Stratification and Circulation in a Shallow Turbid Waterbody

Shallow waterbodies are often assumed to be well mixed in the vertical. However, when they are characterised by high turbidity levels, absoption of solar heating within a relatively thin surface layer can produce thermal stratification. Results from an intensive monitoring program have been combined with three-dimensional circulation modelling to examine the diurnal stratification cycles in a small turbid waterbody. The waterbody, known as Rushy Billabong, is located in southeastern Australia and its high turbidity coupled with forcing by wind and solar radiation resulted in regular diurnal cycles of stratification and overturning. Under conditions of light wind and high solar radiation, the model results were generally consistent with the observed temperature field. However, under stronger winds, preferential cooling and sinking of shallow water around the edge of the lake began to contribute significantly to the interior stratification. Model estimates then became more sensitive to the detailed bathymetry and the choice of turbulence parameterisation. The level of stratification is also shown to influence the circulation in the billabong by trapping the wind-driven flow near the surface. Insights provided by the observations and modelling may have broader implications for the management of small turbid systems such as settling ponds, aquaculture ponds, and some natural wetlands.     

Flows through forest canopies in complex terrain

Recent progress on boundary layer flow within and above tall forest canopies in complex terrain is reviewed from the perspective of developing methods to interpret carbon dioxide fluxes from tower measurements in real terrain. Two examples of complex terrain are considered in detail: a forest edge, which exemplifies nonuniform forests, and hilly terrain, which can lead to drainage currents at night. Dynamical arguments show that, when boundary layer winds approach a forest edge, the mean wind adjusts on a length scale of approximately 3L(c), where L(c) is the canopy drag length scale, which depends inversely on the leaf area density of the forest. Over a further distance that also scales on L(c), turbulence in the flow adjusts, and the mixing and transport in the canopy approaches the homogeneous limit. Even low hills change the neutral flow within and above the forest canopy substantially. When the canopy is tall, pressure gradients drive flow up both the upwind and downwind slopes of the hill, leading to an ejection of air out of the top of the canopy just downwind of the crest. This flow at the crest can then advect scalar out of the top of the forest, leading to large variations in the flux of scalar across the hill. At night, when the air near the ground cools and becomes stably stratified, turbulence within the canopy can collapse, even when the flow above the canopy remains turbulent. This leads to a decoupling of the air motions within the canopy from those above. The air above the canopy can then continue to pass up and over the hill, as it does in the neutral case, but at the same time, air within the canopy drains down the hill slopes as drainage currents. These analyses will help us understand when flux towers are reliably measuring the net ecosystem exchange and suggest ways of correcting the flux tower data in more complex situations.     

Quantifying vertical mixing in estuaries

Estuarine turbulence is notable in that both the dissipation rate and the buoyancy frequency extend to much higher values than in other natural environments. The high dissipation rates lead to a distinct inertial subrange in the velocity and scalar spectra, which can be exploited for quantifying the turbulence quantities. However, high buoyancy frequencies lead to small Ozmidov scales, which require high sampling rates and small spatial aperture to resolve the turbulent fluxes. A set of observations in a highly stratified estuary demonstrate the effectiveness of a vessel-mounted turbulence array for resolving turbulent processes, and for relating the turbulence to the forcing by the Reynolds-averaged flow. The observations focus on the ebb, when most of the buoyancy flux occurs. Three stages of mixing are observed: (1) intermittent and localized but intense shear instability during the early ebb; (2) continuous and relatively homogeneous shear-induced mixing during the mid-ebb, and weakly stratified, boundary-layer mixing during the late ebb. The mixing efficiency as quantified by the flux Richardson number Rf was frequently observed to be higher than the canonical value of 0.15 from Osborn (J Phys Oceanogr 10:83–89, 1980). The high efficiency may be linked to the temporal–spatial evolution of shear instabilities.     

Canopy-wake dynamics and wind sheltering effects on Earth surface fluxes

The atmospheric boundary layer adjustment at the abrupt transition from a canopy (forest) to a flat surface (land or water) is investigated in a wind tunnel experiment. Detailed measurements examining the effect of canopy turbulence on flow separation, reduced surface shear stress and wake recovery are compared to data for the classical case of a solid backward-facing step. Results provide new insights into the interpretation for flux estimation by eddy-covariance and flux gradient methods and for the assessment of surface boundary conditions in turbulence models of the atmospheric boundary layer in complex landscapes and over water bodies affected by canopy wakes. The wind tunnel results indicate that the wake of a forest canopy strongly affects surface momentum flux within a distance of 35–100 times the step or canopy height, and mean turbulence quantities require distances of at least 100 times the canopy height to adjust to the new surface. The near-surface mixing length in the wake exhibits characteristic length scales of canopy flows at the canopy edge, of the flow separation in the near wake and adjusts to surface layer scaling in the far wake. Components of the momentum budget are examined individually to determine the impact of the canopy wake. The results demonstrate why a constant flux layer does not form until far downwind in the wake. An empirical model for surface shear stress distribution from a forest canopy to a clearing or lake is proposed.     

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.     

Vertical Buoyant Jets in a Linearly Stratified Ambient Cross-Stream

In this study a numerical simulation is performed to investigate the effect of ambient density stratification on the characteristic of a vertical buoyant jet in a stably linearly stratified ambient cross-stream. Based on the ensemble integral method, the theoretical formulation for such a flow field consists of a set of elliptic Reynolds-averaged equations incorporating with the k– transport equations for the turbulence closure. An oscillating motion can be observed in the computed jet trajectory, and the corresponding alternative variation of dominant quantities for the induced momentum and buoyancy of the jet are examined by direct integration on a cross-section along the jet axis. The influences on the jet development both by the ambient cross-stream and the stratification are investigated. The oscillation characteristic shows that a linear relation holds between the wavenumber of jet trajectory, crossflow velocity and the Brunt–Väisälä frequency of ambient stratification. Computational results indicate that the formation of the secondary and a third pairs of vortices, which are not induced in the unstratified environment, causes the jet flow oscillation from its maximum height-of-rise in the flowing direction. The ambient stratification prohibits the growth of the plume radius and reduces the mixing rate as well as the plume rise. The developed flow indicates the transformation of entrainment mechanism in stratified crossflow.     

Turbulence suppression by suspended sediment within a geophysical flow

Experiments are performed in a mixing box to evaluate the effect of suspended sediment on turbulence generated by an oscillating grid. Quartz-density sand of varying sizes and concentrations is used, and particle image velocimetry is employed to quantify only the fluid phase. Results show that (1) while a relatively large secondary flow field is present in the box, turbulence is a maximum near the grid and it decreases systematically toward the water surface; (2) relatively high concentrations of fine sediment can markedly alter this secondary flow field and significantly decrease both the time-mean and turbulent kinetic energy within the flow, yet these same sediment concentrations have little effect on the integral time and length scales derived for each velocity component; and (3) the overall turbulence suppression observed can be related to the transfer of energy from the fluid to the sediment and the maintenance of a suspended sediment load rather than commonly employed turbulence modulation criteria. These experimental data demonstrate unequivocally that the presence of a suspended sediment load can significantly reduce overall turbulent kinetic energy, and these results should be applicable to a range of sediment-laden geophysical flows.     

The influence of water stability on the vertical structure of a phytoplankton community

The vertical distribution of the phytoplankton community in association with water column stability was examined for 1 year in an inshore area of the Southern Aegean Sea. An analysis of variance model (split-plot design) was applied to evaluate the variations in the vertical profile of diatoms, flagellates and coccolithophores. When either weak stratification or mixing conditions prevailed, diatoms in general were uniformly distributed throughout the water column while flagellates and coccolithophores appeared occasionally stratified. During the strong stratification period, all taxa demonstrated significant variations in abundance between depths in most cases. However, none of these taxa was confined to a single depth stratum during either the water mixing or the stratification period, but were all present at all depths during all seasons. The results demonstrate clearly that the parameter taxon is an important component in ecological observations on the vertical distribution of phytoplankton.     

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.

     

The Chemistry of Throughfall, Stemflow and Soil Water Beneath Oak Woodland and Moorland Vegetation in Upland Wales

The chemistry of bulk precipitation, throughfall, stemflow and soil waters beneath an oak wood (Quercus petraea) canopy and soil waters under moorland vegetation were measured at two sites on acid brown podzolic soils near Llyn Brianne in rural mid-Wales, UK. Between March 1986 and November 1988, precipitation was 4354 mm and annual interception losses from the oak canopy averaged 13% of incident precipitation. Throughfall and stemflow were more acid and concentrations of most solutes were increased 2- to 4-fold compared with bulk precipitation. Nitrate was the only solute retained within the tree canopy. Throughfall collected beneath patches of bracken on the forest floor was less acidic but contained substantially higher concentrations of major ions than bulk precipitation and oak throughfall. the moorland soil was more acidic, contained more exchangeable calcium but less exchangeable aluminium and potassium than the woodland soil. Soil waters beneath both vegetation types were acidic (mean pH range 4.5-4.9) and dominated by sodium and chloride. with the exception of calcium, soil water solute concentrations were greater beneath oak. These differences are ascribed to larger atmospheric inputs beneath the oak canopy compared with the shorter grasses, combined with the effect of differences in nutrient dynamics and water fluxes. Variations in soil water aluminium chemistry are explained in terms of ion exchange and podzolisa-tion processes. the water quality implications of increased upland afforestation of moorland by broadleaved trees are discussed.     

The Chemistry of Throughfall,Stemflow and Soil Water Beneath Oak Woodland and Moorland Vegetation in Upland Wales

The chemistry of bulk precipitation, throughfall, stemflow and soil waters beneath an oak wood (Quercus petraea) canopy and soil waters under moorland vegetation were measured at two sites on acid brown podzolic soils near Llyn Brianne in rural mid-Wales, UK. Between March 1986 and November 1988, precipitation was 4354 mm and annual interception losses from the oak canopy averaged 13% of incident precipitation. Throughfall and stemflow were more acid and concentrations of most solutes were increased 2- to 4-fold compared with bulk precipitation. Nitrate was the only solute retained within the tree canopy. Throughfall collected beneath patches of bracken on the forest floor was less acidic but contained substantially higher concentrations of major ions than bulk precipitation and oak throughfall. the moorland soil was more acidic, contained more exchangeable calcium but less exchangeable aluminium and potassium than the woodland soil. Soil waters beneath both vegetation types were acidic (mean pH range 4.5-4.9) and dominated by sodium and chloride. with the exception of calcium, soil water solute concentrations were greater beneath oak. These differences are ascribed to larger atmospheric inputs beneath the oak canopy compared with the shorter grasses, combined with the effect of differences in nutrient dynamics and water fluxes. Variations in soil water aluminium chemistry are explained in terms of ion exchange and podzolisa-tion processes. the water quality implications of increased upland afforestation of moorland by broadleaved trees are discussed.     

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.     

On Disturbances Introduced by Impulse Source into Stratified Two-Component Media

The paper considers the problem concerning the response of a stably stratified two-component medium (salt water, moist air) in the presence of a stationary source of vertical impulse. For a homogeneous vertical distribution of the impulse source (i.e., the applied vertical force), due to the symmetry of the problem, one succeeded in finding the explicit analytical solution of the stationary problem for arbitrary source amplitude. The solution is expressed through Kelvin’s cylindrical functions and represents the stationary vertical jet. The two-component character of the medium can influence substantially the quality of the properties of the solution. In particular, the jet parameters are not defined uniquely by the buoyancy frequency (density stratification). In the solution, the stratifications of the two hydrodynamic components have the distinctive influences that are defined by values of corresponding exchange coefficients. For example, in salt water the solution dependence on salinity stratification may be much more than on temperature stratification.     

Turbulence characteristics within sparse and dense canopies

Boundary layer interactions with canopies control various environmental processes. In the case of dense and homogeneous canopies, the so-called mixing layer analogy is most generally used. When the canopy becomes sparser, a transition occurs between the mixing layer and the boundary layer perturbed by interactions between element wakes. This transition has still to be fully understood and characterized. The experimental work presented here deals with the effect of the canopy density on the flow turbulence and involves an artificial canopy placed in a fully developed turbulent boundary layer. One and two-component velocity measurements are performed, both within and above the canopy. The influence of the spacing between canopy elements is studied. Longitudinal velocity statistical moments and Reynolds stresses are calculated and compared to literature data. For spacings greater than the canopy height, evidences of this transition are found in the evolution of the skewness factor, shear length scale and mixing length.     

The effects of littoral zone vegetation on turbulent mixing in lakes

Micro-scale thermal profile data were acquired in four lakes in northwest England and southeast Australia that ranged from a small, sheltered pond with a surface area of about 1 ha to more open lakes with surface areas of several square kilometres. These lakes provided a range of topographic and climatic contexts, basin morphologies and dominant macrophyte species. The data were acquired using two SCAMP profilers, one deployed in the open water and the other mounted on a field traverse deployed within the vegetated littoral zone. From these profile data, turbulence parameters were calculated. The results show the variation in the influence of vegetation on turbulence in the four lakes, which depends on the combination of wind stress, solar radiative forcing and macrophyte mechanical properties. In the sheltered pond, the vegetation alters the light climate within the water, thus reducing stratification and allowing weak, thermally-driven mixing. In the larger lakes, however, the primary action of the vegetation is to prevent surface-generated TKE from penetrating the water column, although this effect becomes less important as the plant separation increases. A simple mechanistic model, calibrated against the field data, suggests that the macrophyte mechanical properties are most important in determining the turbulent kinetic energy (TKE) profile. Increasing the number of turbulence-generating plants reduces the transport of surface-generated TKE into the deeper water, consistent with the field observations. The model suggests that solar forcing, as measured by the temperature gradient between the surface and bottom waters, is of less importance since the TKE profile is similar in runs with different gradients. Perhaps most surprisingly, the value of the surface-wind stress used in the model is not important, within the limitations of the model, as it does not change the TKE profile, except in a thin surface layer.     

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.     

Large eddy simulation of flow and scalar transport in a vegetated channel

Predicting flow and mass transport in vegetated regions has a broad range of applications in ecology and engineering practice. This paper presents large eddy simulation (LES) of turbulent flow and scalar transport within a fully developed open-channel with submerged vegetation. To properly represent the scalar transport, an additional diffusivity was introduced within the canopy to account for the contribution of stem wakes, which were not resolved by the LES, to turbulent diffusion. The LES produced good agreement with the velocity and concentration fields measured in a flume experiment. The simulation revealed a secondary flow distributed symmetrically about the channel centerline, which differed significantly from the circulation in a bare channel. The secondary circulation accelerated the vertical spread of the plume both within and above the canopy layer. Quadrant analysis was used to identify the form and shape of canopy-scale turbulent structures within and above the vegetation canopy. Within the canopy, sweep events contributed more to momentum transfer than ejection events, whereas the opposite occurred above the canopy. The coherent structures were similar to those observed in terrestrial canopies, but smaller in scale due to the constraint of the water surface.     

Turbulent kinetic energy budgets in a model canopy: comparisons between LES and wind-tunnel experiments

A comparative study of turbulence in a wind-tunnel model canopy is performed, using Large eddy simulation (LES) and experimental data from PIV and hot-wire anemometry measurements. The model canopy is composed of thin cylindrical stalks. In the LES, these are represented using a plant-scale approach, while the scale-dependent Lagrangian dynamic model is used as subgrid-scale model. LES predictions of turbulence statistics and energy spectra are found to be in good agreement with the experimental data. Turbulent kinetic energy (TKE) budgets from the LES simulation are analyzed to provide more information absent in the measurements. Results confirm that sloshing motions at the low levels of the canopy are mainly driven by pressure fluctuations. A difference between the energy flux obtained from the energy spectrum and the SGS dissipation rate is observed, consistent with a spectral bypass mechanism in which the real spectral flux due to cascade is smaller than that implied by the energy-spectrum level, due to direct drain by the canopy.     

Large-eddy simulation of low-level jet-like flow in a canopy

The computational method of Large-Eddy Simulations has been used to study the weak, neutrally stable drainage flow within tree canopies. The computational results show that a secondary velocity maximum that resembles a jet is formed within the canopy under the nocturnal flow conditions. This jet-like flow is important in the analysis and measurements of the net ecosystem-atmosphere exchange (NEE) for carbon dioxide (CO₂). A uniformly distributed, plane source was placed within the canopy in order to simulate the nocturnal production of CO₂. The NEE is calculated as the sum of the integration of the rate of change of the concentration of CO₂ over the computational domain, the vertical turbulent flux measured directly by eddy-covariance (EC) method, and the advection terms, which are not taken into account in the EC method. Numerical results of the velocity and concentration fields, within and above the canopy, are presented and their impact on the CO₂ transport is investigated in detail. The computational results show that 15–20% of NEE is drained out by the advection process under the canopy. The results also show that the turbulent fluctuations in the lateral direction are also significant and may result in 2–5% CO₂ transport.     

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

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