Solution of an unstable axisymmetric Cauchy–Poisson problem of dispersive water waves for a spectrum with compact support

 It has been known that the axisymmetric Cauchy–Poisson problem for dispersive water waves is well posed in the sense of stability. Thereby time evolution solutions of wave propagation depend continuously on initial conditions. However, in this paper, it is demonstrated that the axisymmetric Cauchy–Poisson problem is ill posed in the sense of stability for a certain class of initial conditions, so that the propagating solutions do not depend continuously on the initial conditions. In order to overcome the difficulty of the discontinuity, Landweber–Fridman's regularization, famous and well known in applied mathematics, are introduced and investigated to learn whether it is applicable to the present axisymmetric wave propagation problem. From the numerical experiments, it is shown that stable and accurate solutions are realized by the regularization, so that it can be applicable to the determination of the ill-posed Cauchy–Poisson problem.     

Plankton distribution and vertical flux of biogenic matter during high summer stratification in the Krka estuary (Eastern Adriatic)

The aim of this study was to investigate phytoplankton abundance, composition and vertical export in the highly stratified Krka estuary, Croatia. The estuary is stratified throughout the year, and an interface between fresh- and brackish water plays an important role in production and degradation of biogenic matter. Vertical export of particulate organic carbon (POC), phytoplankton carbon (PPC) and faecal pellet carbon (FPC) was studied by deploying sediment traps in the middle and lower reach of the estuary and in the adjacent coastal zone. Zooplankton faecal pellet (FP) production experiments were conducted to provide additional information on the potential contribution of FP to the total carbon flux. High suspended concentrations of POC, chlorophyll a and phytoplankton was found in the lower reaches of the Krka estuary, adjacent to a source of anthropogenic eutrophication. The fraction of organic detritus to the total POC flux was 61–69% inside the estuary but only 7% at the marine station. This indicates that the primary producers in the surface layer of the Krka estuary are decomposed in and below the interface and then settle as detritus to the bottom. Low sedimentation rates in the coastal zone outside the estuary revealed that the eutrophication does not spread out of the estuary. Mesozooplankton played a modest role in vertical flux regulation, due to their low abundance and dominance of smaller forms as well as low faecal pellet production rates. It is concluded that processes taking place at the freshwater-seawater interface are of major importance for the vertical carbon flux in the investigated area.     

Organic matter origin and distribution in suspended particulate materials and surficial sediments from the western Adriatic Sea (Italy)

In this study, organic carbon (OC), total nitrogen (TN), stable carbon isotopic (δ¹³C_OC) and CuO reaction product compositions were used to identify the sources of organic matter (OM) and to quantify the relative importance of allochthonous and autochthonous contributions to the western Adriatic Sea, Italy. Suspended particulate material (195 samples) and surficial sediments (0–1 cm, 70 samples) from shallow cross-shelf transects were collected in February and May 2003, respectively. Vertical water column profiles were acquired along the same transects. Data include depth, potential temperature, salinity, density and chlorophyll fluorimetry.Along the western Adriatic shelf in the near-shore region, the phytoplankton growth was influenced by dynamics of the buoyant plumes from the Po and Appennine rivers. A small amount of very fine terrigenous material remained suspended within the coastal current and was exported southward along the shelf to the slope. High variability in the bulk composition was detected in the Po prodelta surficial sediments, whereas the western Adriatic shelf, although a larger area, exhibited a narrower range of values.A significant decoupling was observed between suspended particles in the water column and surficial deposits. The organic material collected in the water column was compositionally heterogeneous, with contributions from marine phytoplankton, riverine–estuarine phytoplankton and soil-derived OM. Frequent physical reworking of surficial sediments likely leads to the efficient oxidation of marine OC, resulting in the observed accumulation and preservation of refractory soil-derived OC delivered by the Po and Appennine rivers.     

Dynamic processes and their influence on the transformation of the passive admixture in the sea of Azov

In this model, we apply a nonlinear three-dimensional sigma-coordinate model to study the waves and currents in the Sea of Azov generated by different fields of wind forcing: a constant wind, a quickly varying real wind obtained using the data of reanalysis applying the SKIRON model, and the wind resulting from their combined forcing. This mathematical model was also applied to study the transformation of the passive admixture appearing under the influence of wind fields in the Sea of Azov considered here. We compared the results of numerical calculations with the field data obtained under the wind forcing at a number of hydrological stations. We found the regularities of the water transport driven by onshore and offshore winds, the velocities of the currents, and the characteristics of the evolution of polluted regions at different depths as functions of the nonstationary wind intensity and the velocities of the stationary currents.     

An unsteady wave driver for narrowbanded waves: modeling nearshore circulation driven by wave groups

In this paper, we derive an unsteady refraction–diffraction model for narrowbanded water waves for use in computing coupled wave–current motion in the nearshore. The end result is a variable coefficient, nonlinear Schrödinger-type wave driver (describing the envelope of narrow-banded incident waves) coupled to forced nonlinear shallow water equations (describing steady or unsteady mean flows driven by the short-wave field). Comparisons with experimental data show that good accuracy can be obtained for cases of nonbreaking wave transformation. Numerical simulations show that the interaction of wave groups with longshore topographic nonuniformities generates strong edge wave resonances, providing a generating mechanism for low-order edge waves.     

A nitrate and silicate budget in the equatorial Pacific Ocean: a coupled physical–biological model study

A coupled physical–biological model was developed to simulate the low-silicate, high-nitrate, and low-chlorophyll (LSHNLC) conditions in the equatorial Pacific Ocean and used to compute a detailed budget in the Wyrtki box (5°N–5°S, 180–90°W) for the major sources and cycling of nitrogen and silicon in the equatorial Pacific. With the incorporation of biogenic silicon dissolution, NH₄ regeneration from organic nitrogen and nitrification of ammonia in the model, we show that silicon recycling in the upper ocean is less efficient than nitrogen. As the major source of nutrients to the equatorial Pacific, the Equatorial Undercurrent provides slightly less Si(OH)₄ than NO₃ to the upwelling zone, which is defined as 2.5°N–2.5°S. As a result, the equatorial upwelling supplies less Si(OH)₄ than NO₃ into the euphotic zone in the Wyrtki box, having a Si/N supply ratio of about 0.85 (2.5 vs. 2.96 mmolm⁻² day⁻¹). More Si(OH)₄ than NO₃ is taken up with a Si/N ratio of 1.17 (2.72 vs. 2.33 mmolm⁻² day⁻¹) within the euphotic zone. The difference between upwelling supply and biological uptake is balanced by nutrient regeneration and horizontal advection. Excluding regeneration, the net silicate and nitrate uptakes are nearly equal (1.76 vs. 1.84 mmolm⁻² day⁻¹). However, biogenic silica export production is slightly higher than organic nitrogen (1.74 vs. 1.59 mmolm⁻² day⁻¹) following a 1.1 Si/N ratio. In the central equatorial Pacific, low silicate concentrations limit diatom growth; therefore non-diatom new production accounts for most of the new production. Higher silicate supply in the east maintains elevated diatom growth rates and new production associated with diatoms dominate upwelling zone. In contrast, the new production associated with small phytoplankton is nearly constant or decreases eastward along the equator. The total new production has a higher rate in the east than in the west, following the pattern of surface silicate. This suggests that silicate regulates the diatom production, total new production, and thereby carbon cycle in this area. The modeled mean primary production is 48.4 mmolCm⁻² day⁻¹, representing the lower end of direct field measurements, while new production is 15.0 mmolCm⁻² day⁻¹, which compares well with previous estimates.     

Dynamic properties of green water event in the overtopping of extreme waves on a fixed dock

A statistical model is developed to predict wave overtopping volume and rate of extreme waves on a fixed deck. The probability density function for the volume and rate of overtopping water are formulated based on the truncated Weibull distribution with the assumption of local sinusoidal profile for small amplitude waves. Sensitivity to the wave nonlinearity parameter and deck clearance is discussed. The statistical model is compared to laboratory data of the instantaneous free surface elevation measured in front of a fixed deck, and overtopping volume and overtopping rate measured at the leading edge of the deck. The statistical theory compared well with the measured exceedance probability seaward of the deck. The model prediction of the exceedance probability of deck overtopping gave qualitatively good agreement for large overtopping values.     

Radioelement distribution in river,beach, and offshore areas and their significance to Chavara placer deposit,Southern Kerala Coast of India

The radioelement and heavy mineral distribution in river, beach and innershelf areas of the southern Kerala coast is related to placer mineral concentration on the beaches at Chavara. Southern Kerala rivers—Neyyar, Karamana and Vamanapuram—transport higher amounts of radioactive elements than the larger Kallada River due to higher radioactive minerals in the hinterland rocks. Coastal configurations and the seasonal longshore current pattern seems to control along-shore distribution of minerals. The proposed model for placer concentration suggests that the energy difference and seasonal current direction along this coast is important.     

Exchange of water in a stratified estuary with an application to Krka (Adriatic Sea)

A method of computing the exchange time of freshwater and marine water in a stratified estuary is presented. The method is based on the inflow of the river and its tributaries, the depth of the halocline and salinity in the upper brackish water layer. Exchange time of freshwater and seawater in the Krka Estuary is shorter during winter than during summer. During winter the exchange time of freshwater is between 6 and 20 days, whereas during summer it is up to 80 days. The exchange time of marine water during winter is from 50 to 100 days, whereas during summer it lengthens to 250 days. The renewal time of water in the Krka Estuary as a whole may be approximated by the exchange time.     

Tidally incised valleys on tropical carbonate shelves: An example from the northern Great Barrier Reef, Australia

The formation of incised valleys on continental shelves is generally attributed to fluvial erosion under low sea level conditions. However, there are exceptions. A multibeam sonar survey at the northern end of Australia's Great Barrier Reef, adjacent to the southern edge of the Gulf of Papua, mapped a shelf valley system up to 220 m deep that extends for more than 90 km across the continental shelf. This is the deepest shelf valley yet found in the Great Barrier Reef and is well below the maximum depth of fluvial incision that could have occurred under a − 120 m, eustatic sea level low-stand, as what occurred on this margin during the last ice age. These valleys appear to have formed by a combination of reef growth and tidal current scour, probably in relation to a sea level at around 30–50 m below its present position.

Tidally incised depressions in the valley floor exhibit closed bathymetric contours at both ends. Valley floor sediments are mainly calcareous muddy, gravelly sand on the middle shelf, giving way to well-sorted, gravely sand containing a large relict fraction on the outer shelf. The valley extends between broad platform reefs and framework coral growth, which accumulated through the late Quaternary, coincides with tidal current scour to produce steep-sided (locally vertical) valley walls. The deepest segments of the valley were probably the sites of lakes during the last ice age, when Torres Strait formed an emergent land-bridge between Australia and Papua New Guinea. Numerical modeling predicts that the strongest tidal currents occur over the deepest, outer-shelf segment of the valley when sea level is about 40–50 m below its present position. These results are consistent with a Pleistocene age and relict origin of the valley.

Based on these observations, we propose a new conceptual model for the formation of tidally incised shelf valleys. Tidal erosion on meso- to macro-tidal, rimmed carbonate shelves is enhanced during sea level rise and fall when a tidal, hydraulic pressure gradient is established between the shelf-lagoon and the adjacent ocean basin. Tidal flows attain a maximum, and channel incision is greatest, when a large hydraulic pressure gradient coincides with small channel cross sections. Our tidal-incision model may explain the observation of other workers, that sediment is exported from the Great Barrier Reef shelf to the adjacent ocean basins during intermediate (rather than last glacial maximum) low-stand, sea level positions. The model may apply to other rimmed shelves, both modern and ancient.