Magnetohydrodynamic thermal rotating shallow water systems

Tasmania hangs from the map of Australia like a drop in freefall from the substance of the mainland. Often the whole state is mislaid from Australian maps and logos (Reddit). Tasmania has, at least since federation, been considered peripheral—a region seen as isolated, a ‘problem’ economically, politically, and culturally. However, Tasmania not only cleaves to the ‘north island’ of Australia but is also subject to the gravitational pull of an even greater land mass—Antarctica. In this article, we upturn the political conventions of map-making that place both Antarctica and Tasmania in obscure positions at the base of the globe. We show how a changing global climate re-frames Antarctica and the Southern Ocean as key drivers of worldwide environmental shifts. The liquid and solid water between Tasmania and Antarctica is revealed not as a homogenous barrier, but as a dynamic and relational medium linking the Tasmanian archipelago with Antarctica. When Antarctica becomes the focus, the script is flipped: Tasmania is no longer on the edge, but core to a network of gateways into the southern land. The state’s capital of Hobart can from this perspective be understood as an "Antarctic city", central to the geopolitics, economy, and culture of the frozen continent (Salazar et al.). Viewed from the south, we argue, Tasmania is not a problem, but an opportunity for a form of ecological, cultural, economic, and political sustainability that opens up the southern continent to science, discovery, and imagination.

I tested the hypothesis that the quantity and quality of suspended and sediment organic matter in shallow coastal waters is affected by wind-induced resuspension at a smaller depth scale (<1 m) than usually assumed. Water and sediment surface (0 to 1 cm) samples were collected on a seasonal basis and analyzed for total suspended matter, organic fraction, and phytopigments at 12 shallow sites representing a depth gradient from 0.2 to 2.0 m along the western shore of Sicily. Water column concentrations of all measured variables decreased rapidly with increasing water column depth, and concentrations levelled off at about 1 m water column depth. The likelihood of sediment resuspension by wind for various combinations of water column depth and fetch length was modelled using the CERC (U.S. Army Corps of Engineers, Coastal Engineering Centre, Washington D.C. US) model for 10 years of local wind data. The simulations indicated that even light winds (2 m s−1) increased the likelihood of resuspension in the shallowest basin (0.2 m depth) with an effective fetch of 250 m. This study provides evidence that shallow water systems should not be investigated by considering the entire water column as a single homogenous layer. Investigations of shallow water ecosystems should consider 2 main layers with different ecological conditions and functions: a shallow surface turbulent layer from the surface to a depth of 1 m that is strongly affected by wind-driven physical forces and a deeper, below 1 m to the sediment surface, layer where wind-driven turbulence has less impact.

The shallow water magnetohydrodynamic system describes the thin layer evolution of the solar tachocline. It is obtained from the three dimensional incompressible magnetohydrodynamic system similarly as the classical shallow water system is obtained from the incompressible Navier---Stokes equations. The system is hyperbolic and has two additional waves with respect to the shallow water system, the Alfven waves. These are linearly degenerate, and thus do not generate dissipation. In the present work we introduce a 5-wave approximate Riemann solver for the shallow water magnetohydrodynamic system, that has the property to be non dissipative on Alfven waves. It is obtained by solving a relaxation system of Suliciu type, and is similar to HLLC type solvers. The solver is positive and entropy satisfying, ensuring its robustness. It has sharp wave speeds, and does not involve any iterative procedure.

Improved FVM for two-layer shallow-water models: Application to the Strait of Gibraltar

The paper focuses on the global analysis of FPSOs in shallow water, with an emphasis on vessel motions and offsets, mooring and riser design. The paper emphasizes the complex hydrodynamic interaction between the vessel and the environment, and the prediction of the vessel responses unique to shallow water. This done by using two examples of FPSOs moored in shallow water using an external turret mooring system and a tower yoke mooring system. Results are presented that illustrate the unique nature of both mooring systems and their sensitivity to variation in the environment and system damping. The design of compatible riser systems for both mooring systems is also presented and discussed. Introduction The Floating Production, Storage and Offloading (FPSO) system is the most mature of all floating production systems with over 100 installed and operating worldwide. It is also one of the most versatile floating production systems being installed in water depths from 20 meters to over 1800 meters, for a wide range of environmental conditions and can be easily extended to water depths even greater than 3000 meters. The majority of the FPSOs have been installed in water depths less than 200 meters of water. This is in contrast with other floating production systems that are focused on deepwater (greater than 500 meters). The market for shallow water FPSOs or Floating Storage and Offloading Systems (FSOs) is still very strong with a large number of facilities being designed and planned for water depths of 100 meters or less. From a global analysis perspective, shallow water FPSO/FSO systems can be much more challenging to analyze and design than ultra-deepwater systems. This is due to the:Environmental loading on the system in shallow water,"Hardening" nonlinear stiffness of the mooring system that at extreme offsets can result in large variability in loads,Low level of associated damping in the system, andDesign of an appropriate riser system for fluid transfer. The first objective of this paper is to provide the reader with the basic information to understand the analysis and design methodologies for a shallow water FPSO system focusing on the four items discussed above. Due to the focus on ultra-deepwater systems, the complexity and challenges of shallow water hydrodynamic design are not always well understood, and software tools and global analysis methodologies are being developed for these ultra-deepwater systems without much verification or application to shallow water systems. The second objective of the paper is to review two typical shallow water FPSO systems and the associated riser systems and relate their response to the discussion above. The examples are based on actual mooring system designs and help illustrate the challenges and solutions available for mooring FPSOs in shallow water. These examples are also important as they apply to future shallow water concepts, e.g. LNG offloading terminals. Typical Shallow Water FPSO Mooring Systems Shallow water FPSO systems have been developed using a number of vessel-mooring configurations depending on site specific and project requirements. Typical configurations include mooring to a CALM buoy using hawsers or hard yokes, spread-moored, internal or external turret catenary mooring systems, or mechanical mooring systems like tower yoke moorings.

Extended F-expansion method is proposed to seek exact solutions of the integrable nonlinear Kaup–Boussinesq shallow water system, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the extended F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously a number of periodic wave solutions expressed by various Jacobi elliptic functions for the integrable nonlinear Kaup-Boussinesq shallow water system. In the limiting cases, the solitary wave solutions are obtained as well.

The success of marine protected areas (MPAs) as a tool for conservation and fisheries management has been well documented. However, these results have typically been seen in shallow water systems and questions remain whether this management strategy could be successfully applied to deepwater ecosystems. Our objectives were to determine the efficacy of four deepwater MPAs called bottomfish restricted fishing areas (BRFAs), with various time spans of protection, monitored at depths between 90 and 310 m from 2007 to 2011 for six species of deepwater snapper and one grouper harvested in the Main Hawaiian Islands. Our results suggested that the duration of protection influenced reserve effects, particularly for target species. Mean fish length, and in some cases abundance, increased for one or more of the most economically important target species inside nearly all tested BRFAs. In addition, more mature fish were seen inside the BRFA with the longest duration of protection (~14 years); species richness increased outside this area while inside it remained the same. Here, we provide the first evidence that deepwater MPAs can have positive effects on deepwater species and that many protection effects were consistent with results found in shallow water ecosystems. While these findings are novel, additional data over greater temporal scales will be necessary to determine whether these trends will continue and if others will become important over time.

A parallel 2d finite volume scheme for solving systems of balance laws with nonconservative products: Application to shallow flows

In this work, several parallel implementations of a numerical model of pollutant transport on a shallow water system are presented. These parallel implementations are developed in two phases. First, the sequential code is rewritten to exploit the stream programming model. And second, the streamed code is targeted for current multi-threaded systems, in particular, multi-core CPUs and modern GPUs. The performance is evaluated on a multi-core CPU using OpenMP, and on a GPU using the streaming-oriented programming language Brook+, as well as the standard language for heterogeneous systems, OpenCL.

Time-iterative strategies for obtaining steady state solutions to the shallow water equations are developed using reduced-order, multistage Runge-Kutta (RK) methods. The shallow water system is formulated using a streamline upwind/Petrov-Galerkin technique that includes an additional operator for control of steep gradients. Numerical results are given to illustrate the performance of the RK methods.

We present a systematic and constructive methodology to devise various hybridized discontinuous Galerkin (HDG) methods for linearized shallow water equations. It is shown that using the Rankine--Hugoniot condition to solve the Riemann problem is a natural approach to deriving HDG methods. At the heart of our development is an upwind HDG framework obtained by hybridizing the upwind flux in the standard discontinuous Galerkin (DG) approach. Essentially, the HDG framework is a redesign of the standard DG approach to reducing the number of coupled unknowns. An upwind and three other HDG methods are constructed and analyzed for linearized shallow water systems. Rigorous stability and convergence analysis for both semidiscrete and fully discrete systems are provided. We extend the upwind HDG method to a family of penalty HDG schemes and rigorously analyze their well-posedness, stability, and convergence rates. Numerical results for the linear standing wave and the Kelvin wave for oceanic shallow water systems are presented to verify our theoretical findings.

Two-dimensional shallow water systems are frequently used in engineering practice to model environmental flows. The benefit of these systems are that, by integration over the water depth, a two-dimensional system is obtained which approximates the full three-dimensional problem. Nevertheless, for most applications the need to propagate waves over many wavelengths means that the numerical solution of these equations remains particularly challenging. The requirement for an accurate discretization in geometrically complex domains makes the use of spectral/hp elements attractive. However, to allow for the possibility of discontinuous solutions the most natural formulation of the system is within a discontinuous Galerkin (DG) framework. In this paper we consider the unstructured spectral/hp DG formulation of (i) weakly nonlinear dispersive Boussinesq equations and (ii) nonlinear shallow water equations (a subset of the Boussinesq equations). Discretization of the Boussinesq equations involves resolving third order mixed derivatives. To efficiently handle these high order terms a new scalar formulation based on the divergence of the momentum equations is presented. Numerical computations illustrate the exponential convergence with regard to expansion order and finally, we simulate solitary wave solutions.

Two-layer shallow water equations describe flows that consist of two layers of inviscid fluid of different (constant) densities flowing over bottom topography. Unlike the single-layer shallow water system, the two-layer one is only conditionally hyperbolic: the system loses its hyperbolicity because of the momentum exchange terms between the layers and as a result its solutions may develop instabilities. We study a three-layer approximation of the two-layer shallow water equations by introducing an intermediate layer of a small depth. We examine the hyperbolicity range of the three-layer model and demonstrate that while it still may lose hyperbolicity, the three-layer approximation may improve stability properties of the two-layer shallow water system.

The aim of this paper is to present a survey and a detailed numerical study on a remarkable Boussinesq system describing weakly nonlinear, long surface water waves. In the one‐dimensional case, this system can be viewed as a dispersive perturbation of the hyperbolic Saint‐Venant (shallow water) system. The asymptotic stability of the solitary waves is numerically established. Blow‐up of solutions for initial data not satisfying the noncavitation condition as well as the appearance of dispersive shock waves are studied.

Hamiltonian regularisation of the unidimensional barotropic Euler equations