Multinomial solutions of the beach equation

Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.

Recognising the necessity for Indo-Pacific seagrass conservation.

Seagrass meadows are declining globally at an unprecedented rate, yet these valuable ecosystem service providers remain marginalized within many conservation agendas. In the Indo-Pacific, this is principally because marine conservation priorities do not recognize the economic and ecological value of the goods and services that seagrasses provide. Dependency on coastal marine resources in the Indo-Pacific for daily protein needs is high relative to other regions and has been found in some places to be up to 100%. Habitat loss therefore may have negative consequences for food security in the region. Whether seagrass resources comprise an important contribution to this dependency remains largely untested. Here, we assemble information sources from throughout the Indo-Pacific region that discuss shallow water fisheries, and examine the role of seagrass meadows in supporting production, both directly, and indirectly through process of habitat connectivity (e.g., nursery function and foraging areas). We find information to support the premise that seagrass meadows are important for fisheries production. They are important fishery areas, and they support the productivity and biodiversity of coral reefs. We argue the value of a different paradigm to the current consensus on marine conservation priorities within the Indo-Pacific that places seagrass conservation as a priority.

Multinomial solutions of the beach equation

Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.

Coastal environmental gradients – Key to reproduction habitat mapping of freshwater fish in the Baltic Sea

Habitat requirements of fish are most strict during the early life stages, and the quality and quantity of reproduction habitats lays the basis for fish production. A considerable number of fish species in the northern Baltic Sea reproduce in the shallow coastal areas, which are also the most heavily exploited parts of the brackish marine area. However, the coastal fish reproduction habitats in the northern Baltic Sea are poorly known. The studies presented in this thesis focused on the influence of environmental conditions on the distribution of coastal reproduction habitats of freshwater fish. They were conducted in vegetated littoral zone along an exposure and salinity gradient extending from the innermost bays to the outer archipelago on the south-western and southern coasts of Finland, in the northern Baltic Sea. Special emphasis was placed on reed-covered Phragmites australis shores, which form a dominant vegetation type in several coastal archipelago areas. The main aims of this research were to (1) develop and test new survey and mapping methods, (2) investigate the environmental requirements that govern the reproduction of freshwater fish in the coastal area and (3) survey, map and model the distribution of the reproduction habitats of pike (Esox lucius) and roach (Rutilus rutilus). The white plate and scoop method with a standardized sampling time and effort was demonstrated to be a functional method for sampling the early life stages of fish in dense vegetation and shallow water. Reed-covered shores were shown to form especially important reproduction habitats for several freshwater fish species, such as pike, roach, other cyprinids and burbot, in the northern Baltic Sea. The reproduction habitats of pike were limited to sheltered reed- and moss-covered shores of the inner and middle archipelago, where suitable zooplankton prey were available and the influence of the open sea was low. The reproduction habitats of roach were even more limited and roach reproduction was successful only in the very sheltered reed-covered shores of the innermost bay areas, where salinity remained low (< 4‰) during the spawning season due to freshwater inflow. After identifying the critical factors restricting the reproduction of pike and roach, the spatial distribution of their reproduction habitats was successfully mapped and modelled along the environmental gradients using only a few environmental predictor variables. Reproduction habitat maps are a valuable tool promoting the sustainable use and management of exploited coastal areas and helping to maintain the sustainability of fish populations. However, the large environmental gradients and the extensiveness of the archipelago zone in the northern Baltic Sea demand an especially high spatial resolution of the coastal predictor variables. Therefore, the current lack of accurate large-scale, high-resolution spatial data gathered at exactly the right time is a considerable limitation for predictive modelling of shallow coastal waters.

Benthic-pelagic coupling in the northern Baltic Sea: importance of bioturbation and benthic predation

Benthic-pelagic coupling describes processes that operate across and between the seafloor and open-water ecosystems. In soft-sediment communities, bioturbation by sediment-dwelling and epibenthic organisms may strongly shape habitat characteristics and influence processes, e.g. biogeochemical cycling, which supplies bioavailable nutrients to pelagic primary producers. In addition, benthic fauna may mediate benthic-pelagic coupling by affecting the survival and hatching of zooplankton dormant eggs in the sediment. In the shallow waters and seasonally fluctuating environment of the Baltic Sea, emergence from the seafloor essentially contributes to the dynamics of zooplankton pelagic populations. In this thesis, I examine how benthic organisms with different functional traits affect the link between the benthic and pelagic systems in the northern Baltic Sea. By means of experimental laboratory studies, the effects of sediment-dwelling (Monoporeia affinis, Macoma balthica and Marenzelleria spp.) and nectobenthic (Mysis spp.) taxa on the survival and hatching of zooplankton benthic eggs and on benthic nutrient fluxes and sediment structure were investigated. In the predation studies, the nectobenthic mysids Mysis spp. preyed upon benthic eggs of the cladoceran Bosmina longispina maritima (syn. B. coregoni maritima), both in pelagic and benthic environments. Of the sediment-dwelling species, the amphipod M. affinis and the bivalve M. balthica reduced the number of cladoceran eggs in the sediment, whereas the polychaetes Marenzelleria spp. had no effects on cladoceran eggs. Both M. balthica and M. affinis also increased the mortality rates of benthic eggs of copepods and rotifers. It was estimated that zooplankton eggs provide an additional carbon source for food-limited benthic communities. The results indicate that predation pressure on zooplankton benthic eggs may be strong, but varies widely depending on the season and the functional characteristics of the macrofauna. Macoma balthica buried cladoceran eggs and a fluorescent tracer from the sediment surface to a depth of 3 4 cm, indicating efficient sediment mixing. In contrast, the other taxa had fewer effects on particle distributions. In addition to organic matter mineralization, particle mixing is crucial to the success of benthic recruitment of zooplankton, since only eggs close to the sediment surface may hatch. Macoma balthica and M. affinis altered the patterns of zooplankton emergence from the sediment. In general, the highest emergence rates were observed in the absence of macroscopic fauna, and M. balthica exerted a stronger suppressive effect than M. affinis. Moreover, copepods were less severely affected than cladocerans, while only one species (Temora longicornis) clearly benefited from the presence of the macrofauna. These differences probably result from species-specific differences in the resistance of eggs to disturbances. The results show that benthic fauna may considerably alter the patterns of zooplankton emergence from the seafloor, thereby shaping zooplankton pelagic populations. The semi-motile M. balthica and Marenzelleria spp. increased the fluxes of phosphate and ammonium from the sediment to the water, whereas the motile M. affinis and Mysis mixta had a contrasting effect. In the eutrophied Baltic Sea, efficient internal cycling of bioavailable nutrients forms a strong feedback inhibiting the recovery of the ecosystem. Based on the results, a change in species dominance from the two motile taxa, susceptible to oxygen deficiency, to the more tolerant semi-motile taxa provides additional feedback, strengthening internal nutrient cycling and accelerating eutrophication, with deteriorating near-bottom oxygen conditions and changes in the benthic communities. In shallow-water ecosystems, benthic nutrient regeneration plays a key role in determining the overall productivity of the ecosystem. In addition, the results of this study show that the communities in the benthos may essentially contribute to the structure of those in the plankton.

Molecular characterization of sediment bacterial communities affected by fish farming

Fish farming introduces nutrients, microbes and a wide variety of chemicals such as heavy metals, antifoulants and antibiotics to the surrounding environment. Introduction of antibiotics has been linked with the increased incidence of antibiotic resistant pathogenic bacteria in the farm vicinities. In this thesis molecular methods such as quantitative PCR and DNA sequencing were applied to analyze bacterial communities in sediments from fish farms and pristine locations. Altogether four farms and four pristine sites were sampled in the Baltic Sea. Two farm and two pristine locations were sampled over a surveillance period of four years. Furthermore, a new methodology was developed as a part of the study that permits amplifying single microbial genomes and capturing them according to any genetic traits, including antibiotic resistance genes. The study revealed that several resistance genes for tetracycline were found at the sediment underneath the aquaculture farms. The copy number of these genes remained elevated even at a farm that had not used any antibiotics since year 2000, six years before this study started. Similarly, an increase in the amount of mercury resistance gene merA was observed at the aquaculture sediment. The persistence of the resistance genes in absence of any selection pressure from antibiotics or heavy metals suggests that the genes may be introduced to the sediment by the farming process. This is also supported by the diversity pattern of the merA gene between farm and pristine sediments. The bacterial community-level changes in response to fish farming were very complex and no single phylogenetic groups were found that would be typical to fish farm sediments. However, the community structures had some correlation with the exposure to fish farming. Our studies suggest that the established approaches to deal with antibiotic resistance at the aquaculture, such as antibiotic cycling, are fundamentally flawed because they cannot prevent the introduction of the resistance genes and resistant bacteria to the farm area by the farming process. Further studies are required to study the entire fish farming process to identify the sources of the resistance genes and the resistant bacteria. The results also suggest that in order to prevent major microbiological changes in the surrounding aquatic environment, the farms should not be founded in shallow water where currents do not transport sedimenting matter from the farms. Finally, the technique to amplify and select microbial genomes will potentially have a considerable impact in microbial ecology and genomics.

Late Pleistocene and Holocene environmental evolution of the Murchisonfjorden area, Nordaustlandet, Svalbard

The purpose of this study was to establish the palaeoenvironmental conditions during the late Quaternary in Murchisonfjorden, Nordaustlandet, based on foraminiferal assemblage compositions, and to determine the onset and termination of the Weichselian glaciations. The foraminiferal assemblage compositions were studied in marine sediments from three different archives, from sections next to the present shoreline in the Bay of Isvika, from a core in the Bay of Isvika and from a core from Lake Einstaken. OSL and AMS 14C age determinations were performed on samples from the three archives, and the results show deposition of marine sediments during ice-free periods of the Early Weichselian, the Middle Weichselian and the Late Weichselian, as well as during the Holocene in the investigated area. Marine sediments from the Early and Middle Weichselian were sampled from isostatically uplifted sections along the present shoreline.Sediments from the transition from the Late Weichselian to early Holocene time intervals were found in the bottom of the core from Lake Einstaken. Holocene sediments were investigated in the sections and in the core from the Bay of Isvika. The marine sediments from the sections are comprised of five benthic foraminiferal assemblages. The Early Weichselian is represented by two foraminiferal assemblages, the Middle Weichselian, the early and the late Holocene each by one. All five foraminiferal assemblages were deposited in glacier-distal shallow-water environments, which had a connection to the open ocean. Changes in the composition of the assemblages can be ascribed to differences in the bottom-water currents and changes in the salinity. The Middle Weichselian assemblage is of special importance, because it is the first foraminiferal assemblage to be described from this time interval from Svalbard. Four benthic foraminiferal assemblages were deposited shortly before the marine to lacustrine transition at the boundary between the Late Weichselian and Holocene in Lake Einstaken. The foraminiferal assemblages show a change from a high-arctic, normal marine shallow-water environment to an even shallower environment with highly fluctuating salinity. The analyses of the core from 100 m water depth in the Bay of Isvika resulted in the determination of four foraminiferal assemblages. These indicated changes from a glacier-proximal environment during deglaciation, to a more glacier-distal environment during the Early Holocene. This was followed by a period with a marked change to a considerably cooler environment and finally to a closed fjord environment in the middle and late Holocene times. Additional sedimentological analyses of the marine and glacially derived sediments from the uplifted sections, as well as observations of multiple striae on the bedrock, observations of deeply weathered bedrock and findings of tills interlayered with marine sediments complete the investigations in the study area. They indicate weak glacial erosion in the study area. It can be concluded that marine deposition occurred in the investigated area during three time intervals in the Weichselian and during most of the Holocene. The foraminiferal assemblages in the Holocene are characterized by a transition from glacier-proximal to glacier-distal faunas. The palaeogeographical change from an open fjord to a closed fjord environment is a result of the isostatic uplift of the area after the LGM and is clearly reflected in the foraminiferal assemblages. Another influencing factor on the foraminiferal assemblage composition are changes in the inflow of warmer Atlantic waters to the study area.

On subspace method for source localization

A method of source localization in shallow water, based on subspace concept, is described. It is shown that a vector representing the source in the image space spanned by the direction vectors of the source images is orthogonal to the noise eigenspace of the covariance matrix. Computer simulation has shown that a horizontal array of eight sensors can accurately localize one or more uncorrelated sources in shallow water dominated by multipath propagation.

Stability of developing film flow down an inclined surface

Film flows on inclined surfaces are often assumed to be of constant thickness, which ensures that the velocity profile is half-Poiseuille. It is shown here that by shallow water theory, only flows in a portion of Reynolds number-Froude number (Re-Fr) plane can asymptotically attain constant film thickness. In another portion on the plane, the constant thickness solution appears as an unstable fixed point, while in other regions the film thickness seems to asymptote to a positive slope. Our simulations of the Navier-Stokes equations confirm the predictions of shallow water theory at higher Froude numbers, but disagree with them at lower Froude numbers. We show that different regimes of film flow show completely different stability behaviour from that predicted earlier. Supercritical decelerating flows are shown to be always unstable, whereas accelerating flows become unstable below a certain Reynolds number for a given Froude number. Subcritical flows on the other hand are shown to be unstable above a certain Reynolds number. In some range of parameters, two solutions for the base flowexist, and the attached profile is found to be more stable. All flows except those with separation become more stable as they proceed downstream. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4758299]

Directional Diffusion Regulator (DDR) for some numerical solvers of hyperbolic conservation laws

A computational tool called ``Directional Diffusion Regulator (DDR)'' is proposed to bring forth real multidimensional physics into the upwind discretization in some numerical schemes of hyperbolic conservation laws. The direction based regulator when used with dimension splitting solvers, is set to moderate the excess multidimensional diffusion and hence cause genuine multidimensional upwinding like effect. The basic idea of this regulator driven method is to retain a full upwind scheme across local discontinuities, with the upwind bias decreasing smoothly to a minimum in the farthest direction. The discontinuous solutions are quantified as gradients and the regulator parameter across a typical finite volume interface or a finite difference interpolation point is formulated based on fractional local maximum gradient in any of the weak solution flow variables (say density, pressure, temperature, Mach number or even wave velocity etc.). DDR is applied to both the non-convective as well as whole unsplit dissipative flux terms of some numerical schemes, mainly of Local Lax-Friedrichs, to solve some benchmark problems describing inviscid compressible flow, shallow water dynamics and magneto-hydrodynamics. The first order solutions consistently improved depending on the extent of grid non-alignment to discontinuities, with the major influence due to regulation of non-convective diffusion. The application is also experimented on schemes such as Roe, Jameson-Schmidt-Turkel and some second order accurate methods. The consistent improvement in accuracy either at moderate or marked levels, for a variety of problems and with increasing grid size, reasonably indicate a scope for DDR as a regular tool to impart genuine multidimensional upwinding effect in a simpler framework. (C) 2012 Elsevier Inc. All rights reserved.

Interpreting the upper level structure of the Madden-Julian oscillation

The nonlinear response of a spherical shallow water model to an imposed heat source in the presence of realistic zonal mean zonal winds is investigated numerically. The solutions exhibit elongated, meridionally tilted ridges and troughs indicative of a poleward dispersion of wave activity. As the speed of the jets is increased, the equatorial Kelvin wave is unaffected but the global Rossby wave train coalesces to form a compact, amplified quadrupole structure that bears a striking resemblance to the observed upper level structure of the Madden-Julian oscillation. In the presence of strong subtropical westerly jets, the advection of planetary vorticity by the meridional flow and relative vorticity by the zonally averaged background flow conspire to create the distinctive quadrupole configuration of flanking Rossby waves.

Quasi-geostrophic dynamics in the presence of moisture gradients

The derivation of a quasi-geostrophic system from the rotating shallow-water equations on a midlatitude -plane coupled with moisture is presented. Condensation is prescribed to occur whenever the moisture at a point exceeds a prescribed saturation value. It is seen that a slow condensation time-scale is required to obtain a consistent set of equations at leading order. Further, since the advecting wind fields are geostrophic, changes in moisture (and hence precipitation) occur only via non-divergent mechanisms. Following observations, a saturation profile with gradients in the zonal and meridional directions is prescribed. A purely meridional gradient has the effect of slowing down the dry Rossby waves, through a reduction in the equivalent gradient' of the background potential vorticity. A large-scale unstable moist mode results on the inclusion of a zonal gradient by itself, or in conjunction with a meridional moisture gradient. For gradients that are are representative of the atmosphere, the most unstable moist mode propagates zonally in the direction of increasing moisture, matures over an intraseasonal time-scale and has small phase speed.

Rossby Vortex Simulation on a Paraboloidal Coordinate System Using the Lattice Boltzmann Method

In this paper, we apply our compressible lattice Boltzmann model to a rotating parabolic coordinate system to simulate Rossby vortices emerging in a layer of shallow water flowing zonally in a rotating paraboloidal vessel. By introducing a scaling factor, nonuniform curvilinear mesh can be mapped to a flat uniform mesh and then normal lattice Boltzmann method works. Since the mass per unit area on the two-dimensional (2D) surface varies with the thickness of the water layer, the 2D flow seems to be "compressible" and our compressible model is applied. Simulation solutions meet with the experimental observations qualitatively. Based on this research, quantitative solutions and many natural phenomena simulations in planetary atmospheres, oceans, and magnetized plasma, such as the famous Jovian Giant Red Spot, the Galactic Spiral-vortex, the Gulf Stream, and the Kuroshio Current, etc,, can be expected.

Non-Linear Wave-Induced Transient Response of Soil Around a Trenched Pipeline

Submarine pipelines are always trenched within a seabed for reducing wave loads and thereby enhancing their stability. Based on Biot’s poroelastic theory, a two-dimensional finite element model is developed to investigate non-linear wave-induced responses of soil around a trenched pipeline, which is verified with the flume test results by Sudhan et al. [Sudhan, C.M., Sundar, V., Rao, S.N., 2002. Wave induced forces around buried pipeline. Ocean Engineering, 29, 533–544] and Turcotte et al. [Turcotte, B.R., Liu, P.L.F., Kulhawy, F.H., 1984. Laboratory evaluation of wave tank parameters for wave-sediment interaction. Joseph H. Defree Hydraulic Laboratory Report 84-1, School of Civil and Environmental Engineering, Cornell University]. Non-linear wave-induced transient pore pressure around pipeline at various phases of wave loading is examined firstly. Unlike most previous investigations, in which only a single sediment layer and linear wave loading were concerned, in this study, the influences of the non-linearity of wave loading, the physical properties of backfill materials and the geometry profile of trenches on the excess pore pressures within the soil around pipeline, respectively, were explored, taking into account the in situ conditions of buried pipeline in the shallow ocean zones. Based on the parametric study, it is concluded that the shear modulus and permeability of backfill soils significantly affect the wave-induced excess pore pressures around trenched pipeline, and that the effect of wave non-linearity becomes more pronounced and comparable with that of trench depth, especially at high wave steepness in shallow water.

The interaction of two pairs of solitary waves in a two-fluid system

This paper deals with the interaction of solitary waves in a two-fluid system which consistsof two superimposed incompressible inviscid fluids with a free surface and a horizontal rigidbottom. Under the assumption of shallow water wave, we first derive the basic equationssuitable for the model considered, a generalized form of the Boussinesq equations, then usingthe PLK method and the reductive perturbation method, obtain the second-order approximatesolution for the head-on collision between two pairs of interface and surface solitary waves,and give their maximum amplitudes during the collision and the nonuniform phase shiftsafter the collision which lead to the distortion of the wave profiles.