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.     

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.     

An equation of motion for particles of finite Reynolds number and size

In order to simulate the motion of bubbles, drops, and particles, it is often important to consider finite Reynolds number effects on drag, lift, torque, and history force. Herein, an equation of motion is developed for spherical particles with a no-slip surface based on theoretical analysis, experimental data, and surface-resolved simulations. The equation of motion is then extended to account for finite particle size. This extension is critical for particles which will have a size significantly larger than the grid cell size, particularly important for bubbles, and low-density particles. The extension to finite particle size is accomplished through spatial-averaging (both volume-based and surface-based) of the continuous flow properties. This averaging is consistent with the Faxen limit for solid spheres at small Reynolds numbers and added mass and fluid stress forces at inviscid limits. The finite Re _p corrections are shown to have good agreements with experiments and resolved-surface simulations. The finite size corrections are generally fourth-order accurate and an order of magnitude more accurate than point-force expressions (which neglect quadratic and higher spatial gradients) for particles with size on the order of the gradient length-scales. However, further work is needed for more quantitative assessment of the truncation terms and the overall model robustness and accuracy in complex flows.     

Turbulent secondary flows in wall turbulence: vortex forcing,scaling arguments,and similarity solution

Spanwise surface heterogeneity beneath high-Reynolds number, fully-rough wall turbulence is known to induce a mean secondary flow in the form of counter-rotating streamwise vortices—this arrangement is prevalent, for example, in open-channel flows relevant to hydraulic engineering. These counter-rotating vortices flank regions of predominant excess(deficit) in mean streamwise velocity and downwelling(upwelling) in mean vertical velocity. The secondary flows have been definitively attributed to the lower surface conditions, and are now known to be a manifestation of Prandtl’s secondary flow of the second kind—driven and sustained by spatial heterogeneity of components of the turbulent (Reynolds averaged) stress tensor (Anderson et al. J Fluid Mech 768:316–347, 2015). The spacing between adjacent surface heterogeneities serves as a control on the spatial extent of the counter-rotating cells, while their intensity is controlled by the spanwise gradient in imposed drag (where larger gradients associated with more dramatic transitions in roughness induce stronger cells). In this work, we have performed an order of magnitude analysis of the mean (Reynolds averaged) transport equation for streamwise vorticity, which has revealed the scaling dependence of streamwise circulation intensity upon characteristics of the problem. The scaling arguments are supported by a recent numerical parametric study on the effect of spacing. Then, we demonstrate that mean streamwise velocity can be predicted a priori via a similarity solution to the mean streamwise vorticity transport equation. A vortex forcing term has been used to represent the effects of spanwise topographic heterogeneity within the flow. Efficacy of the vortex forcing term was established with a series of large-eddy simulation cases wherein vortex forcing model parameters were altered to capture different values of spanwise spacing, all of which demonstrate that the model can impose the effects of spanwise topographic heterogeneity (absent the need to actually model roughness elements); these results also justify use of the vortex forcing model in the similarity solution.     

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.     

Formation of tidal starting-jet vortices through idealized barotropic inlets with finite length

This paper presents a surface particle image velocimetry study to investigate the dynamics of shallow starting-jet dipoles formed by tidal flow through inlets and their interaction with vorticity formed at the inlet channel lateral boundaries. Vortical structure in the flow field is identified using a local swirl strength criterion evaluated from the two-dimensional flow field. The starting jet dipole vortices and vortices formed as the lateral boundary layers are expelled during flow reversal are characterized by their trajectory, size, and circulation. Using these quantities, a model is developed to predict the size and strength of the expelled lateral boundary layer vortices based on the inlet velocity, channel length, and width of the lateral boundary layer. The expelled boundary layer vortices are found to disrupt the formation of the primary tidal jet dipole through two mechanisms. First, because the boundary layer vortices themselves form a dipole with each half of the starting-jet dipole, the starting-jet vortices are pulled apart and advected away from the inlet mouth early in the tidal cycle, resulting in a reduction in the spin-up time and the amount of vorticity input during starting-jet vortex formation. Second, the advection of each dipole away from the inlet disconnects each starting-jet vortex from the starting jet; hence, the vortices are not fed by fluid in the jet or energized by shear in the jet boundary layers. These influences of the lateral boundary layer on the starting-jet vortices’ formation and propagation are found to be a function of the channel length L, maximum velocity U, and tidal period T, resulting in a predictive value to characterize their trajectory, strength, and evolution.     

Interaction between flow, transport and vegetation spatial structure

This paper summarizes recent advances in vegetation hydrodynamics and uses the new concepts to explore not only how vegetation impacts flow and transport, but also how flow feedbacks can influence vegetation spatial structure. Sparse and dense submerged canopies are defined based on the relative contribution of turbulent stress and canopy drag to the momentum balance. In sparse canopies turbulent stress remains elevated within the canopy and suspended sediment concentration is comparable to that in unvegetated regions. In dense canopies turbulent stress is reduced by canopy drag and suspended sediment concentration is also reduced. Further, for dense canopies, the length-scale of turbulence penetration into the canopy, δ _e , is shown to predict both the roughness height and the displacement height of the overflow profile. In a second case study, the relation between flow speed and spatial structure of a seagrass meadow gives insight into the stability of different spatial structures, defined by the area fraction covered by vegetation. In the last case study, a momentum balance suggests that in natural channels the total resistance is set predominantly by the area fraction occupied by vegetation, called the blockage factor, with little direct dependence on the specific canopy morphology.     

Direct measurements of the drag force over aligned arrays of cubes exposed to boundary-layer flows

Wind tunnel measurements of the total drag force for aligned arrays of cubes exposed to two different boundary-layer flows at three flow velocities are discussed. The drag force for eight different building packing densities λ _p (from 0.028 to 1) is measured with a standard load cell generating a novel dataset. Different λ _p are reproduced by increasing the number of buildings on the same lot area; this represents a real situation that an urban planner is faced with when a lot area of a given (fixed) size is allocated to the development of new built areas. It is assumed that the surrounding terrain is uniform and there is a transition from a given roughness (smooth) to a new roughness (rough). The approaching flow will adjust itself over the new surface within a distance that in general may be larger than the horizontal length covered by the array. We investigate the region where the flow adjustment occurs. The wide range of packing densities allowed us to analyse in detail the evolution of the drag force. The drag force increases with increasing packing densities until it reaches a maximum at an intermediate packing density (λ _p  = 0.25 in our case) followed by a slight decrease at larger packing densities. The value of the drag force depends on the flow adjustment along the array which is evaluated by introducing the parameter “drag area” to retrieve information about the drag distribution at different λ _p . Results clearly suggest a change of the distribution of the drag force, which is found to be relatively uniform at low packing densities, while most of the force acts on first rows of the arrays at large packing densities. The drag area constitutes the basis for the formulation of a new adjustment length scale defined as the ratio between the volume of the air within the array and the drag area. The proposed adjustment length scale automatically takes into account the change in drag distribution along the array for a better parameterization of urban effects in dispersion models.     

A Numerical Study for Turbulent Flow and Thermal Influence over Inhomogenous Canopy of Roughness Elements

A large-eddy simulation with transitional structure function(TSF) subgrid model we previously proposed was performed to investigate the turbulent flow with thermal influence over an inhomogeneous canopy, which was represented as alternative large and small roughness elements. The aerodynamic and thermodynamic effects of the presence of a layer of large roughness elements were modelled by adding a drag term to the three-dimensional Navier–Stokes equations and a heat source/sink term to the scalar equation, respectively. The layer of small roughness elements was simply treated using the method as described in paper (Moeng 1984, J. Atmos Sci. 41, 2052–2062) for homogeneous rough surface. The horizontally averaged statistics such as mean vertical profiles of wind velocity, air temperature, et al., are in reasonable agreement with Gao et al.(1989, Boundary layer meteorol. 47, 349–377) field observation (homogeneous canopy). Not surprisingly, the calculated instantaneous velocity and temperature fields show that the roughness elements considerably changed the turbulent structure within the canopy. The adjustment of the mean vertical profiles of velocity and temperature was studied, which was found qualitatively comparable with Belcher et al. (2003, J Fluid Mech. 488, 369–398)’s theoretical results. The urban heat island(UHI) was investigated imposing heat source in the region of large roughness elements. An elevated inversion layer, a phenomenon often observed in the urban area (Sang et al., J Wind Eng. Ind. Aesodyn. 87, 243–258)’s was successfully simulated above the canopy. The cool island(CI) was also investigated imposing heat sink to simply model the evaporation of plant canopy. An inversion layer was found very stable and robust within the canopy.     

Stability and Mixing of a Vertical Axisymmetric Buoyant Jet in Shallow Water

The stability, mixing and effect of downstream control on axisymmetric turbulent buoyant jets discharging vertically into shallow stagnant water is studied using 3D Reynolds-averaged Navier–Stokes equations (RANS) combined with a buoyancy-extended k –ε model. The steady axisymmetric turbulent flow, temperature (or tracer concentration) and turbulence fields are computed using the finite volume method on a high resolution grid. The numerical predictions demonstrate two generic flow patterns for different turbulent heated jet discharges and environmental parameters (i) a stable buoyant discharge with the mixed fluid leaving the vertical jet region in a surface warm water layer; and (ii) an unstable buoyant discharge with flow recirculation and re-entrainment of heated water. A stratified counterflow region always appears in the far-field for both stable and unstable buoyant discharges. Provided that the domain radius L exceeds about 6H, the near field interaction and hence discharge stability is governed chiefly by the jet momentum length scale to depth ratio l_M/H, regardless of downstream control. The near field jet stability criterion is determined to be l_M/H = 3.5. A radial internal hydraulic jump always exists beyond the surface impingement region, with a 3- to 6-fold increase in dilution across the jump compared with vertical buoyant jet mixing. The predicted stability category, velocity and temperature/concentration fields are well-supported by experiments of all previous investigators.     

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.     

Habitat-induced morphological variation influences photosynthesis and drag on the marine macroalga <Emphasis Type="Italic">Pachydictyon coriaceum</Emphasis>

Photosynthesis, growth, distribution, and persistence of macroalgae are determined in part by the physical environment in which they live. Therefore, discerning how macroalgae interact with their physical environment is necessary to better understand their physiological performance. The purpose of this study was to examine what photosynthetic and hydrodynamic costs and benefits the morphology of Pachydictyon coriaceum (Phaeophyta) confers on the thallus in a given environment. Principal components analysis of morphometric measurements of Pachydictyon coriaceum from different flow habitats and depths separated thalli into three distinct morphs: shallow wave-exposed, shallow wave-protected, and deep. To test the hypothesis that thallus morphology affects net photosynthesis (NP), thalli of three morphotypes of P. coriaceum were incubated in an enclosed recirculating flume under three simulated light/water flow environments representing conditions from which the three morphotypes were collected. The wave-protected and deep morphs had significantly higher rates of photosynthesis than the wave-exposed morph for all three simulated environments. The dense, compact shape of the wave-exposed morph readily streamlines with flow and in doing so, potentially shades many of its internal blades likely accounting for its lower biomass-specific NP. Drag coefficients (C _d) were estimated for the three morphotypes over a range of flow velocities between 0.08 and 0.47 m s⁻¹. At lower water flow velocities (0.08–0.21 m s⁻¹), wave-exposed morphs had the lowest C _d among the three morphotypes. But drag coefficients of the three morphotypes converged with increasing flow velocities, and at velocities >0.31 m s⁻¹ there were no differences in C _d among the three morphotypes. The results of this study indicate that the environmentally-shaped morphs influence photosynthesis and, to a lesser degree, hydrodynamic forces acting on P. coriaceum.     

Experimental Study of Gas-Liquid Interfacial Properties in a Stepped Cascade Flow

Gas-liquid interface measurements were conducted in a strongly turbulent free-surface flow (i.e., stepped cascade). Local void fractions, bubble count rates, bubble size distributions and gas-liquid interface areas were measured simultaneously in the air-water flow region using resistivity probes. The results highlight the air-water mass transfer potential of a stepped cascade with measured specific interface area over 650 m^–1 and depth-average specific area up to 310 m^–1. A comparison between single-tip and double-tip resistivity probes suggests that simple robust single-tip probes may provide accurate, although conservative, gas-liquid interfacial properties. The latter device may be used in the field and in prototype plants. Notation a = specific interface area (m^–1); a _mean = depth-average specific interface area (m^–1): a _mean=frac1Y ₉₀limits sup> Y ₉₀ sup ₀(1–C)dy; C = local void fraction; C _gas = dissolved gas concentration (kg m^–3); C _mean = depth-average mean air concentration defined as: C _mean=1–d/Y ₉₀; C _s = saturation concentration (kg m^–3); D = dimensionless air bubble diffusivity (defined by [1]); d = equivalent clear-water flow depth (m): d=limits sup> Y ₉₀ sup ₀(1–C) dy; d_ab = air bubble diameter (m); d_c = critical flow depth (m); for a rectangular channel: d _c=sqrt[3]q _w ²/g; F = air bubble count rate (Hz); F _max = maximum bubble count rate (Hz), often observed for C=50%; g = gravity acceleration (m s^–2); h = step height (m); K _L = liquid film coefficient (m s^–1); K = integration constant defined as: K=tanh ^–1 sqrt0.1)+(2D)^–1 [1]; L = chute length (m); N = velocity distribution exponent; ———– ^*Corresponding author, E-mail: h.chanson@mailbox.uq.edu.au Q _w = water discharge (m³ s^–1); q _w = water discharge per unit width m² s^–1); t = time (s); V = local velocity (m s^–1); V _c = critical flow velocity (m s^–1); for a rectangular channel: V _c=sqrt[3]q _w g V _max = maximum air-water velocity (m s^–1); V ₉₀ = characteristic air-water velocity (m s^–1) where C = 90%; W = channel width (m); x = longitudinal distance (m) measured along the flow direction (i.e., parallel to the pseudo-bottom formed by the step edges); y = distance (m) normal to the pseudo-bottom formed by the step edges; Y₉₀ = characteristic distance (m) where C=0.90; Y ₉₈ = characteristic distance (m) where C=0.98; = slope of pseudo-bottom by the step edges; = diameter (m).     

Structure of pathways in ecological networks: relationships between length and number

In ecosystems network, structure determines adjacent (direct) and non-adjacent (indirect) pathways over which energy, matter, and information can flow. The more pathways, the more possible ways the conservative substance can move in zero-sum transactions between network nodes that the pathways interconnect, and the more possible non-conservative, nonzero-sum relations can be secondarily derived from these. Structural analysis is a tool we employ, from a family of input–output methods for exploring zero- and nonzero-sum attributes of environmental networks, to count pathways of varying length between network nodes. In this paper, we examine the relationship between pathway length (k) and number (P_k) as determined by system size (n, number of nodes) and extent and pattern of connectance (C). We develop a measure (m_a) of pathway growth in numbers with increasing length, and then normalize this to the maximum rate possible (m_a/m_c) for a given system size. These measures apply to two pathway types—paths, m_a(0) and m_a(0)/m_c(0), which forbid adjacent node repetitions, and walks, m_a(1) and m_a(1)/m_c(1), which allow them. We find that network size has a curvilinear effect on the pathway number versus length relationship, and extent and pattern of connectance are convolved. Values computed for the paths and walks of three ecosystem models (oyster reef, freshwater marsh, and reservoir cove) are used to compare their pathway structure.     

Photosynthetic characteristics of nanoplankton and picoplankton from the surface mixed layer

Nanoplankton and picoplankton primary production has been studied at two oceanic stations in the Porcupine Sea-bight and at one shelf station in the Celtic Sea. At both sites, low wind conditions in June and July 1985 resulted in greatly reduced vertical turbulent mixing and a secondary, temporary thermocline developed in what is usually a well-mixed surface layer; as a result, there was physical separation of the phytoplankton within two zones of the surface mixed layer. The photosynthetic characteristics of three size fractions (>5 m, <5 to >1 m and <1 to >0.2 m) of phytoplankton populations from the two zones have been measured. Phytoplankton was more abundant at the oceanic stations and chlorophyll a values were between 1.3 and 2.2 mg chlorophyll a m^-3, compared with 0.3 to 0.6 mg chlorophyll a m^-3 at the shelf station; at both stations, numbers of cyanobacteria were slightly higher in the lower zone of the surface mixed layer. There was no effect of the temporary thermocline on the vertical profiles of primary production and most phtosynthesis occurred in the surface 10 m. Photosynthetic parameters of the three size fractions of phytoplankton have been determined; there was considerable day-to-day variation in the measured photosynthetic parameters. Assimilation number (P _m ^B ) of all >5 m phytoplankton was lower for the deeper than for the surface populations, but there was little change in initial slope (a ^B ). The small oceanic nanoplankton (<5 to >1 m) showed changes similar to the >5 m phytoplankton, but the same size fraction from the shelf station showed changes that were more like those shown by the picoplankton (<1 m) viz, little change in P _m ^B but an increase in a ^B with depth. Values of a ^B were generally greater for the picoplankton fraction than for the larger phytoplankton, but values of adaptation parameter (I _k )(=P _m ^B /) were not always less. There was little evidence to support the hypothesis that these populations of picoplankton were significantly more adapted to low light conditions than the larger phytoplankton cells. When photosynthetic parameters of the picoplankton were normalised to cell number (P _m ^C /a ^C ) rather than chlorophyll a, P _m ^C was comparable to other published data for picoplankton, but a ^C was much lower. The maximum doubling time of the picoplankton at saturating irradiance is calculated to be ca. 8.5 h for the oceanic population and ca. 6.2 h for the shelf population.     

Mass transfer limitation of photosynthesis of coral reef algal turfs

Algal turfs are the major primary producing component on many coral reefs and this production supports higher levels in the complex reef trophic web. Rates of metabolism of algal turfs are related positively to water motion, consistent with limitation by the diffusion of a substance through a boundary layer. Based on engineering mass transfer theory, we hypothesized that photosynthesis of algal turfs is controlled by rates of mass transfer and responses of photosynthesis to increasing flow speed should be predicted by engineering correlations. This hypothesis was tested in ten experiments where photosynthesis was estimated in a flume/respirometer from changes in dissolved oxygen at eight flow speeds between 0.08 and 0.52 m/s. Flow in the flume and over the reef at Kaneohe Bay, Oahu, Hawaii was estimated using hot-film thermistor and electromagnetic current meters. Rates of photosynthesis were related positively to flow in all experiments and plots of the log of the average Sherwood number (Sh _meas) versus log Reynolds number (Re _D) for each experiment are lower than predicted for mass transfer through a turbulent boundary layer. Algal turf-covered plates are characterized as hydrodynamically transitional to fully rough surfaces and the lower than predicted slopes suggest that roughness reduces rates of mass transfer. A negative correlation between algal turf biomass and slopes of the log Sh _meas−log Re _D plots suggests that mass transfer to algal turfs is affected significantly by the physical structure of the algal community. Patterns of photosynthesis based on changes in dissolved oxygen and dissolved inorganic carbon concentrations (DIC) indicate that the flow speed effect is not the result of increased flux of oxygen from the algal turfs, and combined with the short response time to flow speed, suggest that DIC may limit rates of photosynthesis. Although there are differences between flow in the flume and flow over algal turfs on the reef, these results suggest that photosynthesis is controlled, at least in part, by mass transfer. The chemical engineering approach provides a framework to pose further testable hypotheses about how algal canopy height, flow oscillation, turbulence, and substratum roughness may modulate rates of metabolism of coral reef algal turfs.     

A performance comparison between nonlinear similarity functions in bulk parameterization for very stable conditions

Three sets of nonlinear similarity functions for strong stability are selected to compare their performance in bulk parameterization. To uncover their advantages and disadvantages, theoretical and measurement analyses are made with four profile metrics and the Deacon number technique. Main disadvantages include the negligence of the different transfer efficiency between momentum and heat, the flux cutoff due to the upper limit in gradient Richardson number (Ri) and the ignorance of limited stability range where the dimensionless gradient functions ( and ) approach constants. Accordingly, three suggestions are made for future improvement. First, the functions for wind velocity and potential temperature should have the same function form, but with different coefficients. Second, and should approach constants only within a certain stability range. Third, the limit value in Ri should be avoided to widen their applicability in flux modeling. Furthermore, quantitative comparisons in transfer coefficients for moment and sensible heat (C _D and C _H) are made among the similarity functions in the bulk Richardson number (Ri _B) range 0 < Ri _B < 1. Generally, significant discrepancy is found, which may approach a factor of two and three at large Ri _B in C _D and C _H, respectively. Finally, a new recommendation is made to one of the three sets, mainly because of its ability to predict C _D and C _H that decrease rather slowly in very stable conditions.     

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.     

Estimation of far-field horizontal and vertical turbulent diffusion coefficients from the concentration field of a wastewater plume near the Akashi Strait

We carried out a field study of the plume discharged by a near-shore wastewater outfall near the Akashi Strait, Japan. Using an Acoustic Doppler Current Profiler and a tow-body CTD, we measured the near-surface salinity and temperature fields in the region throughout an M₂ tidal cycle. We filtered the data in T–S space to remove water masses other than the wastewater, and then used the adiabatic mixing assumption to calculate the concentration of wastewater in the far field of this plume. Averaging the T–S fields of repeated surveys over a time period during which the tidal regime did not change substantially, allowed comparison of the time-averaged plume with the analytical solution for a plume diffusing in both the horizontal and vertical dimensions. The resulting vertical turbulent diffusion coefficients agreed well with those resulting from Thorpe scales determined via a vertically-profiling CTD, as well as with the canonical value for open channel flow of D _z = 0.067hu _*. The corresponding horizontal turbulent diffusion coefficients, however, were two orders of magnitude larger than those typically observed in straight channels, and an order of magnitude larger than those observed in meandering rivers. This is likely a result of enhanced horizontal mixing due to barotropic eddies generated by the interaction of strong tidal flow with headlands and levees, as well as due to the time-varying nature of tidal flow, and baroclinic spreading of the buoyant wastewater plume.     

Mélange vertical et capacité photosynthétique du phytoplancton estuarien (estuaire du Saint-Laurent)

Time series of chlorophyll a, photosynthetic capacity and many physical parameters were sampled hourly for 167 h in August, 1975, at an anchor station located in the Middle Estuary of the St. Lawrence River, Canada. Sampling was carried out during the transition from neap tides to spring tides. The long-and short-term variations in chlorophyll a are coupled with the advection of water masses which depends on tidal currents. Vertical mixing also influences the chlorophyll a concentration of the cells, since it modifies the physiological state of the phytoplankton. Furthermore, circadian periodicities were observed in the photosynthetic capacity, suggesting that the phytoplankton of this area have a homogeneous light history due to strong vertical mixing. Under these conditions, the photosynthetic capacity is adapted to the mean light intensity in the mixed layer. The semimonthly (M _f) variations of the mean light intensity in the mixed layer depend on the M _f variations in the vertical mixing, whereas in the short-term, the variations in mean light intensity in the mixed layer are circadian.

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Mélange vertical et capacité photosynthétique du phytoplancton estuarien (estuaire du Saint-Laurent)

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Contribution au programme du Groupe interuniversitaire de recherches océanographiques du Québec (GIROQ)