On the planing of a flat plate at high Froude numbers in a two-dimensional case

We seek the solution of the planing of a flat plate at high Froude numbers by a perturbation procedure. The angle of attack of the plate is assumed to vary with the speed of the plate in the present study. A harmonic function K is introduced for the solution of the first-order disturbance potential which becomes the Green function in the limiting case when the Froude number tends to infinity. We get the solution of the first-order potential from Green's theorem applied to K and the first-order potential. Then we obtain the asymptotic solutions of the angle of attack α, lift L and drag D as follows:

where α1. Here W, L_W, and U are the weight of the plate per unit width, wetted length, and speed of the plate, respectively.     

Oxidation of copper(I) in seawater at nanomolar levels

The oxidation and reduction of nanomolar levels of copper in air-saturated seawater and NaCl solutions has been measured as a function of pH (7.17–8.49), temperature (5–35 °C) and ionic strength (0.1–0.7 M). The oxidation rates were fitted to an equation valid at different pH and ionic strength conditions in sodium chloride and seawater solutions:

The reduction of Cu(II) was studied in both media for different initial concentrations of copper(II). When the initial Cu(II) concentration was 200 nM, the copper(I) productions were 20% and 9% for NaCl and seawater, respectively. The effect of speciation of copper(I) reduced from Cu(II) on the rates was studied. The Cu(I) speciation is dominated by the CuCl₂⁻ species. On the other hand, the neutral chloride CuCl species dominates the Cu(I) oxidation in the range of 0.1 M to 0.7 M chloride concentrations.     

Characterization of marine and terrestrial DOM in seawater using excitation-emission matrix spectroscopy

High-resolution fluorescence spectroscopy was used to characterize dissolved organic matter (DOM) in concentrated and unconcentrated water samples from a wide variety of freshwater, coastal and marine environments. Several types of fluorescent signals were observed, including humic-like, tyrosine-like, and tryptophan-like. Humic-like fluorescence consisted of two peaks, one stimulated by UV excitation (peak A) and one by visible excitation (peak C). For all samples, the positions of both excitation and emission maxima for peak C were dependent upon wavelength of observation, with a shift towards longer wavelength emission maximum at longer excitation wavelength and longer wavelength excitation maximum at longer emission wavelength. A trend was observed in the position of wavelength-independent maximum fluorescence () for peak C, with maximum at shorter excitation and emission wavelengths for marine samples than for freshwater samples. Mean positions of these maxima were: rivers = nm; coastal water = nm; marine shallow transitional = nm; marine shallow eutrophic = nm; and marine deep = nm. Differences suggest that the humic material in marine surface waters is chemically different from humic material in the other environments sampled. These results explain previous conflicting reports regarding fluorescence properties of DOM from natural waters and also provide a means of distinguishing between water mass sources in the ocean.     

Phosphorus in Bottom Sediments of Pomeranian Bay (Southern Baltic—Poland)

The paper presents the results of determination of inorganic and organic forms of phosphorus in bottom sediments of Pomeranian Bay. The sediments were collected in March and July of 1996. The following characteristics of the sediments were determined: organic matter content, forms of inorganic phosphorus: loosely adsorbed phosphorus and phosphorus bound to aluminium, calcium and iron, as well as total inorganic phosphorus. Pomeranian Bay is a shallow basin, with depth averaging between 12 and 15 m and sandy sediments prevailing. Smaller silt fractions occur only in the vicinity of the wina River estuary and in deeper northern regions of the Bay. Calcium-bound phosphorus is the dominant form of inorganic phosphorus in the Pomeranian Bay. Iron-bound phosphorus is the second most prevailing form, and aluminium-bound phosphorus the third. Loosely bound phosphorus was present in the lowest amounts. Total inorganic phosphorus in the Bay consisted of the four forms listed above, except in estuarine regions where an additional form of phosphorus occurred, most probably occluded phosphorus. High organic phosphorus concentrations were found at the wina River estuary and in the northern part of the Bay (Saßnitz Deep) corresponding to the higher organic matter content of these sediments. Sediments of Pomeranian Bay contained less phosphorus than those from the Gulf of Gda sk or Puck Bay and other parts of the Baltic Sea, suggesting that the amount of phosphorus in the sediments was determined by a number of inter-related factors, such as sediment type, amount of organic matter, the chemical composition of the sediment and oxygen content of near-bottom water.     

Numerical model simulations of continental shelf flows off northern California

The three-dimensional circulation on the continental shelf off northern California in the wind events and shelf transport (WEST) experiment region during summer 2001 is studied using the primitive equation regional ocean modeling system (ROMS). The simulations are performed with realistic topography and initial stratification in a limited-area domain with a high-resolution grid. Forcing consists of measured wind-stress and heat flux values obtained from a WEST surface buoy. The general response shows a southward coastal upwelling jet of up to and a weakening or reversal of currents inshore of the jet when upwelling winds relax. Model results are compared to WEST moored velocity and temperature measurements at five locations, to CODAR surface current observations between Pt. Reyes and Bodega Bay, and to hydrographic measurements along shipboard survey lines. The model performs reasonably well, with the highest depth-averaged velocity correlation (0.81) at the inshore mooring (40 m water depth) and lowest correlation (0.68) at the mid-depth mooring (90 m depth). The model shows generally stronger velocities than those observed, especially at the inshore moorings, and a lack in complete reversal of southward velocities observed when upwelling winds relax. The comparison of surface velocities with CODAR measurements shows good agreement of the mean and the dominant mode of variability. The hydrography compares closely at the southern and northern edges of the survey region (correlation coefficients between 0.90 and 0.97), with weaker correlations at the three interior survey lines (correlation coefficients between 0.44 and 0.76). Mean model fields over the summer upwelling period show slight coastal jet separation off Pt. Arena and significant separation off Pt. Reyes. The cape regions also experience relatively strong bottom velocities and nonlinearity in the surface flow. Across-shelf velocity sections examined along the shelf reveal a double jet structure that appears just north of Bodega Bay and shows the offshore jet strengthening to the south. We examine the dynamics during an upwelling and subsequent relaxation event in May 2001 in which the WEST measurements show evidence of a strong flow response. The alongshelf variability in the upwelling and relaxation response introduced by Pt. Reyes is evident. Analysis of term balances from the depth-averaged momentum equations helps to clarify the event dynamics in different regions over the shelf. A clear pattern in the nonlinear advection term is due to the spatial acceleration of the southward jet around the capes of Pt. Arena and Pt. Reyes during upwelling. Results from a three-dimensional Lagrangian analysis of water parcel displacement show significant southward displacement in the coastal jet region, including a strong signal from the double jet. Alongshelf variability in parcel displacements and upwelling source waters due to the presence of Pt. Arena and Pt. Reyes is also apparent from the Lagrangian fields. A cyclonic eddy-like recirculation feature offshore of Pt. Arena prior to the upwelling event causes large patches of onshore-displaced parcels. Additionally, across-shelf variability in the response of water parcels along the D line includes decreased vertical displacement and increased alongshelf displacement in the offshore direction.     

The influence of light on nitrogen cycling and the primary nitrite maximum in a seasonally stratified sea

In the seasonally stratified Gulf of Aqaba Red Sea, both release by phytoplankton and oxidation by nitrifying microbes contributed to the formation of a primary nitrite maximum (PNM) over different seasons and depths in the water column. In the winter and during the days immediately following spring stratification, formation was strongly correlated (R² = 0.99) with decreasing irradiance and chlorophyll, suggesting that incomplete reduction by light limited phytoplankton was a major source of . However, as stratification progressed, continued to be generated below the euphotic depth by microbial oxidation, likely due to differential photoinhibition of and oxidizing populations. Natural abundance stable nitrogen isotope analyses revealed a decoupling of the δ¹⁵N and δ¹⁸O in the combined and pool, suggesting that assimilation and nitrification were co-occurring in surface waters. As stratification progressed, the δ¹⁵N of particulate N below the euphotic depth increased from −5‰ to up to +20‰.N uptake rates were also influenced by light; based on ¹⁵N tracer experiments, assimilation of , , and urea was more rapid in the light (434 ± 24, 94 ± 17, and 1194 ± 48 nmol N L⁻¹ day⁻¹ respectively) than in the dark (58 ± 14, 29 ± 14, and 476 ± 31 nmol N L⁻¹ day⁻¹ respectively). Dark assimilation was 314 ± 31 nmol N L⁻¹ day⁻¹, while light assimilation was much faster, resulting in complete consumption of the ¹⁵N spike in less than 7 h from spike addition. The overall rate of coupled urea mineralization and oxidation (14.1 ± 7.6 nmol N L⁻¹ day⁻¹) was similar to that of oxidation alone (16.4 ± 8.1 nmol N L⁻¹ day⁻¹), suggesting that mineralization of labile dissolved organic N compounds like urea was not a rate limiting step for nitrification. Our results suggest that assimilation and nitrification compete for and that N transformation rates throughout the water column are influenced by light over diel and seasonal cycles, allowing phytoplankton and nitrifying microbes to contribute jointly to PNM formation. We identify important factors that influence the N cycle throughout the year, including light intensity, substrate availability, and microbial community structure. These processes could be relevant to other regions worldwide where seasonal variability in mixing depth and stratification influence the contributions of phytoplankton and non-photosynthetic microbes to the N cycle.     

Damage identification in a ship’s structure using neural networks

Visual inspection of large and complex structures such as a ship is difficult and costly due to problems of accessibility. In this paper, a neural network technique is developed for identifying the damage occurrence in the side shell of a ship’s structure. The side shell is modeled as a stiffened plate. The input to the network is the autocorrelation function of the vibration response of the structure. The response was obtained using a finite element model of the structure. The output is a single function , which was formed by adding together the damping and a part of the restoring forces. The function is used to identify not only the damage occurrence in the model but also its extent and location. The results show that the method presented in this work is successful in identifying the occurrence of damage. The detection of the extent and location of damage is promising, however, more work has to be done in this area.     

Direct measurements of diapycnal mixing in a fjord reach—Puget Sound's Main Basin

In the spring of 1988, time series of microstructure and ADCP current profiles were collected at four locations in the North Main Basin of Puget Sound, Washington. Depth and time averages of diapycnal diffusivity at the four stations (1.8−67.0×10⁻⁴ m² s⁻¹) were one to three decades above typical open-ocean thermocline levels. The buoyancy frequency-squared N² was near open-ocean levels, but unlike the open-ocean where N²S², finescale shear-squared S² was three to six times N² over significant portions of the water column at two of the stations. The time and space mean of all measurements ( ) is close to inferred vertical eddy diffusivity from a primitive equation model for Puget Sound (K_z=3×10⁻³ m² s⁻¹) (J. Geophys. Res. 96 (1991) 16779). Large time and space variability of K_ρ was found, with differences of inter-station, depth–time means over one decade. A simple scaling argument using the observed K_ρ suggests significant exchange of mass between the layers of the subtidal flow over the basin's residence time. Additionally, measurements show that local mixing may be comparable to volume-weighted sill mixing in modifying the Main Basin's stratification. Both are contrary to the “advective reach” simplification of fjord dynamics. The mixing levels were dominated by the passage of a mid-depth, southward-flowing density intrusion and what we interpret as a strongly advected, non-linear internal tide. These mechanisms elevated profile-averaged K_ρ by more than 10 times background levels, with sustained patches of K_ρ≥1×10⁻² m² s⁻¹. Critical 8-m gradient Richardson numbers (Ri₈<0.25) matching regions of overturns (>20 m) and strong turbulence suggest that shear instabilities dominated the turbulence production, though there was support for double-diffusive convection in the warm core of the density intrusion.     

Dissociation constants of protonated cysteine species in seawater media

The dissociation constants (pK₁, pK₂ and pK₃) for cysteine have been measured in seawater as a function of temperature (5 to 45 °C) and salinity (S = 5 to 35). The seawater values were lower than the values in NaCl at the same ionic strength. In an attempt to understand these differences, we have made measurements of the constants in Na–Mg–Cl solutions at 25 °C. The measured values have been compared to those calculated from the Pitzer ionic interaction model. The lower values of pK₃ in the Na–Mg–Cl solutions have been attributed to the formation of Mg²⁺ complexes with Cys²⁻ anions

Mg²⁺ + Cys²⁻ = MgCys

The stability constants have been fitted to

after corrections are made for the interaction of Mg²⁺ with H⁺.The pK₁ seawater measurements indicate that H₃Cys⁺ interacts with SO₄²⁻. The Pitzer parameters β⁰(H₃CysSO₄), β¹(H₃CysSO₄) and C(H₃CysSO₄) have been determined for this interaction. The formation of CaCys as well as MgCys are needed to account for the values of pK₂ and pK₃ in seawater.The consideration of the formation of MgCys and CaCys in seawater yields model calculated values of pK₁, pK₂ and pK₃ that agree with the measured values to within the experimental error of the measurements. This study shows that it is important to consider all of the ionic interactions in natural waters when examining the dissociation of organic acids.     

A general theory of three-dimensional wave groups Part I: The formal derivation

If we know that a wave of given exceptionally large crest-to-trough height occurs at a fixed point at an instant t_o in a random wind-generated sea state, we can predict what happens with a very high probability before and after t_o in an area surrounding . The expressions of the surface displacement and velocity potential in this area are obtained in closed form. They are exact to the first order in a Stokes expansion and hold for nearly arbitrary bandwidth and solid boundary. It will be shown in Part II that these expressions represent either the evolution of a single three-dimensional wave group or the collision of two wave groups, according to the configuration of the solid boundary. The theory was developed in a series of papers starting on 1981. This paper presents the whole theory in a compact form thanks to a radical simplification of the mathematical proof.     

Effect of seasonal changes in bottom water oxygenation on sediment N oxides and N2O cycling in the coastal upwelling regime off central Chile (36.5°S)

An intensive and seasonal coastal upwelling process, which attains maximal expression during late austral spring and summer, drives well-known changes in organic matter production and, therefore, in O₂ content in the water column. These variables have a concomitant effect on N sediment processes over the continental shelf off central Chile (36.5°S), which, in turn, can affect the , , and N₂O content in the bottom water. Hydrographic characteristics, benthic and fluxes, and denitrification rates were measured from 1998 to 2001 (with at least seasonal frequency). In order to elucidate how benthic N₂O recycling responds to different O₂ and nutrient levels and how it affects the bottom water N₂O content, net N₂O cycling was measured in December 2001 in sediment slurry incubations under different manipulated dissolved O₂ levels (anoxic: 0 μM; hypoxic: 22.3 μM; oxic: 44.6 μM) and without (natural) and with the addition of and (enriched experiments). Dissolved O₂ and contents (and also ) showed clear seasonal patterns according to the oceanographic regime, i.e., from hypoxic waters rich in nutrients during the upwelling season to oxic waters with less nutrient contents during the non-upwelling season. The bottom water, on the other hand, was influenced by benthic organic mineralization, which consumes O₂ as well as other electron acceptor N-species such as . Benthic fluxes (2.62-5.08 mmol m⁻² d⁻¹) were always directed into the sediments, whereas denitrification rates varied from 0.6 to 2.9 mmol m⁻² d⁻¹. N₂O was also consumed at rates of 5.53 and 4.56 μmol m⁻² d⁻¹ under anoxia and hypoxia, but N₂O consumption rates were reduced to almost half under oxic conditions in both natural and a -enriched experiments. With the -enriched experiments, however, N₂O consumption was very high (up to 24.25 μmol m⁻² d⁻¹) under anoxic and hypoxic conditions, suggesting that high levels induce more N₂O reduction to N₂ by denitrification. N₂O production rates were only measured when oxic conditions were observed in the -enriched experiment, suggesting some role of nitrification. Thus, N cycling in the sediments seems to affect the observed , NO²⁻, and N₂O content in the bottom water and, therefore, in the entire water column due to vertical advection associated with coastal upwelling.     

Anthropogenic carbon in the East Greenland Current

Sections of dissolved inorganic anthropogenic carbon () based on 2002 data in the East Greenland Current (EGC) are presented. The has been estimated using a model based on optimum multiparameter analysis with predefined source water types. Values of have been assigned to the source water types through age estimations based on the transit time distribution (TTD) technique. The validity of this approach is discussed and compared to other methods. The results indicated that the EGC had rather high levels of in the whole water column, and the anthropogenic signal of the different source areas were detected along the southward transit. We estimated an annual transport of with the Denmark Strait overflow (σ_θ > 27.8 kg m⁻³) of ∼0.036 ± 0.005 Gt C y⁻¹. The mean concentration in this density range was ∼30 μmol kg⁻¹. The main contribution was from Atlantic derived waters, the Polar Intermediate Water and the Greenland Sea Arctic Intermediate Water.     

Nutrient gradients from the eutrophic Changjiang (Yangtze River) Estuary to the oligotrophic Kuroshio waters and re-evaluation of budgets for the East China Sea Shelf

Eutrophication has become an overwhelming phenomenon in the coastal environment off the Changjiang (Yangtze River) Estuary, illustrated by an increase in nutrient concentration, frequent red-tide events and hypoxia in near-bottom waters, while the open East China Sea Shelf and Kuroshio waters remain oligotrophic. Observations made in the Changjiang Estuary and the East China Sea in 1999–2003 cover a broad range of hydrographic and chemical properties. The concentration gradients of nutrients across the shelf indicate that high levels from land-sources are constrained to the coastal and inner-shelf region by the complex circulation regime. In surface waters, nutrient species gradually decrease from eutrophic coastal to oligotrophic open shelf waters, depending on the hydrographic stages of the Changjiang, although biological uptake and regeneration in the upper water column can produce patchy character of nutrient distribution. Taiwan Current Warm Water and Kuroshio Surface Water are devoid of nutrients. Remineralization of nutrient species takes place in the near-bottom waters in the inner-shelf following extensive bacterial demand for organic matter. Hence the burial efficiency is low with regard to the biogenic species, either allochthonous or autochthonous, or both. The Kuroshio Sub-surface Waters are rich in nutrients, and their incursion into the East China Sea can be tracked by salinity and temperature, reaching within water depth of 50–100 m at mid-shelf. Relative to shelf waters, the Kuroshio intrusion is characterized by high and DIP/DOP ratios. In the water column, the ratio of DIP/DOP to is higher than the Redfield P/N value, suggesting rapid regeneration of phosphorus relative to nitrogen in the East China Sea. The results of a box-model suggest that the East China Sea Shelf do likely not export substantial amounts of dissolved biogenic elements to the open Northwest Pacific Ocean.     

Physical dynamics and biological implications of a mesoscale eddy in the lee of Hawai’i: Cyclone Opal observations during E-Flux III

E-Flux III (March 10–28, 2005) was the third and last field experiment of the E-Flux project. The main goal of the project was to investigate the physical, biological and chemical characteristics of mesoscale eddies that form in the lee of Maui and the Island of Hawai’i, focusing on the physical–biogeochemical interactions. The primary focus of E-Flux III was the cyclonic cold-core eddy Opal, which first appeared in the NOAA GOES sea-surface temperature (SST) imagery during the second half of February 2005. During the experiment, Cyclone Opal moved over 160 km, generally southward. Thus, the sampling design had to be constantly adjusted in order to obtain quasi-synoptic observations of the eddy. Analyses of ship transect-depth profiles of CTD, optical and acoustic Doppler current profiler (ADCP) data revealed a well-developed feature characterized by a fairly symmetric circular shape with a radius of about 80 km. Depth profiles of temperature, salinity and density were characterized by an intense doming of isothermal, isohaline and isopycnal surfaces. Isopleths of nutrient concentrations were roughly parallel to isopycnals, indicating the upwelling of deep nutrient-rich water. The deep chlorophyll maximum layer (DCML) shoaled from a depth of about 130 m in the outer regions of the eddy to about 60 m in the center. Chlorophyll concentrations reached their maximum values in Opal's core region (about 40 km in diameter), where nutrients were upwelled into the euphotic layer. ADCP velocity data clearly showed the cyclonic circulation associated with Opal. Vertical sections of tangential velocities were characterized by values that increased linearly with radial distance from near zero close to the center to a maximum of about at roughly 25 km from the center, and then slowly decayed. The vertical extent of the cyclonic circulation was primarily limited to the upper mixed layer, as tangential velocities decayed quite rapidly within a depth range of 90–130 m. Potential vorticity analysis suggests that only a relatively small (about 50 km in diameter) and shallow (to a depth of approximately 70 m) portion of the eddy is isolated from the surrounding waters. Radial movements of water can occur between the center of the eddy and the outer regions along density surfaces within an isopycnal range of σ–t_23.6 () and σ–t_24.4 (). Thus the biogeochemistry of the system might have been greatly influenced by these lateral exchanges of water at depth, especially during Opal's southward migration. While the eddy was translating, deep water in front of the eddy might have been upwelled into the core region, leading to an additional injection of nutrients into the euphotic zone. At the same time, part of the chlorophyll-rich waters in the core region might have remained behind the translating eddy and, thus contributed to the formation of an eddy wake characterized by relatively high chlorophyll concentrations.     

Bifurcation analysis of 3D ocean flows using a parallel fully-implicit ocean model

To understand the physics and dynamics of the ocean circulation, techniques of numerical bifurcation theory such as continuation methods have proved to be useful. Up to now these techniques have been applied to models with relatively few degrees of freedom such as multi-layer quasi-geostrophic and shallow-water models and relatively low-resolution (e.g., 4° horizontal resolution) primitive equation models. In this paper, we present a new approach in which continuation methods are combined with parallel numerical linear system solvers. With this implementation, we show that it is possible to compute steady states versus parameters (and perform fully implicit time integration) of primitive equation ocean models with up to a few million degrees of freedom.     

Reynolds number dependence of mixing in a lock-exchange system from direct numerical and large eddy simulations

Turbulent mixing of water masses of different temperatures and salinities is an important process for both coastal and large-scale ocean circulation. It is, however, difficult to capture computationally. One of the reasons is that mixing in the ocean occurs at a wide range of complexity, with the Reynolds number reaching , or even higher.In this study, we continue to investigate whether large eddy simulation (LES) can be a reliable computational tool for stratified mixing in turbulent oceanic flows. LES is attractive because it can be times faster than a direct numerical simulation (DNS) of stratified mixing in turbulent flows. Before using the LES methodology to compute mixing in realistic oceanic flows, however, a careful assessment of the LES sensitivity with respect to Re needs to be performed first. The main objectives of this study are: (i) to investigate the performance of different LES models at high Re, such as those encountered in oceanic flows; and (ii) to study how mixing varies as a function of Re. To this end, as a benchmark we use the lock-exchange problem, which is described by unambigous and simple initial and boundary conditions. The background potential energy, which accurately quantifies irreversible mixing in an enclosed system, is used as the main criterion in a posteriori testing of LES.This study has two main achievements. The first is that we investigate the accuracy of six combinations of two different classes of LES models, namely eddy-viscosity and approximate deconvolution types, for 3×10³Re3×10⁴, for which DNS data is computed. We find that all LES models almost always provide significantly more accurate results than cases without LES models. Nevertheless, no single LES model that is persistently superior to others over this Re range could be identified. Then, an ensemble of the four best performing LES models is selected in order to estimate mixing taking place in this system at Re=10⁵ and 10⁶, for which DNS is presently not feasible. Thus the second achievement of this study is to quantify mixing taking place in this system over an Re range that changes by three orders of magnitude. We find that the background potential energy increases by about 67% when Re is increased from Re=10³ to Re=10⁶, within the computation period, with the most significant increase taking place from Re=3×10³ to Re=10⁵.     

Chromium(VI) reduction by sulphur(IV) in aqueous solutions

The rates of the reduction of Cr(VI) with S(IV) were measured in deaerated NaCl solution as a function of pH, temperature and ionic strength. The rates of the reaction were found to be first order with respect to Cr(VI) and second order with respect to S(IV), in agreement with previous results obtained at concentrations two order higher than the present study. The reaction also showed a first-order dependence of the rates on the concentration of the proton and a small influence of temperature with an apparent energy of activation ΔH_app of 22.8 ± 3.4 kJ/mol. The rates were independent of ionic strength from 0.01 to 1 M. The rate of Cr(VI) reduction is described by the general expression

−d[Cr(VI)]/dt=k[Cr(VI)][S(IV)]²