Velocity potential formulations of highly accurate Boussinesq-type models     

Harry B. Bingham  Per A. Madsen  David R. Fuhrman 《Coastal Engineering》2009

The highly accurate Boussinesq-type equations of Madsen et al. (Madsen, P.A., Bingham, H.B., Schäffer, H.A., 2003. Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: Derivation and analysis. Proc. R. Soc. Lond. A 459, 1075–1104; Madsen, P.A., Fuhrman, D.R., Wang, B., 2006. A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry. Coast. Eng. 53, 487–504); Jamois et al. (Jamois, E., Fuhrman, D.R., Bingham, H.B., Molin, B., 2006. Wave-structure interactions and nonlinear wave processes on the weather side of reflective structures. Coast. Eng. 53, 929–945) are re-derived in a more general framework which establishes the correct relationship between the model in a velocity formulation and a velocity potential formulation. Although most work with this model has used the velocity formulation, the potential formulation is of interest because it reduces the computational effort by approximately a factor of two and facilitates a coupling to other potential flow solvers. A new shoaling enhancement operator is introduced to derive new models (in both formulations) with a velocity profile which is always consistent with the kinematic bottom boundary condition. The true behaviour of the velocity potential formulation with respect to linear shoaling is given for the first time, correcting errors made by Jamois et al. (Jamois, E., Fuhrman, D.R., Bingham, H.B., Molin, B., 2006. Wave-structure interactions and nonlinear wave processes on the weather side of reflective structures. Coast. Eng. 53, 929–945). An exact infinite series solution for the potential is obtained via a Taylor expansion about an arbitrary vertical position z = zˆ. For practical implementation however, the solution is expanded based on a slow variation of zˆ and terms are retained to first-order. With shoaling enhancement, the new models obtain a comparable accuracy in linear shoaling to the original velocity formulation. General consistency relations are also derived which are convenient for verifying that the differential operators satisfy a potential flow and/or conserve mass up to the order of truncation of the model. The performance of the new formulation is validated using computations of linear and nonlinear shoaling problems. The behaviour on a rapidly varying bathymetry is also checked using linear wave reflection from a shelf and Bragg scattering from an undulating bottom. Although the new models perform equally well for Bragg scattering they fail earlier than the existing model for reflection/transmission problems in very deep water.  相似文献   

Tsunami generation,propagation, and run-up with a high-order Boussinesq model   总被引：1，自引：0，他引：1  

David R. Fuhrman  Per A. Madsen 《Coastal Engineering》2009

In this work we extend a high-order Boussinesq-type (finite difference) model, capable of simulating waves out to wavenumber times depth kh < 25, to include a moving sea-bed, for the simulation of earthquake- and landslide-induced tsunamis. The extension is straight forward, requiring only an additional term within the kinematic bottom condition. As first test cases we simulate linear and nonlinear surface waves generated from both positive and negative impulsive bottom movements. The computed results compare well against earlier theoretical, numerical, and experimental values. Additionally, we show that the long-time (fully nonlinear) evolution of waves resulting from an upthrusted bottom can eventually result in true solitary waves, consistent with theoretical predictions. It is stressed, however, that the nonlinearity used far exceeds that typical of geophysical tsunamis in the open ocean. The Boussinesq-type model is then used to simulate numerous tsunami-type events generated from submerged landslides, in both one and two horizontal dimensions. The results again compare well against previous experiments and/or numerical simulations. The new extension compliments recently developed run-up capabilities within this approach, and as demonstrated, the model can therefore treat tsunami events from their initial generation, through their later propagation, and final run-up phases. The developed model is shown to maintain reasonable computational efficiency, and is therefore attractive for the simulation of such events, especially in cases where dispersion is important.  相似文献   

Honey, I cooled the cods: Modelling the effect of temperature on the structure of Boreal/Arctic fish ecosystems     

John G. Pope  Jannike Falk-Pedersen  Simon Jennings  Jake C. Rice  Henrik Gislason  Niels Daan   《Deep Sea Research Part II: Topical Studies in Oceanography》2009,56(21-22):2097

Historically colder regions of the North Atlantic had fisheries dominated by only a few fish species; principally cod and capelin. Possible population dynamic mechanisms that lead to such dominance are investigated by considering how a charmingly simple published multispecies model of the North Sea would react if the system operated at a lower temperature. The existing model equations were modified to describe temperature effects on growth, fecundity and recruitment and the model was rerun based on typical temperatures for the North Sea and a colder system. The results suggest that total fish biomass in the colder system increases but the community is more vulnerable to a given rate of fishing mortality. In the colder system, within species density dependence is reduced but relative predation rates are higher. Consequently, intermediate-sized species are vulnerable to relatively high levels of predation throughout their life history and tend to be excluded, leading to a system dominated by small and large species. The model helps to explain how temperature may govern coexistence and competitive exclusion in fish communities and accounts for the observed dominance of small and large species in Boreal/Arctic ecosystems.  相似文献   

Simulation of nonlinear wave run-up with a high-order Boussinesq model   总被引：2，自引：0，他引：2  

David R. Fuhrman  Per A. Madsen 《Coastal Engineering》2008

This paper considers the numerical simulation of nonlinear wave run-up within a highly accurate Boussinesq-type model. Moving wet–dry boundary algorithms based on so-called extrapolating boundary techniques are utilized, and a new variant of this approach is proposed in two horizontal dimensions. As validation, computed results involving the nonlinear run-up of periodic as well as transient waves on a sloping beach are considered in a single horizontal dimension, demonstrating excellent agreement with analytical solutions for both the free surface and horizontal velocity. In two horizontal dimensions cases involving long wave resonance in a parabolic basin, solitary wave evolution in a triangular channel, and solitary wave run-up on a circular conical island are considered. In each case the computed results compare well against available analytical solutions or experimental measurements. The ability to accurately simulate a moving wet–dry boundary is of considerable practical importance within coastal engineering, and the extension described in this work significantly improves the nearshore versatility of the present high-order Boussinesq approach.  相似文献   

A tilted Bianchi type-V perfect fluid solution for stiff matter     

Grant Baillie  Mark S. Madsen 《Astrophysics and Space Science》1985,115(2):413-415

We present a solution to the Einstein field equations for a massless scalar field in a Bianchi type-V spacetime, which can be interpreted as a solution for a perfect fluid with the equation of state of stiff matter. This solution complements a solution previously given by us for an anisotropic fluid.  相似文献   

Nitrogen geochemistry as a tracer of fluid flow in a hydrothermal vent complex in the Karoo Basin, South Africa     

Henrik Svensen  Gray Bebout  Long Li  Luc Chevallier 《Geochimica et cosmochimica acta》2008,72(20):4929-4947

We have investigated the N geochemistry of minerals and rocks from contact metamorphic aureoles and hydrothermal vent complexes (HVC) in the Karoo Basin in South Africa. The HVC formed during phreatic eruptions associated with rapid devolatilization and pressure build-up in contact aureoles around early Jurassic sill intrusions. By combining outcrop data from a HVC and core data from contact aureoles, we investigate the relationship between light element release during metamorphism and vertical fluid migration. Sandstone and breccia from the HVC contain early-diagenetic ammonium -bearing feldspar (buddingtonite) and illite. Ammonium occupies up to 95% of the A site in feldspar, corresponding to concentrations up to 5.2 wt% N. Bulk-rock N isotope data for rocks from inside and outside the hydrothermal vent complex fall into two distinct groups. Background samples have δ¹⁵N_air between +1.5‰ and +4.9‰, whereas minerals from the vent complex have δ¹⁵N in the range +7.5 to +10.6‰. The N geochemistry of contact metamorphic shale from the lower stratigraphic units of the Karoo Basin shows that the vitrinite reflectance and δ¹⁵N values are positively correlated. Shale with reflectivity values >4%Ro are enriched in ¹⁵N, with δ¹⁵N values between +6‰ and +14‰, implying the release of isotopically light N into metamorphic fluids (probably as N₂). We suggest that the relatively high δ¹⁵N values of the early-diagenetic buddingtonite in the HVC reflect exchange of buddingtonite with N-bearing fluids ascending from greater depth after their release during contact metamorphism and dehydration. We present a qualitative model whereby hydrothermal vent complexes represent fluid flow structures after their formation, focusing N-bearing metamorphic fluids sourced in deeper levels of the basin. The release of organic N from sediments at depth in volcanic basins could play a role in the geochemical cycle of N, becoming particularly important during periods of intense volcanic activity.  相似文献   

Thermodynamic and kinetic control on anaerobic oxidation of methane in marine sediments     

Nina J. Knab  Andrew W. Dale  Henrik Fossing 《Geochimica et cosmochimica acta》2008,72(15):3746-3757

The free energy yield of microbial respiration reactions in anaerobic marine sediments must be sufficient to be conserved as biologically usable energy in the form of ATP. Anaerobic oxidation of methane (AOM) coupled to sulfate reduction (SRR) has a very low standard free energy yield of ΔG^° = −33 kJ mol⁻¹, but the in situ energy yield strongly depends on the concentrations of substrates and products in the pore water of the sediment. In this work ΔG for the AOM-SRR process was calculated from the pore water concentrations of methane, sulfate, sulfide, and dissolved inorganic carbon (DIC) in sediment cores from different sites of the European continental margin in order to determine the influence of thermodynamic regulation on the activity and distribution of microorganisms mediating AOM-SRR. In the zone of methane and sulfate coexistence, the methane-sulfate transition zone (SMTZ), the energy yield was rarely less than −20 kJ mol⁻¹ and was mostly rather constant throughout this zone. The kinetic drive was highest at the lower part of the SMTZ, matching the occurrence of maximum AOM rates. The results show that the location of maximum AOM rates is determined by a combination of thermodynamic and kinetic drive, whereas the rate activity mainly depends on kinetic regulation.  相似文献   

Palaeohydrogeology: A methodology based on fracture mineral studies     

Eva-Lena Tullborg  Henrik Drake  Björn Sandström 《Applied Geochemistry》2008

Two sites on the east coast of Sweden (Forsmark and Laxemar/Simpevarp) are currently being investigated as potential geologic hosts for a deep repository isolating high-level nuclear waste. In this paper, a methodology for fracture mineral studies is suggested with focus on the variation in depth of the fresh/saline water interface and location of the redox front in the bedrock. The most commonly precipitated fracture minerals in crystalline rocks are chlorite, calcite, quartz, K-feldspar, Ca–Al-silicates like epidote, prehnite and laumontite, sulphides and Fe-oxides. Of these, calcite is the mineral best suited for palaeohydrological studies since it precipitates during a wide range of conditions including low-temperature conditions during the Pleistocene and Holocene epochs. Sulphides and Fe-oxides/hydroxides provide information on the position of the redox front. In order to carry out palaeohydrological studies, a number of prerequisites are required such as; high quality drill core material, geological knowledge of the sequence of fracture mineralizations; the post-glacial (Holocene) evolution in the area; high quality groundwater chemistry, including stable isotopes; and a conceptual model of the hydrogeochemistry that is to be tested. The choice of methods used here is based on the fact that both the Forsmark and Laxemar/Simpevarp sites are situated in Palaeoproterozoic crystalline rocks with reactivation of fractures over at least 1.5 Ga, and they have been exposed to glaciations/deglaciations and transgressions/regressions of the Baltic Sea during the Quaternary. This has resulted in a palaeohydrology with a range of groundwaters of quite different chemistry and stable isotopic composition. The suggested scheme for solving the variation in depth of the fresh/saline water interface focuses on fracture calcite. It includes a step-by-step procedure with;

(1)

Initial δ¹⁸O and δ¹³C, analyses and complementary petrographic studies of thin sections and crystal morphology followed by  相似文献   

Provenance of the Lower Triassic Bunter Sandstone Formation: implications for distribution and architecture of aeolian vs. fluvial reservoirs in the North German Basin          下载免费PDF全文

Mette Olivarius  Rikke Weibel  Henrik Friis  Lars O. Boldreel  Nynke Keulen  Tonny B. Thomsen 《Basin Research》2017,29(Z1):113-130

Zircon U–Pb geochronometry, heavy mineral analyses and conventional seismic reflection data were used to interpret the provenance of the Lower Triassic Bunter Sandstone Formation. The succession was sampled in five Danish wells in the northern part of the North German Basin. The results show that sediment supply was mainly derived from the Ringkøbing‐Fyn High situated north of the basin and from the Variscan belt located south of the basin. Seismic reflection data document that the Ringkøbing‐Fyn High was a local barrier for sediment transport during the Early Triassic. Hence, the Fennoscandian Shield did not supply much sediment to the basin as opposed to what was previously believed. Sediment from the Variscan belt was transported by wind activity across the North German Basin when it was dried out during deposition of the aeolian part of the Volpriehausen Member (lower Bunter Sandstone). Fluvial sand was supplied from the Ringkøbing‐Fyn High to the basin during precipitation events which occurred most frequently when the Solling Member was deposited (upper Bunter Sandstone). Late Neoproterozoic to Carboniferous zircon ages predominate in the Volpriehausen Member where the dominant age population with a peak age of 337 Ma corresponds to the culmination of Variscan high‐grade metamorphism, whereas a secondary age population with a peak at 300 Ma matches the timing of volcanism and magmatism at the Carboniferous/Permian boundary in the northern Variscan belt. Parts of the basement in the Ringkøbing‐Fyn High were outcropping during the Early Triassic and zircon ages similar to this Mesoproterozoic basement are present in the Bunter Sandstone. The heavy mineral assemblage of the Solling Member is uniform and has a high garnet content compared to the contemporaneous sediments in the Norwegian‐Danish Basin and in the southern part of the North German Basin. This finding confirms that a local source in the Ringkøbing‐Fyn High supplied most of the fluvial sediment in the northern part of the North German Basin. The northernmost part of the Bunter Sandstone is situated on a platform area that is separated from the basin area by a broad WNW–ESE‐oriented fault zone. The most promising reservoir in the basin area is the aeolian Volpriehausen Member since the sandstone has a wide lateral distribution and a constant thickness. The alluvial to ephemeral fluvial Solling Member may be a good reservoir in the platform area and marginal basin area, but the complex sand‐body architecture makes it difficult to predict the reservoir quality.  相似文献   

Thermal stability of extended clusters in dravite: a combined EMP,SREF and FTIR study     

Ferdinando Bosi  Henrik Skogby  Tonči Balić-Žunić 《Physics and Chemistry of Minerals》2016,43(6):395-407

A dravite from Yemen of near end-member composition was treated in air and hydrogen atmospheres at 600–900 °C to reveal changes in Mg and Al order over the octahedrally coordinated Y and Z sites, and to explore related changes in the characteristic vibrational bands in the principal (OH)-stretching frequency. Relevant information was obtained using electron microprobe analysis (EMPA), structural refinement (SREF) and polarized infrared (IR) single-crystal spectroscopy. Overall, the EMPA, SREF and IR data show that only minor changes occur during thermal treatment up to at least 800 °C, including variations in structural parameters, Mg–Al order–disorder and (OH)-stretching bands, indicating limited hydrogen loss. Untreated and treated dravite samples have very similar long-range and short-range atomic structures, which may be related to the occurrence of stable Al–Mg extended clusters around the O1 (=W) and O3 (=V) sites: ^W(F)–^Y(MgMgMg)–^V(OH)₃–^Z[AlAlAlAlAl(Al,Mg)]; ^W(OH)–^Y(MgMgAl)–^V(OH)₃–^Z[AlAlAlAlAl(Al,Mg)]; ^W(O^2–)–^Y(AlAlAl)–^V(OH)₃–^Z[AlAlAlAlAl(Al,Mg)]. These extended clusters remain stable to temperatures close to the observed start of decomposition (~900 °C).  相似文献