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

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

A reliability index for models

Since the prediction of environmental changes depends heavily on mathematical models, environmental planners have a definite need for a general test that can be easily applied to determine the reliability of a model or to choose between available models. In this paper a ‘reliability index’ for a model is defined. This index is a number k ? 1 which is determined from a set x₁,x₂,…,x_n of model predictions and a corresponding set y₁,y₂,…,y_n of observations. One interpretation of the index k is that the model predictions agree with observations, in some sense, within a factor of k. The index k is defined using an intuitive, geometric approach and is justified through agreement with another index developed using statistical techniques. Examples are given for a model which predicts the atmospheric movement of radon-222 originating from a concentrated source of radium-226, such as a uranium tailings pile.     

Models for the physiological effects of short O3 exposures on plants

Some published effects of ozone on plant photosynthesis and evaporation are detailed, and attempts were made to develop explanatory models of increasing complexity. Stomatal regulation, which keeps the CO₂ concentration inside the lead constant, is assumed. The O₃ concentration inside the leaf is assumed to be neglible, so O₃ uptake, CO₂ uptake and stomatal conductance must be proportional. The suppression of photosynthesis is assumed to be proportional to the integrated effective O₃ uptake. For a first model, a differential equation is derived from these assumptions and a simple analytical solution is found. A second model includes a threshold O₃ flux. The repair process is discussed and three models are investigated with a constant repair rate, a repair rate dependent on the stage of injury, and with a repair rate dependent on the photosynthetic rate. A comparison of the analytical solutions of the appropriate differential equations with literature data shows that the model with repair dependent on photosytheesis is the most successful one, but a constant repair rate also gives a fair approximation. The model with repair dependent on photosynthesis implies the existence of a threshold level for the suppression of photosynthesis which separates reversible and irreversible O₃ effects. With the assumption of an inhomogeneous leaf a model to predict visible leaf injury is derived. The possible existence of a maximum leaf injury index for one exposure concentration is explained from the properties of the models. The restrictions and possible extensions of the models are discussed. The concept of a threshold O₃ flux and of a critical suppression of photosynthesis are shown to give possible explanations of antagonistic and synergistic effects of O₃, SO₂ and NO₂.     

Sensitivity analysis of the asymptotic behavior of a model for the environmental movement of radionuclides

The asymptotic behavior of a linear compartment model for the environmental movement of radionuclides is investigated. Here, the expression asymptotic behavior is used to designate the behavior of q(t) as t → ∞, where q is the solution of a vector differential equation of the form dq/dt = h + Kq. The asymptotic behavior of such equations is described. For the model and conditions under consideration, each element of q converges monotonically to a steady-state value. A hydrologic system is defined and used to illustrate this behavior. An approach to sensitivity analysis employing Latin hypercube sampling, rank transformations and stepwise regression is presented and then applied to this system. A total of 20 independent variables is introduced and the following dependent variables are investigated for the various components of the system: amount of radionuclide present at steady state. concentration of radionuclide at steady state, and time required to reach 90% of steady state. Finally, an application of asymptotic behavior in the analysis of a hypothetical site for the geologic isolation of high-level radioactive waste is described and a brief discussion of differential sensitivity analysis is given.     

Ultrastructure of the mature spermatozoon of the coconut crabBirgus latro (Coenobitidae: Paguroidea: Decapoda)

The spermatozoon ofBirgus latro (Linnaeus, 1767) is approx 14µm in length. It is composed of a large multi-layered oblong-ovoid acrosome which is capped by a conical operculum and lies anterior to a small ring of cytoplasm and an amorphous nucleus which is drawn out into a series of arms or extensions. Originating from the cytoplasmic area are three further long microtubular arms. The sperm ofB. latro is very similar to the sperm of the only other genus in the Coenobitidae,Coenobita, of whichC. clypeatus is a representative species. They share a suite of ultrastructural characters including: a long, cylindrical, capsule-bound acrosome containing an inner acrosome core, a large acrosome ray zone and a thin outer acrosome zone; an apical operculum anterior to a subopercular zone divided into two areas of differing density; an invaginated perforatorial zone with a bipartite granular matrix; microvillus-like extensions of the inner acrosome core projecting into the perforatorial invagination; a ring of cytoplasm, around the base of the acrosome, containing numerous mitochondria, extensive lamellar systems and the bases of three microtubular arms; granular nuclear material forming irregular arms; and at the posterior portion of the cell membrane a combination of nuclear and plasma membranes. Some ultrastructural characters which separate the two genera are: a domed operculum inC. clypeatus as opposed to a conical one inB. latro; inB. latro there is some residual cytoplasm external to the operculum and centrioles are absent from the mature spermatozoon; inC. clypeatus the inner acrosome core does not appear to invest the perforatorium and a series of dense rods are found subjacent and internal to the operculum. Similarities between the two coenobitids are greater than those shared with the paguridEupagurus bernhardus. In this latter species, the acrosome is more ovoid than cylindrical and the acrosome zones are less conspicuous; the operculum is absent from the mature sperm (although present during spermiohistogenesis); no subopercular zone is present; the perforatorium contains longitudinally arranged microtubules and extends the full length of the acrosome; and the nuclear material does not form separate nuclear arms. Sperm ultrastructure supports monophyly of the Paguroidea, while distinguishing coenobitids from pagurids within this superfamily.     

What Is Consumer′s Surplus Per Day of Use, When Is It a Constant Independent of the Number of Days of Use, and What Does It Tell Us about Consumers Surplus?

An individual′s consumer′s surplus per day of use for a change in the price of recreational site is the price change, so it is a constant, independent of the number of days of use. Consumer′s surplus per day of use for a change in a site′s characteristics is not, in general, a constant. When a constant compensating variation per day of use exists, it multiplied by the number of days at the site in the original state (proposed state) bounds the compensating variation, CV, from below (above). The average of these two approximations is an almost second-order approximation to the CV. Simulations indicate the approximation biases can be large.     

Semi-parametric Bayesian density estimation using ranked set sample in the presence of ranking error

In this paper, we propose a Bayesian method to estimate the underlying density function of a study variable Y using a ranked set sample in which an auxiliary variable X is used to rank the sampling units. The amount of association between X and Y is not known, resulting in an unknown degree of ranking error. We assume that (X, Y) follows a Morgenstern family of distributions. The study variable Y is assumed to have a parametric distribution, with the distribution of the parameters having a Dirichlet process prior. A Markov chain Monte Carlo procedure is developed to obtain a Bayesian estimator of the desired density function as well as of the ranking error. A simulation study is used to evaluate the performance of the proposed method. An example from forestry is used to illustrate a real-life application of the proposed methodology.     

Synthesizing units as modeling tool for photosynthesizing organisms with photoinhibition and nutrient limitation

This paper develops a mechanistic ecological model of photosynthesis based on a synthesizing unit with terms for nutrient limitation and wavelength dependent photoinhibition. The model satisfactorily fits standard P-I data with a clear inhibitory impact of excess radiation. Furthermore, the model satisfactorily discriminates between the inhibitory impact of PAR, UVA and UVB. The inhibitory potential of UVA is less than 1 order of magnitude higher than that of PAR, whereas that of UVB is about 2 orders of magnitude higher than PAR. The model can also satisfactorily describe photosynthesis rates as a function of both PAR and environmental nitrate concentrations. At relatively low nutrient levels, the model produces a curve that ascends quickly to a near saturation level; this is a trend often observed in experimental data and described well by a hyperbolic tangent. The results in this paper suggest that nutrient limitation is an overlooked factor in the experimental design for obtaining P-I data. The SU model in this paper is the simplest possible model of photosynthesis with nutrient limitation and photoinhibition that is consistent with Dynamic Energy Budget theory, in which the model can be embedded to obtain dynamic properties.     

Assessing the Leakage Rates from Punctured Submerged Vessels

The leakage of fluid leaving a puncture in a pressurized vessel immersed in a quiescent, miscible medium is studied under steady flow conditions. This problem has engineering applications in submerged pipelines and hazardous gas lines. The leakage rate for the puncture is characterized as functions of various hydrodynamic and geometric conditions. Dimensional analysis shows that the leakage percent, Q*, is a function of the Reynolds number, the pressure ratio between the center of the tube and the external hydrostatic pressure, P^*, and the hole-to-main tube diameter ratio, D^*. The effect of puncture shape is also examined, rectangular and circular. A 3-D finite volume computational model is constructed for laminar flow of a Newtonian fluid under steady conditions and validated with supporting experiments. The results show that the fractional leakage rate Q* increases with P^* and approaches a constant value at high P^* for a fixed Reynolds number. In addition, it is found that the leakage rate increases with decreasing Reynolds number at a fixed pressure ratio. The geometric effect of the diameter ratio is shown to have a more pronounced effect near a pressure ratio of two with more fluid exiting the puncture for larger diameter ratios. The results of the shape analysis show that the circular puncture has the largest fractional leakage when compared to a rectangle with an equivalent cross-sectional area.     

Zur physiologie der aminbildung bei der marinen rotalge Polysiphonia urceolata

The ceramiaceaen Polysiphonia urceolata rapidly degrades ¹⁴C(U)-L-leucine, added to sea water at a final concentration of 2.5x10^-5 M/l, to isoamylamine. Under experimental conditions, 22% of the total radioactivity is found in the amine within 160 min. The amino acid decarboxylase responsible for this reaction has been characterized by Hartmann (1972a). No other mechanisms of leucine degradation could be detected, and the rate of ¹⁴C-incorporation into algal proteins is considerably lower than that of decarboxylation. The rate of decarboxylation is optimal at a leucine concentration of about 5x10^-5 M/l. The amine formed is found in almost equal amounts in algal extract and environment. No further degradation of isoamylamine could be detected. The amine is a metabolic end product in P. urceolata. When ¹⁴C-isoamylamine is used as a tracer, relatively high amounts of amine are found in the algal extracts. It is supposed that the amine does not accumulate within the algal cells, but rather is bound to the acid polysaccharides of the cell walls by means of ionic exchange. The results strongly suggest that decarboxylation is the main route by which P. ureolata metabolizes amino acids from the environment which are substrates of the decarboxylase. The endogenous amino acid pool does not seem to be available to the enzyme as a substrate source. A possible ecological significance of amino acid decarboxylations is discussed.     

Separability, partial demand systems, and consumer's surplus measures

In practice, complete demand systems are not estimated. Rather, either an incomplete demand system is estimated, or separability is invoked and a partial demand system is estimated. This paper considers the relationship between the conventional compensating variation (equivalent variation) and the corresponding welfare measure that can be derived from a partial demand system and the current budget allocation to the separable group. Even assuming the separability assumption invoked is appropriate, these partial measures provide, in general, only a limited amount of information about the compensating variation and no information about the equivalent variation. Great care is therefore needed when using partial welfare measures to evaluate policy.     

Aspects of a zooplankton,phytoplankton, phosphorus system

In this paper a three-dimensional dynamical system which models the three-species system made up of phytoplankton, zooplankton and organic phosphorus nutrient in a lake environment is studied. The system is part of a more general limnological model for eutrophic lakes and impoundments which has been developed by Battelle Northwest Laboratories. It is shown that this system, henceforth referred to as Z-P-P, has a phase portrait comprised of a plane portrait embedded in the three-dimensional space R³ as an “attractor”.¹ Under a small perturbation of the nutrient equation it is shown that the system is essentially a classical Volterra-Lotka system embedded in a three-dimensional phase space R³.The system derived from Z-P-P by the addition of a term to the nutrient equation which represents the organic phosphorus contribution of dying phytoplankton is also considered. The equilibria of this system are studied and what can be deduced of the phase portrait is compared with that of the above systems. It is found that these phase portraits are qualitatively indifferent to the form of the growth rate functions for zooplankton and phytoplankton provided they are monotone increasing. Some discussion about the stability of these systems is included. Throughout this paper results are interpreted in limnological terms.     

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.     

The composition of natrophosphate (sodium fluoride phosphate hydrate)

Natrophosphate is a common trace mineral in alkaline rocks and a major salt in alkaline nuclear waste that complicates waste processing. Natrophosphate has historically been assigned the composition Na₇F(PO₄)₂·19H₂O, but this conflicts with a more recent solubility study that claimed natrophosphate is a solid solution of NaF and Na₃PO₄. It is not possible to model the solubility of natrophosphate in nuclear waste until this controversy is resolved. The present study mixed stock solutions of 0.9 M NaF and Na₃PO₄ at different ratios at 8 °C. The compositions of the liquid phase and wet natrophosphate sample were measured by ion chromatography. Plotting the tie-lines between the solid and liquid phase composition showed convergence on a single composition, indicating that natrophosphate is not a solid solution. The resulting composition is approximately the same as the composition first reported more than 140 years ago. Thus, this study resolves the long-standing controversy in the literature concerning the composition of natrophosphate.     

Different proxies for the reactivity of aquatic sediments towards oxygen: A model assessment

Information on benthic carbon mineralization rates is often derived from the analysis of oxygen microprofiles in sediments. To enable a direct comparison of different sediment environments, it is often desirable to characterize sediments by a single proxy that expresses their “reactivity” towards oxygen. For this, there are three commonly used proxies: the oxygen penetration depth (OPD), the oxygen flux at the sediment-water interface (DOU), and the maximum volumetric oxygen consumption rate (R_max). The OPD can be directly determined from the oxygen depth profile, while the DOU is usually obtained by a linear fit to the oxygen gradient either in diffusive boundary layer. The oxygen consumption rate R_max requires the fitting of a reactive-transport model to the data profile. This article shows that the OPD alone is a suboptimal proxy, because it shows a strong dependence on the half-saturation constant K_s, and secondly, because it is sensitive to the particular re-oxidation conditions right above the oxic-anoxic interface. Similarly, the volumetric oxygen consumption rate R_max is rather strongly dependent on the kinetic model formulation employed. To show this we fitted three different (Bouldin, Blackman and Monod) kinetics to the same oxygen data profiles. When fitting these models, the R_max values obtained differed by 20% for exactly the same oxygen profile. Accordingly, if one reports R_max values, it is crucial to specify the kinetic model alongside. Overall, DOU emerges as sediment reactivity proxy which is the least model dependent.     

Feasibility and stability in randomly assembled Lotka-Volterra models

For a Lotka-Volterra model to represent a viable ecosystem it's nontrivial equilibrium must be feasible. If m is the number of species, it is shown that in a set of randomly assembled Lotka-Volterra models, the fraction of models with a feasible equilibrium is some function of m which behaves like 2^?m. Moreover a subset of Lotka-Volterra models, each of which has a feasible equilibrium, has the same stability property as a set of linear models which is assembled randomly in the same manner. This contradicts a recent claim that a Lotka-Volterra model with a feasible equilibrium tends to be stable. Thus for two reasons the probability that a Lotka-Volterra model represents a viable and stable ecosystem decreases rapidly with the number of species. This supports the theme developed by May that stability in model ecosystems decreases with diversity.     

Recycling flows in emergy evaluation: A mathematical paradox?

This paper is a contribution to the emergy evaluation of systems involving recycling or reuse of waste. If waste exergy (its residual usefulness) is not negligible, wastes could serve as input to another process or be recycled. In cases of continuous waste recycle or reuse, what then is the role of emergy? Emergy is carried by matter and its value is shown to be the product of specific energy with mass flow rate and its transformity. This transformity (τ) given as the ratio of the total emergy input and the useful available energy in the product (exergy) is commonly calculated over a specific period of time (usually yearly) which makes transformity a time dependent factor. Assuming a process in which a part of the non-renewable input is an output (waste) from a previous system, for the waste to be reused, an emergy investment is needed. The transformity of the reused or recycled material should be calculated based on the pathway of the reused material at a certain time (T) which results in a specific transformity value (τ). In case of a second recycle of the same material that had undergone the previous recycle, the material pathway has a new time (T + T₁) which results in a transformity value (τ₁). Recycling flows as in the case of feedback is a dynamic process and as such the process introduces its own time period depending on its pathway which has to be considered in emergy evaluations. Through the inspiration of previous emergy studies, authors have tried to develop formulae which could be used in such cases of continuous recycling of material in this paper. The developed approach is then applied to a case study to give the reader a better understanding of the concept. As a result, a ‘factor’ is introduced which could be included on emergy evaluation tables to account for subsequent transformity changes in multiple recycling. This factor can be used to solve the difficulties in evaluating aggregated systems, serve as a correction factor to up-level such models keeping the correct evaluation and also solve problems of memory loss in emergy evaluation. The discussion deals with the questions; is it a pure mathematical paradox in the rules of emergy? Is it consistent with previous work? What were the previous solutions to avoid the cumulative problem in a reuse? What are the consequences?     

Energetics of mixing for the filling box and the emptying-filling box

The mixing efficiency of a plume in a filling box and an emptying-filling box is calculated for both transient and steady states. The mixing efficiency of a plume in a filling box in an asymptotic state is 1/2, independent of the details of this state or how the plume is modelled. The mixing efficiency of a plume in an emptying-filling box in steady state is \(1 - \xi \), where \(\xi = h/H\), the depth of the ambient layer h normalised by the height of the box H. A deeper mixed layer therefore corresponds to a higher mixing efficiency. These results shed light on the interpretation of mixing efficiencies of open and closed systems.

     

Modeling plant competition along an environmental gradient

The effect of an environmental gradient on inter-specific plant competitive interactions is modeled in a simple empirical model with biologically interpretable parameters. The model allows testing of hypotheses on the effect of the gradient on plant competitive interactions, as well as making ecological predictions from simple competition experiments using standard statistical procedures. The model, which is general and can be applied to different abiotic and biotic environmental gradients, is applied to a specific case of two competing Arabidopsis thaliana genotypes along a gradient of the general fungal pathogen Peronospora parasitica. One of the A. thaliana genotype is susceptible to the fungal pathogen P. parasitica and the other genotype is resistant. The Bayesian posterior distribution of the probability that the resistant genotype outcompetes the susceptible genotype is calculated as a function of the pathogen level. The design of the studied A. thaliana competition experiments is the minimum required experimental design needed to apply the model.     

The role of trail following in the homing of intertidal chitons: A comparison between threeAcanthopleura spp.

Three species of intertidal tropical chitons observed between 1984 and 1986, exhibit different movement patterns:Acanthopleura gemmata (Indian and Pacific Ocean) is a strict homer;A. granulata (Caribbean Sea) is mostly a ranger but sometimes shows homing behaviour;A. brevispinosa (Western Indian Ocean) alternates homing and ranging for different excursions. The three species have been studied in the field using a motographic technique to assess the importance of intra-individual trail following in homing. The fraction of the path which overlaps with earlier segments of an individual's trail is different in the three species: when returning from feeding groundsA. gemmata follows almost the whole of the outgoing path; inA. granulata the path coincidence is minimal, whileA. brevispinosa shows intermediate trail following values. InA. gemmata andA. brevispinosa trail overlap rises rapidly just after feeding, and trail following is mostly backward along the outgoing path. On the other hand,A. granulata shows a linear increase in trail coincidence with increasing path covered and the proportion of forward trail following is relatively higher. Nevertheless, all specimens of the three species which show a high homing performance invariably show a large trail following also. These findings confirm that, despite the interspecific difference in ecology and the related variation in spatial organization of foraging excursions, trail following is the basic mechanism for homing in intertidal chitons.