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.     

Three-dimensional analysis of coherent turbulent flow structure around a single circular bridge pier

The coherent turbulent flow around a single circular bridge pier and its effects on the bed scouring pattern is investigated in this study. The coherent turbulent flow and associated shear stresses play a major role in sediment entrainment from the bed particularly around a bridge pier where complex vortex structures exist. The conventional two-dimensional quadrant analysis of the bursting process is unable to define sediment entrainment, particularly where fully three-dimensional flow structures exist. In this paper, three-dimensional octant analysis was used to improve understanding of the role of bursting events in the process of particle entrainment. In this study, the three-dimensional velocity of flow was measured at 102 points near the bed of an open channel using an Acoustic Doppler Velocity meter (Micro-ADV). The pattern of bed scouring was measured during the experiment. The velocity data were analysed using the Markov process to investigate the sequential occurrence of bursting events and to determine the transition probability of the bursting events. The results showed that external sweep and internal ejection events were an effective mechanism for sediment entrainment around a single circular bridge pier. The results are useful in understanding scour patterns around bridge piers.     

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.     

Markovian–Octant analysis based stable turbulent shear stresses in near-bed bursting phenomena of vortex settling chamber

The coherent structure in near-bed turbulent boundary layer of vortex chamber, particularly the bursting events and their associated shear stresses play the main role in sediment flushing process and consequently the trap efficiency of the vortex settling chamber. Hence, three-dimensional velocity measurements were made at 48 points near the bed of physical model of vortex chamber by using Micro-ADV. The pattern of sediment deposition at the bed of vortex settling chamber reveals three separate regions formed by three predominant currents of inlet flow, flushing flow and outlet over flow. Additionally, due to the instability and three-dimensional nature of the bursting events near the bed of chamber, the new method of Markovian–Octant analysis was applied to study the different classes of near-bed stable shear stresses of vortex chamber in three dimensions. Moreover, the role of each class of stable shear stresses on Sediment transport mechanism at the bed of vortex chamber is investigated.     

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.     

Bioavailability and accumulation of trace elements in soils and plants of a highly contaminated estuary (Domingo Rubio tidal channel,SW Spain)

The Domingo Rubio tidal channel (Palos de la Frontera, Huelva, Spain) is an estuary located in the mouth of the Tinto River. The estuary is affected by different sources of pollution (waters of the Tinto River, contaminated with trace elements from the Iberian Pyrite belt, and effluent from the Huelva chemical industrial area). Soil and the most frequent plant species were collected in 2004 and 2006 at six different locations on the estuary. In general, N-Kjedahl, Total Organic Carbon values, salinity and contamination (total trace elements up to 1,000 mg kg⁻¹ As, 6 mg kg⁻¹ Cd, 2,500 mg kg⁻¹ Cu, 1,900 mg kg⁻¹ Pb and 1,300 mg kg⁻¹ Zn) tended to increase downstream of the tidal channel. Soil biochemical properties were not negatively affected either by the high salinity or by trace element contamination. Despite the high values of the trace elements, analysed plant samples showed that Cu was the only metal that could be a serious risk for the food chain.     

Graphical spatial models: a new view on interpreting spatial pattern

Graphical models provide an important tool for facilitating communication between scientists, decision-makers, and statisticians—many complicated ecological processes can be described in terms of “box-and-arrow” conceptual diagrams (e.g., Shipley in Cause and correlation in biology: a user’s guide to path analysis, structural equations and causal inferences, Cambridge Universtiy Press, Cambridge, 2000; Clark and Gelfand TRENDS in Ecology and Evolution 21:375–380, 2006). In particular, problems in landscape ecology often involve modeling relationships among multiple physical and/or biological variables that may operate on differing spatial scales (e.g., Rossi et al. in Ecol Monographs 62:277–314, 1992; Legendre et al. in Ecography 25:601–615, 2002; Overmars et al. in Ecol Model 164:257–270, 2003; Brown and Spector in J Appl Ecol 45:1639–1648, 2008; Koniak and Noy-Meir in Ecol Model 220:1148–1158, 2008). These problems are inherently multivariate, though researchers commonly rely on univariate methods, such as spatial regression models, to address them. In this paper, we introduce a multivariate method—graphical spatial models—that extends path analysis to incorporate spatial autocorrelation in one or more variables in a directed graph. We show how both exogenous and endogenous ecological processes as defined by Legendre et al. (Ecography 25:601–615, 2002) and Lichstein et al. (Ecol Monographs 72:445–463, 2002) can be represented in a graph. Most importantly, we show how to translate graphs representing these ecological processes into statistically estimable models. We motivate our theoretical results using an example of stream health data from the Willamette Valley, Oregon. For these data we are interested in the spatial pattern within both riparian land use and an index of stream health, and whether there is an association between land use and stream health, after accounting for these spatial patterns. We use a graphical spatial model to address these ecological questions simultaneously. We find that the health of a stream decreases as the percent of developed land within a 120-m riparian buffer increases; interestingly, there is only evidence of spatial pattern within land use.     

Coupling soil water and shoot dynamics in three grass species: A spatial stochastic model on water competition in Neotropical savanna

Savannas are ecosystems known for their high environmental and economic value. They cover at least 20% of the global land surface and, in some cases, can act as a boundary between tropical rainforest and deserts. Water is an important determinant of savanna ecosystems.In this paper, we present a theoretical stochastic model of root competition for water, which couples, soil water availability, phenology, and root and shoot architecture applied to three Neotropical savanna grasses. Soil moisture was simulated using a daily balance, as proposed by Rodriguez-Iturbe et al. [Rodriguez-Iturbe, I., Porporato, A., Ridolfi, L., Isham, V., Cox, D.R., 1999. Probabilistic modelling of water balance at a point: the role of climate, soil and vegetation. Proc. R. Soc. London, Ser. A 455, 3789–3805.]. To simulate rainfall stochasticity, we used daily precipitation data from the airport weather station in the State of Barinas, Venezuela, for the period 1991–2007. Competition among neighbouring plants took into account the spatial distribution of the individuals. As a final step, the model allowed us to calculate the shoot dynamic of the species as a function of soil water availability.Using these data, we compared the behaviour of isolated plants, pairs and trios, and we found below-ground competition to be a fundamental component of global (shoot + root) competition. Finally, our model suggests various circumstances that allow poor competitor plants to coexist in competition for water with more successful competitors. Apparently, this is not only due to transpiration rates, but also to differences in shoot emergence and shoot growth.     

Diving deep in a foraging hotspot: acoustic insights into bottlenose dolphin dive depths and feeding behaviour

To exploit resources in their environment, odontocete cetaceans have evolved sophisticated diving abilities to allow effective foraging. However, data on the diving behaviour and underwater foraging behaviour remains limited. This study made use of echolocation clicks and other calls to study the diving behaviour of bottlenose dolphins. Dolphins used the full water column and consistently dived to depths of around 50 m, close to the seabed. However, the majority of their time appeared to be spent within the surface layers of the water column. In addition, by localising calls that have been associated with prey capture events (Janik, Proc R Soc Lond Ser B 267:923–927, 2000a), it appeared that certain forms of feeding behaviour occurred primarily at depths of between 20 and 30 m. Furthermore, data on the depth of clicks made before and after these feeding calls suggested that during the minute before the calls, dolphins were consistently diving from the surface to depths close to the seabed, and were subsequently returning to the surface after the calls. This passive acoustic technique proved an accurate method for studying the depth distribution of dolphin vocalisations. By exploiting the natural sounds made by these wild odontocetes, this investigation provided a previously unavailable perspective on the the 3D nature of bottlenose dolphins foraging behaviour. It confirmed that while the dolphins spent the majority of time close to the surface, the full water column was exploited during foraging events.     

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.     

Large Eddy Simulation of turbulence generated by a weak breaking tidal bore

A tidal bore is a natural and fragile phenomenon, which is of great importance for the ecology of an estuary. The bore development is closely linked with the tidal range and the river mouth shape, and its existence is sensitive to any small change in boundary conditions. Despite their ecological and cultural value, little is known on the flow field, turbulent mixing and sediment motion beneath tidal bores. Indeed, some striking features can be highlighted in two-dimensional simulations, such as large velocity fluctuations and flow recirculation structures. Using Large Eddy Simulation method, the numerical results emphasised the complicated turbulent structures and their unsteadiness under a tidal bore.     

Environmental variables and fisheries diversity of the Naaf River Estuary,Bangladesh

The Naaf River estuary is one of the large estuaries in the Bangladesh coastal region not to have been affected by extensive human disturbance. This research provides information about the fisheries diversity status by Estuarine Set Bag Net (ESBN) sampling relation to physicochemical variables in both spatio-temporal scales. About 25 km of the lower estuary was divided into six zones for sample collection by considering the accessibility and availability of the ESBN operation, fish landing centers and location of the fishing villages. In total 48 samples have been analyzed which were taken throughout March to October 2006. To quantify the species diversity, all fisheries data were analyzed by using EstimateS and EcoSim software which accounts the different diversity indices viz., species richness, Shannon–Wiener diversity Index, Dominance and Evenness index. The research results demonstrate that the Naaf River estuary is a habitat of 161 (species richness, Sobs = 161, Choa 1 = 162 ± 2.34, ACE = 161.73) different species which belong to 98 fin fishes, 23 shrimps and prawns, 13 crabs, 11 molluscs, 3 echinoderms, 4 other crustaceans; while 9 remain unidentified. Results on the aquatic environment, mainly salinity and turbidity were found to have a major influence on their occurrence and distribution. All the findings indicated that the Naaf River estuary is a highly productive system and provides a favourable environment for large variety of estuarine species assemblages.     

Parameterization of the roughness length over the sea in forced and free convection

In the condition of free convection, the Charnock relation is inadequate. In this paper we extend the Charnock relation to include the effect of free convection on the roughness length. As a result, the singularity in the Monin–Obukhov similarity theory can be avoided. This paper shows two approaches to derive the roughness length formula in the forced and free convections. The first approach is based on the mixing length theory and the use of the observational data of the vertical velocity variance. We introduce a new vertical velocity scale based on the vertical velocity variance; this velocity variance is well behaved in the atmospheric boundary layer and easy to obtain from field experiments. The second approach is based on the theoretical framework of Sykes et al. (Q R Met Soc, 119: 409–421). From that framework, we develop a theory to obtain the roughness length formula. The results of these two approaches are in agreement with each other. In the past, a multiplication factor associated with free convection was considered to be a constant. This paper shows that this multiplication factor is, in fact, also dependent on the depth of the mixing height. In previous studies, experimental works were often conducted without taking into account the depth of the mixing height. Not taking into account the mixing height in the estimation of the roughness length in free convection would result in an inaccurate estimate of the roughness length and hence the drag coefficient. An erratum to this article can be found at     

Effects of salinity stress on neurotransmission, energy metabolism, and anti-oxidant biomarkers of Carcinus maenas from two estuaries of the NW Iberian Peninsula

This study investigated the effects of salinity on biomarkers of oxidative stress, energy metabolism, and neurotransmission of Carcinus maenas from an estuary low impacted by pollution and from an estuary under chemical stress in the NW Iberian Peninsula. Crabs were collected in the field and, following an acclimation period, they were exposed for 7 days to five salinity levels ranging from 4 to 45 psu. At the end of the exposure period, stress biomarkers were determined in samples of muscle and digestive gland. The biomarkers assessed in the muscle were the activities of the enzymes cholinesterases (ChE), of which acetylcholinesterase is involved in neurotransmission, and lactate dehydrogenase (LDH) and isocitrate dehydrogenase (IDH) that are involved in energy metabolism. The biomarkers assessed in the digestive gland were (1) the activities of the enzymes glutathione S-transferases (GST), glutathione reductase (GR), and glutathione peroxidase (GPx), involved in phase II biotransformation and the anti-oxidant defence system; (2) the levels of total glutathiones (TG), also belonging to the anti-oxidant system; and (3) the levels of lipid peroxidation as a measure of oxidative damage. The results showed a significant influence of salinity on neurotransmission, energy metabolism, anti-oxidant status, and oxidative damage of C. maenas. For some biomarkers, this influence was dependent on whether the crabs were collected at the low-polluted estuary or at the contaminated estuary. In particular, crabs collected at the low-polluted estuary showed altered neurotransmission and anti-oxidant defences (GR). Crabs collected at the impacted estuary showed alterations in neurotransmission, energy metabolism (IDH and LDH), biotransformation, and anti-oxidant defences (GST, GR, GPx, and TG), as well as in oxidative damage, indicating that salinity change superimposes higher stress on these organisms. For ChE, IDH, and TG, altered responses were induced by both hypo- and hypersalinity.     

LES validation of urban flow,part II: eddy statistics and flow structures

Time-dependent three-dimensional numerical simulations such as large-eddy simulation (LES) play an important role in fundamental research and practical applications in meteorology and wind engineering. Whether these simulations provide a sufficiently accurate picture of the time-dependent structure of the flow, however, is often not determined in enough detail. We propose an application-specific validation procedure for LES that focuses on the time dependent nature of mechanically induced shear-layer turbulence to derive information about strengths and limitations of the model. The validation procedure is tested for LES of turbulent flow in a complex city, for which reference data from wind-tunnel experiments are available. An initial comparison of mean flow statistics and frequency distributions was presented in part I. Part II focuses on comparing eddy statistics and flow structures. Analyses of integral time scales and auto-spectral energy densities show that the tested LES reproduces the temporal characteristics of energy-dominant and flux-carrying eddies accurately. Quadrant analysis of the vertical turbulent momentum flux reveals strong similarities between instantaneous ejection-sweep patterns in the LES and the laboratory flow, also showing comparable occurrence statistics of rare but strong flux events. A further comparison of wavelet-coefficient frequency distributions and associated high-order statistics reveals a strong agreement of location-dependent intermittency patterns induced by resolved eddies in the energy-production range. The validation concept enables wide-ranging conclusions to be drawn about the skill of turbulence-resolving simulations than the traditional approach of comparing only mean flow and turbulence statistics. Based on the accuracy levels determined, it can be stated that the tested LES is sufficiently accurate for its purpose of generating realistic urban wind fields that can be used to drive simpler dispersion models.     

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.     

Modeling estuarine-shelf exchanges in a deltaic estuary: Implications for coastal carbon budgets and hypoxia

The export of wetland-derived materials to the coastal ocean (i.e., the “Outwelling” hypothesis) has received considerable attention over the past several decades. While a number of studies have shown that estuaries export appreciable amounts of nutrients and carbon, few studies have attempted to estimate the importance of estuarine sources for the coastal carbon budgets in river-dominated coastal ecosystems. A novel tidal prism model was developed to examine estuarine-shelf exchanges in the Barataria estuary, a deltaic estuary located in the north-central Gulf of Mexico. This estuary has been the site of a massive wetland loss, and it has been hypothesized that carbon export from the eroding coastal wetlands supports the development of a large hypoxic zone in the coastal Gulf of Mexico. The model results show that the Barataria estuary receives nitrogen through the tidal passes and releases carbon to the coastal ocean. The mean calculated tidal water discharge of 6930 m³ s⁻¹ is equivalent to about 43% of the lower Mississippi River discharge. The annual total organic carbon (TOC) export is 109 million kg, or 57 gC m² yr⁻¹ when prorated to the total water area of the estuary. This carbon export is equivalent to a loss of 0.5 m of wetland soil horizon over an area of 8.4 km², and accounts for about 34% of the observed annual wetland loss in the estuary between 1978 and 2000. Compared to the lower Mississippi River, the Barataria estuary appears to be a very small source of TOC for the northern Gulf of Mexico (2.7% of riverine TOC), and is unlikely to have a significant influence on the development of the Gulf's hypoxia.     

Scales of variation in otolith elemental chemistry of juvenile staghorn sculpin (<Emphasis Type="Italic">Leptocottus armatus</Emphasis>) in three Pacific Northwest estuaries

Although distinct otolith elemental signatures are often observed in fish collected from different estuaries, significant differences are also observed among sites within estuaries. Variation at these smaller spatial scales is not well quantified and has the potential to lead to inappropriate interpretations of otolith elemental data. To quantify variation at multiple scales, the otolith elemental composition (Mg:Ca, Mn:Ca, Sr:Ca, Ba:Ca, and Pb:Ca) of juvenile staghorn sculpin (Leptocottus armatus Girard, 1854) collected from five sites within three estuaries, the Columbia River (two sites) and Coos Bay (one site), Oregon, and Humboldt Bay, California (two sites), was examined. Using laser ablation-inductively coupled plasma mass spectrometry, each otolith was sampled at three zones: (1) within the primordium, which represents the egg and early larval periods; (2) at the outer edge, which represents the juvenile period just prior to collection; and (3) midway between the primordial and edge samples, which represents the late larval and early juvenile period. There were significant differences in otolith metal-to-calcium ratios at all scales examined. Using multi-element otolith signatures, fish were classified to estuary and site within estuary with relatively high levels of accuracy (av = 70–90%). The largest differences in metal-to-calcium ratios were observed between sites within estuaries (<5 km apart) and the smallest differences were observed among otolith zones. Variation in otolith chemistry may be used to provide information on probable habitat use by estuarine fish but studies must be carefully designed. Electronic supplementary material  Supplementary material is available in the online version of this article at and is accessible for authorized users.     

Modelling the effects of extreme events on the dynamics of the amphipod Corophium orientale

The brackish water amphipod Corophium orientale is the dominant macroinvertebrate species in the upper Mira estuary, a small mesotidal system located in the southwest coast of Portugal. As climate changes will increase the frequency and intensity of extreme events such as floods and droughts, these will have a negative effect on benthic estuarine invertebrates, namely C. orientale. In order to understand the effects of these events on C. orientale, a dynamic model, based on published information and calibrated with field data, was developed and different scenarios were tested.For model construction, the annual development of three cohorts of C. orientale, their growth rates, and the establishment of the timing of each cohort rise and extinction are introduced. This structure can be repeated indefinitely, for years, and few parameters are required. The model simulations highlight the need for refuge areas that enable a fast recovery of the amphipod population after an extreme event and the recolozination of the affected areas.     

Effect of light and turbulent mixing on the growth of<Emphasis Type="Italic"> Skeletonema costatum</Emphasis> (Bacillariophyceae)

Skeletonema costatum was grown in an outdoor mesocosm to test the hypothesis that fluctuations in irradiance brought about by changes in mixing time and depth can reduce diatom growth and biomass in the turbulent mixed layer. The light environment and mixing regime within the mesocosm were comparable to those in shallow lakes and coastal waters. Experiments showed no significant differences for 24-h mean and 7-day mean chlorophyll a and carbon-specific growth for mixed depths of 1 m and 3 m, and mixing times between 4 min and 65 min. Fluctuations in irradiance brought about by turbulent mixing had no significant effect on specific growth. The relationship between mixed depths and critical depths for S. costatum was therefore independent of fluctuations in irradiance in the turbulent mixed layer. The results indicated that to control growth of S. costatum mixed depths would have to exceed photic depths by a factor of 15, instead of the conventionally accepted factor of 5. Thus, it is likely that artificial mixing of shallow (<10 m) eutrophic waters will be more effective in controlling slow-growing summer biomass than fast-growing spring blooms dominated by diatoms.Communicated by P.W. Sammarco, Chauvin