Modification to the Hardisty equation, regarding the relationship between sediment transport rate and particle size

Bagnold-type bed-load equations are widely used for the determination of sediment transport rate in marine environments. The accuracy of these equations depends upon the definition of the coefficient k(1) in the equations, which is a function of particle size. Hardisty (1983) has attempted to establish the relationship between k(1) and particle size, but there is an error in his analytical result. Our reanalysis of the original flume data results in new formulae for the coefficient. Furthermore, we found that the k(1) values should be derived using u(1) and u(1cr) data; the use of the vertical mean velocity in flumes to replace u(1) will lead to considerably higher k(1) values and overestimation of sediment transport rates.

The nonlinear evolution equation on the shallow water wave

Based on the variation principle, the nonlinear evolution model for the shallow water waves is established. The research shows the Duffing equation can be introduced to the evolution model of water wave with time.

Asymptotic periodicity of the Volterra equation with infinite delay

For some species, hereditary factors have great effects on their population evolution, which can be described by the well-known Volterra model. A model developed is investigated in this article, considering the seasonal variation of the environment, where the diffusive effect of the population is also considered. The main approaches employed here are the upper-lower solution method and the monotone iteration technique. The results show that whether the species dies out or not depends on the relations among the birth rate, the death rate, the competition rate, the diffusivity and the hereditary effects. The evolution of the population may show asymptotic periodicity, provided a certain condition is satisfied for the above factors. (c) 2006 Elsevier Ltd. All rights reserved.

Asymptotic weighted-periodicity of the impulsive parabolic equation with time delay

The main aim of this paper is to investigate the effects of the impulse and time delay on a type of parabolic equations. In view of the characteristics of the equation, a particular iteration scheme is adopted. The results show that Under certain conditions on the coefficients of the equation and the impulse, the solution oscillates in a particular manner-called "asymptotic weighted-periodicity".

Traveling wave front for the Fisher equation on an infinite band region

Instead of discussing the existence of a one-dimensional traveling wave front solution which connects two constant steady states, the present work deals with the case connecting a constant and a nonhomogeneous steady state on an infinite band region. The corresponding model is the well-known Fisher equation with variational coefficient and Dirichlet boundary condition. (c) 2006 Elsevier Ltd. All rights reserved.

A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio epsilon, represented by the ratio of amplitude to depth, and the dispersion ratio mu, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O(mu(2)). As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

Phytoplankton biomass size structure and its regulation in the Southern Yellow Sea (China): Seasonal variability

Phytoplankton size structure plays a significant role in controlling the carbon flux of marine pelagic ecosystems. The mesoscale distribution and seasonal variation of total and size-fractionated phytoplankton biomass in surface waters. as measured by chlorophyll a (Chl a), was studied in the Southern Yellow Sea using data from four cruises during 2006-2007. The distribution of Chl a showed a high degree of spatial and temporal variation in the study area. Chl a concentrations were relatively high in the summer and autumn, with a mean of 142 and 1.27 mg m(-3), respectively. Conversely, in the winter and spring. the average Chl a levels were only 098 and 0.99 mg m(-3) Total Chl a showed a clear decreasing gradient from coastal areas to the open sea in the summer, autumn and winter cruises. Patches of high Chl a were observed in the central part of the Southern Yellow Sea in the spring due to the onset of the phytoplankton bloom. The eutrophic coastal waters contributed at least 68% of the total phytoplankton biomass in the surface layer. Picophytoplankton showed a consistent and absolute dominance in the central region of the Southern Yellow Sea (>40%) in all of the cruises, while the proportion of microphytoplankton was the highest in coastal waters The relative proportions of pico- and nanophytoplankton decreased with total biomass, whereas the proportion of the micro-fraction increased with total biomass. Relationships between phytoplankton biomass and environmental factors were also analysed. The results showed that the onset of the spring bloom was highly dependent on water column stability. Phytoplankton growth was limited by nutrient availability in the summer due to the strong thermocline. The combined effects of P-limitation and vertical mixing in the autumn restrained the further increase of phytoplankton biomass in the Surface layer. The low phytoplankton biomass in winter was caused by vertical dispersion due to intense mixing. Compared with the availability of nutrients. temperature did not seem to cause direct effects on phytoplankton biomass and its size structure. Although interactions of many different environmental factors affected phytoplankton distributions. hydrodynamic conditions seemed to be the dominant factor. Phytoplankton size structure was determined mainly by the size-differential capacity in acquiring resource. Short time scale events, such as the spring bloom and the extension of Yangtze River plume, can have substantial influences, both on the total Chl a concentration and on the size structure of the phytoplankton. (C) 2009 Elsevier Ltd. All rights reserved.

A field study on the conversion ratio of phytoplankton biomass carbon to chlorophyll-a in Jiaozhou Bay, China

A one-year field study was conducted to determine the conversion ratio of phytoplankton biomass carbon (Phyto-C) to chlorophyll-a (Chl-a) in Jiaozhou Bay, China. We measured suspended particulate organic carbon (POC) and phytoplankton Chl-a samples collected in surface water monthly from March 2005 to February 2006. The temporal and spatial variations of Chl-a and POC concentrations were observed in the bay. Based on the field measurements, a linear regression model II was used to generate the conversion ratio of Phyto-C to Chl-a. In most cases, a good linear correlation was found between the observed POC and Chl-a concentrations, and the calculated conversion ratios ranged from 26 to 250 with a mean value of 56 A mu g A mu g(-1). The conversion ratio in the fall was higher than that in the winter and spring months, and had the lowest values in the summer. The ratios also exhibited spatial variations, generally with low values in the near shore regions and relatively high values in offshore waters. Our study suggests that temperature was likely to be the main factor influencing the observed seasonal variations of conversion ratios while nutrient supply and light penetration played important roles in controlling the spatial variations.

Microbial modulation in the biomass and toxin production of a red-tide causing alga

The effect of S-10, a strain of marine bacteria isolated from sediment in the Western Xiamen Sea, on the growth and paralytic shellfish poison (PSP) production in the alga Alexandrium tamarense (A. tamarense) was studied under controlled experimental conditions. The results of these experiments have shown that the growth of A. tamarense is obviously inhibited by S-10 at high concentrations, however no evident effect on its growth was observed at low concentrations. Its PSP production was also inhibited by S 10 at different concentrations, especially at low concentrations. The toxicity of this strain of A. tamarense is about (0.9512.14) x 10(-6) MU/cell, a peak toxicity value of 12.14 x 10(-6) MU/cell appeared on the 14th day, after which levels decreased gradually. The alga grew well in conditions of pH 6-8 and salinities of 20-34 parts per thousand. The toxicity of the alga varied markedly at different pH and salinity levels. Toxicity decreased as pH increased, while it increased with salinity and reached a peak value at a salinity of 30 parts per thousand, after which it declined gradually. S-10 at a concentration of 1.02 x 10(9) cells/ml inhibited growth and the PSP production of A. tamarense at different pH and salinity levels. S-10 had the strongest inhibitory function on the growth of A. tamarense under conditions of pH 7 and a salinity of 34 parts per thousand. The best inhibitory effect on PSP production by A. tamarense was at pH 7, this inhibitory effect on PSP production did not relate to salinity. Interactions between marine bacteria and A. tamarense were also investigated using the flow cytometer technique (FCM) as well as direct microscope counting. S-10 was identitied as being a member of the genus Bacillus, the difference in 16S rDNA between S-10 and Bacillus halmapalus was only 2%. The mechanism involved in the inhibition of growth and PSP production of A. tamarense by this strain of marine bacteria, and the prospect of using it and other marine bacteria in the biocontrol of red-tides was discussed. (c) 2005 Elsevier Ltd. All rights reserved.

Size dependence of biomass spectra and abundance spectra: the optimal distributions

Based on the hypothesis of self-optimization, we derive four models of biomass spectra and abundance spectra in communities with size-dependent metabolic rates. In Models 1 and 2, the maximum diversity of population abundance in different size classes subject to the constraints of constant mean body mass and constant mean respiration rate is assumed to be the strategy for ecosystems to organize their size structure. In Models 3 and 4, the organizing strategy is defined as the maximum diversity of biomass in different size classes without constraints on mean body mass and subject to the constant mean specific respiration rate of all individuals, i.e. the average specific respiration rate over all individuals of a community or group, which characterizes the mean rate of energy consumption in a community. Models 1 and 2 generate peaked distributions of biomass spectral density whereas Model 3 generates a fiat distribution. In Model 4, the distributions of biomass spectral density and of abundance spectral density depend on the Lagrangian multipler (lambda (2)). When lambda (2) tends to zero or equals zero, the distributions of biomass spectral density and of abundance spectral density correspond to those from Model 3. When lambda (2) has a large negative value, the biomass spectrum is similar to the empirical fiat biomass spectrum organized in logarithmic size intervals. When lambda (2) > 0, the biomass spectral density increases with body mass and the distribution of abundance spectral density is an unimodal curve. (C) 2001 Elsevier Science B.V. All rights reserved.

Sorption and desorption of Cu and Cd by macroalgae and microalgae

The sorption and desorption of Cu and Cd by two species of brown macroalgae and five species of microalgae were studied. The two brown macroalgae, Laminaria japonica and Sargassum kjellmanianum, were found to have high capacities at pHs between 4.0 and 5.0 while for microalgae, optimum pH lay at 6.7. The presence of other cations in solution was found to reduce the sorption of the target cation, suggesting a competition for sorption sites on organisms. Sorption isotherms obeyed the Freundlich equation, suggesting involvement of a multiplicity of mechanisms and sorption sites. For the microalgae tested, Spirulina platensis had the highest capacity for Cd, followed by Nannochloropsis oculata, Phaeodactylum tricornutum, Platymonas cordifolia and Chaetoceros minutissimus. The reversibility of metal sorption by macroalgae was examined and the results show that both HCl and EDTA solutions were very effective in desorbing sorbed metal ions from macroalgae, with up to 99.5% of metals being recovered. The regenerated biomass showed undiminished sorption performance for the two metals studied, suggesting the potential of such material for use in water and wastewater treatment. (C) 1998 Elsevier Science Ltd. All rights reserved.

Size-fractionated phytoplankton biomass in autumn of the Changjiang (Yangtze) River Estuary and its adjacent waters after the Three Gorges Dam construction

A cruise was undertaken from 3rd to 8th November 2004 in Changjiang (Yangtze) River Estuary and its adjacent waters to investigate the spatial biomass distribution and size composition of phytoplankton. Chlorophyll-a (Chl-a) concentration ranged 0.42-1.17 mu g L-1 and 0.41-10.43 mu g L-1 inside and outside the river mouth, with the mean value 0.73 mu g L-1 and 1.86 mu g L-1, respectively. Compared with the Chl-a concentration in summer of 2004, the mean value was much lower inside, and a little higher outside the river mouth. The maximal Chl-a was 10.43 mu g L-1 at station 18 (122.67 degrees E, 31.25 degrees N), and the region of high Chl-a concentration was observed in the central survey area between 122.5 degrees E and 123.0 degrees E. In the stations located east of 122.5 degrees E, Chl-a concentration was generally high in the upper layers above 5 m due to water stratification. In the survey area, the average Chl-a in sizes of > 20 mu m and < 20 mu m was 0.28 mu g L-1 and 1.40 mu g L-1, respectively. High Chl-a concentration of < 20 mu m size-fraction indicated that the nanophytoplankton and picophytoplankton contributed the most to the biomass of phytoplankton. Skeletonema costatum, Prorocentrum micans and Scrippsiella trochoidea were the dominant species in surface water. The spatial distribution of cell abundance of phytoplankton was patchy and did not agree well with that of Chl-a, as the cell abundance could not distinguish the differences in shape and size of phytoplankton cells. Nitrate and silicate behaved conservatively, but the former could probably be the limitation factor to algal biomass at offshore stations. The distribution of phosphate scattered considerably, and its relation to the phytoplankton biomass was complicated.

Fast microzooplankton grazing on fast-growing, low-biomass phytoplankton: a case study in spring in Chesapeake Bay, Delaware Inland Bays and Delaware Bay

Dilution experiments were performed to examine the growth and grazing mortality rates of picophytoplankton (< 2 mu m), nanophytoplankton (2-20 mu m), and microphytoplankton (> 20 mu m) at stations in the Chesapeake Bay (CB), the Delaware Inland Bays (DIB) and the Delaware Bay (DB), in early spring 2005. At station CB microphytoplankton, including chain-forming diatoms were dominant, and the microzooplankton assemblage was mainly composed of the tintinnid Tintinnopsis beroidea. At station DIB, the dominant species were microphytoplanktonic dinoflagellates, while the microzooplankton community was mainly composed of copepod nauplii and the oligotrich ciliate Strombidium sp. At station DB, nanophytoplankton were dominant components, and Strombidium and Tintinnopsis beroidea were the co-dominant microzooplankton. The growth rate and grazing mortality rate were 0.13-3.43 and 0.09-1.92 d(-1) for the different size fractionated phytoplankton. The microzooplankton ingested 73, 171, and 49% of standing stocks, and 95, 70, and 48% of potential primary productivity for total phytoplankton at station CB, DIB, and DB respectively. The carbon flux for total phytoplankton consumed by microzooplankton was 1224.11, 100.76, and 85.85 mu g C 1(-1) d(-1) at station CB, DIB, and DB, respectively. According to the grazing mortality rate, carbon consumption rate and carbon flux turn over rates, microzooplankton in study area mostly preferred to graze on picophytoplankton, which was faster growing but was lowest biomass component of the phytoplankton. The faster grazing on Fast-Growing-Low-Biomass (FGLB) phenomenon in coastal regions is explained as a resource partitioning strategy. This quite likely argues that although microzooplankton grazes strongly on phytoplankton in these regions, these microzooplankton grazers are passive.

Spatial variability in biomass and production of heterotrophic bacteria in the East China Sea and the Yellow Sea

The distributions of heterotrophic bacterial abundance and production were investigated in the East China Sea and the Yellow Sea during the autumn of 2000 and spring of 2001. Bacterial abundance varied in the range 3.2-15.7 (averaging 5.7) x 10(5) and 2.3-13.6 (averaging 6.2) x 10(5) cells cm(-3) in the spring and autumn, respectively. During autumn, bacterial production (BP) (0.27-7.77 mg C m(-3) day(-1)) was on average 3 fold that in spring (0.001-2.04 mg C m(-3) day(-1)). Bacterial average turnover rate (ratio of bacterial production:bacterial biomass, mu=0.21 day(-1)) in autumn was 3 times as high as in spring (0.07 day(-1)). The ratio of integrated bacterial biomass to integrated phytoplankton biomass in the euphotic zone ranged from 4 to 101% (averaging 35%) in spring and 24 to 556% (averaging 121%) in autumn. The results indicate that the distributions of heterotrophic bacteria were controlled generally by temperature in spring and additionally by substrate supply in autumn. (C) 2010 Elsevier Ltd. All rights reserved.

SIZE STRUCTURES OF MICROPLANKTON BIOMASS AND PRODUCTION IN JIAOZHOU BAY, CHINA

Seasonal investigations of size-fractionated biomass and production were carried out from February 1992 to May 1993 in Jiaozhou Bay, China. Microplankton assemblages were separated into three fractions: pico-(0.7-2 mu m), nano- (2-20 mu m) and netplankton (20-200 mu m). The biomass was measured as chlorophyll a (Chl a), particulate organic carbon (POC) and particulate organic nitrogen (PON). The production was determined by C-14 and N-15 tracer techniques. The seasonal patterns in biomass, though variable, were characterized by higher values in spring and lower values in autumn and summer (for Chl a only). The seasonal patterns in production, on the other hand, were more clear with higher values occurring in summer and spring, and lower values occurring in autumn and winter. Averaged over the whole study period, the respective proportions of total biomass accounted for by net-, nano- and picoplankton were 26, 45 and 29% for Chl a, 32, 33 and 35% for POC, and 26, 32 and 42% for PON. The contributions to total primary production by net-, nano- and picoplankton were 31, 35 and 34%, respectively. The respective proportions of total NH4+-N uptake accounted for by net-, nano- and picoplankton were 28, 33 and 39% in the daytime, and 10, 29 and 61% at night. The respective contributions to total NO3--N uptake by net-, nano- and picoplankton were 37, 40 and 23% in the daytime, and 13, 23 and 64% at night. Some comprehensive ratios, including C/N biomass ratio, Chl a/C ratio, C uptake/Chl a ratio, C:N uptake ratio and the f-ratio, were also calculated size separately, and their biological and ecological meanings are discussed.