstructure measurements were collected during a complete cycle of the internal oscillation (`seiching') in the BBL of Lake Alpnach, Switzerland. It was found that even a relatively long seiching period of 24 hours significantly changed the form of the near-bottom current profiles as well as the dynamics of the turbulent dissipation rate compared to the steady-state law-of-the-wall. A logarithmic fit to the measured current profiles starting at a distance of 0.5 m above the sediment led to inconsistent estimates of both friction velocity and roughness length. Moreover, a phase lag between the current and the turbulent dissipation of 1.5 hours and a persistent maximum in the current profile at a height of 2.5 to 3 m above the sediment were observed. The experimental findings were compared to the results of a k- turbulence model and showed good agreement in general. Specifically, the inconsistent logarithmic fitting results and the observed phase lag were reproduced well by the model.     

Turbulence measurements in a small subtropical estuary under king tide conditions

In natural waterways and estuaries, the understanding of turbulent mixing is critical to the knowledge of sediment transport, stormwater runoff during flood events, and release of nutrient-rich wastewater into ecosystems. In the present study, some field measurements were conducted in a small subtropical estuary with micro-tidal range and semi-diurnal tides during king tide conditions: i.e., the tidal range was the largest for both 2009 and 2010. The turbulent velocity measurements were performed continuously at high-frequency (50Hz) for 60?h. Two acoustic Doppler velocimeters (ADVs) were sampled simultaneously in the middle estuarine zone, and a third ADV was deployed in the upper estuary for 12?h only. The results provided an unique characterisation of the turbulence in both middle and upper estuarine zones under the king tide conditions. The present observations showed some marked differences between king tide and neap tide conditions. During the king tide conditions, the tidal forcing was the dominant water exchange and circulation mechanism in the estuary. In contrast, the long-term oscillations linked with internal and external resonance played a major role in the turbulent mixing during neap tides. The data set showed further that the upper estuarine zone was drastically less affected by the spring tide range: the flow motion remained slow, but the turbulent velocity data were affected by the propagation of a transient front during the very early flood tide motion at the sampling site.     

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.     

Turbulence and aeration in hydraulic jumps: free-surface fluctuation and integral turbulent scale measurements

In an open channel, a change from a supercritical to subcritical flow is a strong dissipative process called a hydraulic jump. Herein some new measurements of free-surface fluctuations of the impingement perimeter and integral turbulent time and length scales in the roller are presented with a focus on turbulence in hydraulic jumps with a marked roller. The observations highlighted the fluctuating nature of the impingement perimeter in terms of both longitudinal and transverse locations. The results showed further the close link between the production and detachment of large eddies in jump shear layer, and the longitudinal fluctuations of the jump toe. They highlighted the importance of the impingement perimeter as the origin of the developing shear layer and a source of vorticity. The air–water flow measurements emphasised the intense flow aeration. The turbulent velocity distributions presented a shape similar to a wall jet solution with a marked shear layer downstream of the impingement point. The integral turbulent length scale distributions exhibited a monotonic increase with increasing vertical elevation within 0.2 < L_z/d₁ < 0.8 in the shear layer, where L_z is the integral turbulent length scale and d₁ the inflow depth, while the integral turbulent time scales were about two orders of magnitude smaller than the period of impingement position longitudinal oscillations.     

Performance analysis of WRF and LES in describing the evolution and structure of the planetary boundary layer

We implemented the Weather Research and Forecast (WRF) model and WRF Large-Eddy Simulation (WRF–LES), focusing on calculations for the planetary boundary layer (PBL), and compared the results against a data set of a well-documented campaign, in the Houston–Galveston area, Texas, in summer 2006. A methodology using WRF in a mesoscale and LES was implemented to assess the performance of the model in simulating the evolution and structure of the PBL over Houston during the Vertical Mixing Experiment. Also, the WRF model in a real case mode was examined to explore potential differences between the results of each simulation approach. We analyzed both WRF results for key meteorological parameters like wind speed, wind direction and potential temperature, and compared the model results against the observations. The reasonably good agreement of LES results forced with observed surface fluxes provides confidence that LES describes turbulence quantities such as turbulent kinetic energy correctly and warrants further turbulence structure analysis. The LES results indicate a weak but noticeable nighttime turbulent kinetic energy which was produced by wind shear in Houston’s planetary boundary layer and which may likely be related to intermittent turbulence. This is supported by observations made at the University of Houston Moody Tower air quality station when intermittent peaks of carbon monoxide occurred in the evening, although the variability in wind conditions was very little.     

Preliminary Measurements of Turbulence and Environmental Parameters in a Sub-Tropical Estuary of Eastern Australia

In natural systems, mixing is driven by turbulence, but current knowledge is limited in estuarine zones where predictions of contaminant dispersion are often inaccurate. A series of detailed field studies was conducted in a small sub-tropical creek in eastern Australia. Hydrodynamic, physio-chemical and ecological measurements were conducted simultaneously to assess the complexity of the estuarine zone, notably the interactions between turbulence and environment. The measurements were typically performed at high frequency over a tidal cycle. The results provide an original data set to complement long-term monitoring and a basis for a more detailed study of mixing in sub-tropical systems. Unlike many long-term observations, velocity and water quality scalars were measured herein with sufficient spatial and temporal resolutions to determine quantities of interest in the study of turbulence, while ecological indicators were sampled systematically and simultaneously. In particular the results yielded contrasted outcomes, and the finding impacts on the selection process for key water quality indicators.