Development of similarity relationships for energy dissipation rate and temperature structure parameter in stably stratified flows: a direct numerical simulation approach

In this study, a newly developed direct numerical simulation (DNS) solver is utilized for the simulations of numerous stably stratified open-channel flows with bulk Reynolds number (Re _b ) spanning 3400–16,900. Overall, the simulated bulk Richardson number (\(Ri_b\)) ranges from 0.08 (weakly stable) to 0.49 (very stable). Thus, both continuously turbulent and (globally) intermittently turbulent cases are represented in the DNS database. Using this comprehensive database, various flux-based and gradient-based similarity relationships for energy dissipation rate (ε) and temperature structure parameter (\(C_T^2\)) are developed. Interestingly, these relationships exhibit only minor dependency on Re _b . In order to further probe into this Re _b -effect, similarity relationships are also estimated from a large-eddy simulation (LES) run of an idealized atmospheric boundary layer (very high Re _b ) case study. Despite the fundamental differences in the estimation of ε and \(C_T^2\) from the DNS- and the LES-generated data, the resulting similarity relationships, especially the gradient-based ones, from these numerical approaches are found to be remarkably similar. More importantly, these simulated relationships are also comparable, at least qualitatively, to the traditional observational data-based ones. Since these simulated similarity relationships do not require Taylor’s hypothesis and do not suffer from mesoscale disturbances and/or measurement noise, they have the potential to complement the existing similarity relationships.     

Turbulent Prandtl number and characteristic length scales in stably stratified flows: steady-state analytical solutions

Environmental Fluid Mechanics - In this study, the stability dependence of turbulent Prandtl number ( $$Pr_t$$ ) is quantified via a novel and simple analytical approach. Based on the variance and...     

Laboratory-numerical studies of stratified spin-up flows

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

Energy dissipation, flow resistance and gas-liquid interfacial area in skimming flows on moderate-slope stepped spillways

With the re-evaluation and revision of a number of design floods, several embankment overtopping protection systems have been developed and a common technique is the construction of a stepped spillway on the downstream slope. For such moderate slope stepped channels, detailed air–water flow measurements were performed in a large facility with a focus on the rate of energy dissipation, flow resistance, air–water interfacial areas and re-aeration rates. Past and present experimental results showed a significant aeration of the flow. The median dimensionless residual head was about 3 × d_c for the 21.8° sloping chute and smaller than that for flatter slopes (θ = 3.4° and 15.9°). The flow resistance results yielded an equivalent Darcy friction factor of about 0.25 implying a larger flow resistance for the 21.8° slope angle than for smaller slope angles. The re-aeration rate was deduced from the integration of the mass transfer equation using measured air–water interfacial areas and air–water flow velocities. The results suggested an increasing re-aeration rate with increasing rate of energy dissipation. The stepped invert contributed to intense turbulence production, free-surface aeration and large interfacial areas. The experimental data showed however some distinctive seesaw pattern in the longitudinal distribution of air–water flow properties with a wave length of about two step cavities. While these may be caused by the interactions between successive adjacent step cavities and their interference with the free-surface, the existence of such “instabilities” implies that the traditional concept of normal flow might not exist in skimming flows above moderate-slope stepped spillways.     

Effect of temperature and temperature adaptation on calcification rate in the hermatypic coral Pocillopora damicornis

Using ⁴⁵Ca incorporation into the coral skeleton as a measure of calcification rate, the effect of temperature on clacification rate was studied in the hermatypic coral Pocillopora damicornis. Both immediate and long-term (adaptation) effects were investigated. Temperature has a marked effect on rate — an effect that varies depending on the temperature history of the coral (i.e., temperature adaptation occurs). P. damicornis showed both 27° and 31°C temperature optima, one or the other being dominant depending on the natural water temperature to which the coral was adapted. The two optimum temperatures may indicate two isoenzymes or two alternate metabolic pathways involved in the calcification process.     

On thermally forced flows in urban street canyons

During sunny days with periods of low synoptic wind, buoyancy forces can play a critical role on the air flow, and thus on the dispersion of pollutants in the built urban environments. Earlier studies provide evidence that when a surface inside an urban street canyon is at a higher temperature than that of local ambient air, buoyancy forces can modify the mechanically-induced circulation within the canyons (i.e., gaps between buildings). The aspect ratio of the urban canyon is a critical factor in the manifestation of the buoyancy parameter. In this paper, computational fluid dynamics simulations are performed on urban street canyons with six different aspect ratios, focusing on the special case where the leeward wall is at a greater temperature than local ambient air. A non-dimensional measure of the influence of buoyancy is used to predict demarcations between the flow regimes. Simulations are performed under a range of buoyancy conditions, including beyond those of previous studies. Observations from a field experiment and a wind tunnel experiment are used to validate the results.     

Effect of temperature acclimation on the metabolic rate of sea urchins

Three sea-urchin species were acclimated at 9° and 18°C for 30 days. Following acclimation, oxygen-consumption measurements were made over a broad temperature range (6° to 24°C). The effect of temperature acclimation on the metabolic rate-temperature relationship (R-T curve) was determined for each species. R-T curves of Strongylocentrotus purpuratus generally indicate no compensation (Precht type 4). Some inverse compensation (Precht type 5) is suggested at intermediate test temperatures. R-T curves of Strongylocentrotus franciscanus indicate inverse compensation particularly at intermediate test temperatures. R-T curves of Allocentrotus fragilis generally indicate no compensation. With two species, S. purpuratus and A. fragilis, greater levels of rate-temperature independence were generally reached by cold-acclimated forms at lower test temperatures and by warm-acclimated forms at higher. Rotational (slope) changes in these R-T curves may be more critical than translational (ordinate) changes.Supported in part by a National Science Foundation Institutional Sea Grant to Oregon State University.Submitted in partial fulfillment of the requirements for the degree of Master of Science, Oregon State University, June, 1970.     

On the role of the viscosity ratio on buoyant miscible jet flows

Environmental Fluid Mechanics - In this work, we perform a series of experiments to study a buoyant miscible jet flow wherein a heavy fluid is injected vertically downward into a more viscous light...     

Relation of spawning of the giant scallop,Placopecten magellanicus,to temperature fluctuations during downwelling events

We examined the relation of spawning to biological and physical factors for the scallop Placopecten magellanicus (Gmelin, 1791) over 8 yr (1984 to 1991) in the Baie des Chaleurs, southwestern Gulf of St. Lawrence, Canada. Spawning was always abrupt and occurred between July and mid-September. It did not appear to be related to the abundance of phytoplankton or particulate organic carbon and nitrogen in the water. It further showed no relationship to lunar or tidal phascs or to current velocity. Spawning consistently occurred during the summer temperature maximum, but did not coincide with any critical temperature or cumulative temperature threshold. All but one of the 33 spawning events, for which temperature data were recorded, were associated with temperature changes; 25 of these were sharp temperature increases and 7 were during strong temperature fluctuations when the mean temperature was 9 to 14°C. Both types of temperature changes were caused by downwelling of warm surface water. The delay by about 1 d in time of spawning between sites coincided with the rate at which downwelling events propagated into the bay. Virtually all of the spawning events resulted in gametes being ejected into warm water masses where conditions are likely to favour larval development.     

Effects of salinity fluctuations on the respiration rate of the southern oyster drill Thais haemastoma and the blue crab Callinectes sapidus

Respiration rates of Thais haemastoma and Callinectes sapidus were determined as a function of salinity with a flow-through respirometer at 20°C. Respiration rates were measured at 10, 20 and 30 S for acclimated animals. The effects of 10-5-10, 20-10-20, 30-10-30 and 10-30-10 S semidiurnal cycles (12 h) of fluctuating salinity on the rate of respiration of the oyster drill were studied. During each cycle, salinity was changed from the acclimation salinity over a 4 h interval, held at that salinity for 2 h, returned to the acclimation salinity over 4 h and held at that salinity for 2 h. The effects of diurnal (24.8 h) salinity cycles on respiration in the oyster drill and blue crab were also studied. Salinity was changed from the acclimation salinity over a 10.4 h interval, held at that salinity for 2 h, then returned to the acclimation salinity over 10.4 h and held at that salinity for 2 h. The respiration rate of 30 S acclimated oyster drills (679 l O₂ g dry weight^–1 h^–1) was significantly higher than for individuals acclimated to 10 S (534 l O₂ g dry weight^–1 h^–1). Blue crab respiration was 170 l O₂ g dry weight^–1 h^–1 at 30 S, and was significantly higher at 10 and 20 S than at 30 S. With the exception of the 20-10-20 S semidiurnal cycle, the respiration rate of oyster drills declined as salinity fluctuated in either direction from the acclimation salinity and increased as ambient salinity returned to the acclimation salinity. Semidiurnal cycles (12 h) of fluctuating salinity produced greater changes in the respiration rate of snails than analogous diurnal cycles (24.8 h). A 10-30-10 S pattern of fluctuation caused a greater percentage reduction in the steady state respiration rate of oyster drills than the 30-10-30 S pattern. The respiration rate of blue crabs varied inversely with fluctuating salinity. Relatively minor changes occurred in blue crab respiration rate with fluctuating salinity. Blue crab respiration rate characteristically dropped during the initial phase of declining salinity at a rate directly proportional to the rate of salinity decrease, perhaps representing a metabolic adjustment period by the blue crabs. The respiratory response of T. haemastoma to salinity is consistent with its incomplete volume regulation, while the response of C. sapidus is compatible with its ability to regulate extracellular fluid osmotic and ionic composition.     

Influence of light and temperature on the growth rate of estuarine benthic diatoms in culture

Four species of estuarine benthic diatoms: Amphiprora c. f. paludosa W. Smith, Nitzschia c. f. dissipata (Kützing) Grunow, Navicula arenaria Donkin, and Nitzschia sigma (Kützing) W. Smith were grown in unialgal cultures. The growth rates of the diatoms were determined as the rate of increase of the chlorophyll a content of the cultures. The diatoms were cultured at different combinations of temperture, daylength, and quantum irradiance. The highest growth rates of Navicula arenaria occurred at 16° to 20°C; the other 3 species had their optimum at 25°C or higher. The small-celled species had higher growth rates at their optimum temperature, but at lower temperatures the growth rates of all 4 species became very similar. The minimum daily quantum irradiance that could effect light-saturated growth at 12° and 20°C ranged from 2.5 to 5.0 E.m^-2.day^-1. At 12°C, two species had their highest growth rates under an 8 h daily photoperiod. At 20°C, the three species tested all had highest growth rates under 16 h daily photoperiod. The growth response of the benthic diatoms is comparable to that of several cultures of planktonic diatoms, as described in the literature. The influence of temperature and quantum irradiance on the diatoms in the present investigation was comparable to the influence of temperature and light intensity on the ¹⁴C-fixation of marine benthic diatoms (Colijn and van Buurt, 1975).     

Influence of light and temperature on the photosynthetic rate of marine benthic diatoms

The influence of light and temperature on photosynthetic rate as measured by C¹⁴O₂-fixation of marine benthic diatoms was investigated, using both intact sediment samples (Marshall et al., 1973) and suspensions of diatoms harvested by a lenstissue technique (Eaton and Moss, 1966). After C¹⁴-incubation, sediment samples were filtered, burned in a sample oxidizer, and their activity determined in a liquid scintillation counter. Photosynthetic rate of mixed field populations is saturated by a light intensity of approximately 10,000 lux; at still higher light intensities no photoinhibition was found. In contrast to the mixed field populations, unialgal cultures of the benthic diatom Amphiprora alata Kütz. exhibited strong photoinhibition at higher light intensities (10,000 to 60,000 lux). Within a range of 4° to 20°C, the photosynthetic rate increased about 10%/C^o. No differences in photosynthetic pattern were observed between epipelic and epipsammic species.     

Influence of algal concentration and temperature on the filtration rate of Mytilus edulis

The filtration rates of Mytilus edilis (=galloprovincialis; 40 mm) were determined in relation to food concentration and temperature, using pure suspensions of the unicellular alga Platymonas suecica in concentrations ranging from 3x10⁵ cells/l to 1.5x10⁸ cells/l. The rate of filtration (ml/h/mussel) generally decreased as cell concentrations increased, and dropped to low values when concentrations above 5x10⁷ cells/l were supplied. The amount of water swept clear varied continuously, and noticeable differences in the filtration activity of M. edulis were observed over short time intervals (5 min). Fluctuations of filtered volumes per unit time were greater with lower than with higher concentrations of algae. The influence of temperature on filtration activity was highest between 5°–15°C and 25°–30°C. A temperature increase from 15° to 25°C resulted in only a slight increase in filtration rate. At 5° and 30°C, filtration dropped to very low values, namely 350 and 100 ml/h, respectively. The temperature coefficients for the filtration rates of M. edulis were determined as: Q₁₀ (5° to 15°C)=4.96; Q₁₀ (10° to 20°C)=1.22. The amount of algae cells ingested per mussel per hour is directly related to food concentration. The maximum number of cells filtered/mussel/h in an algal suspension of 70x10⁶ cells/l was 21.5x10⁵ cells/h. Cell concentrations of up to 40x10⁶ cells/l were swept clear without producing pseudofaeces. The critical cell density for M. edulis was reached at algal concentrations of 70 to 80x10⁶ cells/l. Above these concentrations no normal filtration activity was observed.     

Effects of body size and temperature on the metabolic rate of Penaeus monodon

Laboratory measurements of oxygen consumption were made on Penaeus monodon (Fabricius) from protozoea to adult stage at temperatures between 15° and 35°C. The logarithmic relationship between weight-specific respiration rate (WRt) and temperature (T) for two size groups, Protozoea 1 (PZ1) to Postlarva 1 (PL1) and PL to adult, are given as; WRt=10^{0.431+0.0146 (T)} (ml O₂ g^-1 h^-1) and WRt=10^{-0.948+0.0338 (T)} (ml O₂ g^-1 h^-1), respectively. Additionally, equations relating metabolic rate, temperature and size for the two size groups are; PZ1-PL1: log M=0.431+0.0146T+(1.25 (log TL)+0.579), and PL1-adult: log M=-0.948+0.0338T+(2.60(log CL)-0.683), where M=oxygen consumption in ml O₂ individual ^-1h^-1, T=temperature in °C, TL=total length in cm, and CL=carapace length in cm. Activation energies of 6 186.75 J for PZ1-PL1 and 14 066.62 J for PL-adults point to different metabolic pathways or to differences in the ratio between the metabolic pathways used.     

The influence of suspension density and temperature on the filtration rate of Hiatella arctica

The rate of filtering Phaeodactylum tricornutum and Isochrysis galbana was measured in Hiatella arctica (L.) by the indirect suspension depletion method monitored by optical density measurement. The filtration rate of H. arctica was found to be 1.412×10^–2 l/h/g wet weight at a temperature of 15°C when fed with P. tricornutum, at average cell concentrations up to 3.5×10⁶ cells/ml. The filtration rate dropped almost to zero when the concentration of P. tricornutum reached 11×10⁶ cells/ml. The filtration rate of I. galbana diminished at a much lower cell concentration of 1×10⁶ cells/ml, and almost ceased at 3 to 4×10⁶ cells/ml. In mixed cultures of I. galbana and P. tricornutum, the filtration rate ratio was 0.37 to 1.00, and this was believed to be due to a proportion of the smaller former cells passing through the ostia. However, when resuspended in sea water, I. galbana cells were taken at a rate slightly less than P. tricornutum. The medium in which the I. galbana cells had been grown was inhibitory to the filtering activity of H. arctica, since, when cells of either alga were resuspended in the medium, the filtration rate was considerably reduced. No inhibitory factor existed in either of the original nutrient media. Hence, the importance of using low cell concentrations and of eliminating any inhibitory metabolic products when measuring filtration rates of bivalves is stressed. H. arctica shows a typical activity temperature eurve for a boreo-arctic species, with a steady rise from 0°C to a maximum between 15° and 17°C, and a sharp fall in activity to about zero at 25°C. The rates of filtration of various species at temperatures approaching the optimum were compared after allowance was made for fall in filtration rate with increasing body weight. The results suggested that the Mytilacea had the highest filtration rates and that H. arctica possesses one of the lowest filtration rates recorded.     

A stochastic Lagrangian micromixing model for the dispersion of reactive scalars in turbulent flows: role of concentration fluctuations and improvements to the conserved scalar theory under non-homogeneous conditions

Several reaction schemes, based on the conserved scalar theory, are implemented within a stochastic Lagrangian micromixing model to simulate the dispersion of reactive scalars in turbulent flows. In particular, the formulation of the reaction-dominated limit (RDL) reaction scheme is here extended to improve the model performance under non-homogeneous conditions (NHRDL scheme). The validation of the stochastic model is obtained by comparison with the available measurements of reactive pollutant concentrations in a grid-generated turbulent flow. This test case describes the dispersion of two atmospheric reactant species (NO and O₃) and their reaction product (NO₂) in an unbounded turbulent flow. Model inter-comparisons are also assessed, by considering the results of state-of-the-art models for pollutant dispersion. The present validation shows that RDL reaction scheme provides a systematic overestimation (relative error of ca. 85% around the centreline) in computing the local reactant consumption/production rate, whereas the NHRDL scheme drastically reduces this gap (relative error lower than 5% around the centreline). In terms of NO₂ production (or reactant consumption), neglecting concentration fluctuations determines overestimations of the product mean of around 100% and a NO₂ local production of one order of magnitude higher than the reference simulation. In terms of standard deviations, the concentration fluctuations of both the passive and reactive scalars are generally of the same order of magnitude or up to 1 or 2 orders of magnitudes higher than the corresponding ensemble mean values, except for the background reactant close to the plume edges. The study highlights the importance of modelling pollutant reactions depending on the instantaneous instead of the mean concentrations of the reactants, thus quantifying the role of the turbulent fluctuations of concentration, in terms of scalar statistics (mean, standard deviation, intensity of fluctuations, skewness and kurtosis of concentration, segregation coefficient, simulated reaction rate). This stochastic particle method represents an efficient numerical technique to solve the convection–diffusion equation for reactive scalars and involves several application fields: micro-scale air quality (urban and street-canyon scales), accidental releases, impact of odours, water quality and fluid flow industrial processes (e.g. combustion).     

Effect of temperature fluctuations and food supply on the growth and metabolism of juvenile sea scallops (Placopecten magellanicus)

On the eastern shore of Nova Scotia late summer atmospheric systems cause upwelling of shelf water; the associated temperature variations of 10 °C with a 6 to 8 d period are comparable in magnitude to the seasonal variation. A laboratory study was undertaken to assess the effects of these temperature fluctuations on sea scallop (Placopecten magellanicus) growth and metabolism. In a factorial design, scallops were subjected to constant (10 °C) or a variable (6 to 15 °C) 8 d temperature cycle, and either a low (seston in filtered seawater) or high (seston supplemented with cultured phytoplankton) food diet. During the 48 d experiment scallop mortality was low and growth positive in all treatments. Shell and total tissue growth rate did not differ between temperature treatments, but growth in the high food treatments was 40 to 50% higher than in the low food treatments. However, soft tissue (excluding adductor) growth did show a temperature treatment effect; growth rates were significantly higher in the fluctuating temperature treatment, due in part to greater gonad development. Weight-standardized rates of scallop oxygen consumption (V _sO₂ , μmol O₂ g⁻¹ h⁻¹) were 20 to 25% higher in high food than in low food treatments, consistent with the expected increase in respiration due to the higher growth rates. Scallop metabolism did not acclimate to the fluctuating temperature cycle; V _sO₂ and ammonium excretion (V _sNH⁺ ₄, μmol O₂ g⁻¹ h⁻¹) remained dependent on ambient temperature throughout the experiment. V _sNH⁺ ₄ Q₁₀ (2.77) was higher than V _sO₂ Q₁₀ (2.01) which was reflected in a decrease in the O:N ratio at 15 °C, indicating a shift toward increased protein catabolism and a stressed state. At 10 °C, V _sO₂ and V _sNH⁺ ₄ in the variable temperature treatments were 15 to 18% lower than in the constant temperature treatments, a difference that was not detected in growth measurements. Results demonstrate that the metabolism of Placopecten magellanicus, unlike some bivalve species, is tightly coupled to fluctuations in ambient temperature. Although an absence of compensatory acclimation had a minimal effect on growth in this study, if high temperatures were combined with low food conditions a reduction in scallop production could result. Received: 23 June 1998 / Accepted: 8 February 1999     

Influence of temperature on the growth rate of Skeletonema costatum in response to variations in daily light intensity

Daily light intensities (I _o) can vary 10-fold during the winter-spring and late-summer diatom blooms in New England, USA, coastal waters. Laboratory cultures and natural populations incubated in dialysis sacs were examined to determine the time course of growth rate in Skeletonema costatum (Greville) Cleve in response to variations in daily light intensity during two bloom periods in Narragansett Bay, Rhode Island, USA. Log-phase cultures of S. costatum require 2 d to attain maximum growth rates at 2°C following transfer to saturating intensities. At 20°C, only 1 d is required. As temperature increases, Detonula confervacea (Cleve) Gran, Thalassiosira nordenskiöldii Cleve and Ditylum brightwellii (West) Grunow also exhibit rapid increases in mean daily division rates (K) following transfer to saturating light intensities. Thalassiosira pseudonana Hustedt, however, did not alter the time required to achieve maximum K as temperature varied. Natural populations of S. costatum did not show a well-defined relationship between K and light. Throughout a winterspring bloom, K was limited by low temperatures and exhibited no clear response to variations in I _o. A change in K in response to variation in I _o may occur on a daily basis during the summer, when temperatures are near 20°C; this has yet to be verified for in situ populations.