MODELING ONE- AND TWO-DIMENSIONAL SHALLOW WATER FLOWS WITH DISCONTINUOUS GALERKIN METHOD

Numerical models for one- and two-dimensional shallow water flows are developed using discontinuous Galerkin method. Formulation and characteristics of shallow water equations are discussed. The well-balanced property and wetting/drying treatment are provided in the numerical models. The shock-capturing property is achieved by the approximate Riemann solvers in the schemes. Effects of different approximate Riemann solvers are also investigated. The Total Variation Diminishing property is achieved by adoption of slope limiters. Different slope limiters and their effects are compared through numerical tests. Numerical tests are performed to validate the models. These tests include dam-break flows, hydraulic jump and shocks in channels, and flows in natural rivers. Results show that the numerical models developed in present work are robust, accurate, and efficient for modeling shallow water flows. The one-dimensional model shows that the area based slope limiter provided the best solution in natural channels. The slope limiter based on the water depth or water surface elevation performs progressively poorer as the cross-section shape deviates from rectangular. In the approximate Riemann solver, the wave speeds are based on the original form of the equations, although the pressure force and the gravity force terms are combined for solving the shallow water equations with discontinuous Galerkin method. The combined term is discretized, in one- and two-dimensional models, such that the stationarity property is preserved. Different wetting and drying procedures are evaluated for the one- and two-dimensional models. Analytical, laboratory, and field tests are conducted to verify the accuracy of the wetting and drying procedures

A numerical method for junctions in networks of shallow-water channels

There is growing interest in developing mathematical models and appropriate numerical methods for problems involving networks formed by, essentially, one-dimensional (1D) domains joined by junctions. Examples include hyperbolic equations in networks of gas tubes, water channels and vessel networks for blood and lymph in the human circulatory system. A key point in designing numerical methods for such applications is the treatment of junctions, i.e. points at which two or more 1D domains converge and where the flow exhibits multidimensional behaviour. This paper focuses on the design of methods for networks of water channels. Our methods adopt the finite volume approach to make full use of the two-dimensional shallow water equations on the true physical domain, locally at junctions, while solving the usual one-dimensional shallow water equations away from the junctions. In addition to mass conservation, our methods enforce conservation of momentum at junctions; the latter seems to be the missing element in methods currently available. Apart from simplicity and robustness, the salient feature of the proposed methods is their ability to successfully deal with transcritical and supercritical flows at junctions, a property not enjoyed by existing published methodologies. Systematic assessment of the proposed methods for a variety of flow configurations is carried out. The methods are directly applicable to other systems, provided the multidimensional versions of the 1D equations are available

Morphology of rain water channelization in systematically varied model sandy soils

We visualize the formation of fingered flow in dry model sandy soils under different raining conditions using a quasi-2d experimental set-up, and systematically determine the impact of soil grain diameter and surface wetting property on water channelization phenomenon. The model sandy soils we use are random closely-packed glass beads with varied diameters and surface treatments. For hydrophilic sandy soils, our experiments show that rain water infiltrates into a shallow top layer of soil and creates a horizontal water wetting front that grows downward homogeneously until instabilities occur to form fingered flows. For hydrophobic sandy soils, in contrast, we observe that rain water ponds on the top of soil surface until the hydraulic pressure is strong enough to overcome the capillary repellency of soil and create narrow water channels that penetrate the soil packing. Varying the raindrop impinging speed has little influence on water channel formation. However, varying the rain rate causes significant changes in water infiltration depth, water channel width, and water channel separation. At a fixed raining condition, we combine the effects of grain diameter and surface hydrophobicity into a single parameter and determine its influence on water infiltration depth, water channel width, and water channel separation. We also demonstrate the efficiency of several soil water improvement methods that relate to rain water channelization phenomenon, including pre-wetting sandy soils at different level before rainfall, modifying soil surface flatness, and applying superabsorbent hydrogel particles as soil modifiers

Mangarara Formation: exhumed remnants of a middle Miocene, temperate carbonate, submarine channel-fan system on the eastern margin of Taranaki Basin, New Zealand

The middle Miocene Mangarara Formation is a thin (1–60 m), laterally discontinuous unit of moderately to highly calcareous (40–90%) facies of sandy to pure limestone, bioclastic sandstone, and conglomerate that crops out in a few valleys in North Taranaki across the transition from King Country Basin into offshore Taranaki Basin. The unit occurs within hemipelagic (slope) mudstone of Manganui Formation, is stratigraphically associated with redeposited sandstone of Moki Formation, and is overlain by redeposited volcaniclastic sandstone of Mohakatino Formation. The calcareous facies of the Mangarara Formation are interpreted to be mainly mass-emplaced deposits having channelised and sheet-like geometries, sedimentary structures supportive of redeposition, mixed environment fossil associations, and stratigraphic enclosure within bathyal mudrocks and flysch. The carbonate component of the deposits consists mainly of bivalves, larger benthic foraminifers (especially Amphistegina), coralline red algae including rhodoliths (Lithothamnion and Mesophyllum), and bryozoans, a warm-temperate, shallow marine skeletal association. While sediment derivation was partly from an eastern contemporary shelf, the bulk of the skeletal carbonate is inferred to have been sourced from shoal carbonate factories around and upon isolated basement highs (Patea-Tongaporutu High) to the south. The Mangarara sediments were redeposited within slope gullies and broad open submarine channels and lobes in the vicinity of the channel-lobe transition zone of a submarine fan system. Different phases of sediment transport and deposition (lateral-accretion and aggradation stages) are identified in the channel infilling. Dual fan systems likely co-existed, one dominating and predominantly siliciclastic in nature (Moki Formation), and the other infrequent and involving the temperate calcareous deposits of Mangarara Formation. The Mangarara Formation is an outcrop analogue for middle Miocene-age carbonate slope-fan deposits elsewhere in subsurface Taranaki Basin, New Zealand

Erosion and deposition in interplain channels of the Maury channel system

Large turbidity currents originating on the insular margin of southern lceland have flowed clown a 2 500 km-long pathway comprising rise valleys, unchanneled plains and segments of erosional and depositional deep-sea channels that are collectively called the Maury Channel system. Two steep interplain reaches of the channel have been eut up to 100 m through volcanogenic turbidites of probable La te Pleistocene age. Near-bottom observations with side-scan sonars and profllers across the upper channels (at 59°24\u27N, 18°50\u27W, 2 750 m depth) and at the lower interplain channel (around 56°23\u27N, 24°25\u27W, 3 340 m depth) defmed their structure and morphology. The upper channels, and a tributary to the lower channel, start as broad, shallow depressions that deepen and narrow downstream. The lower channel bas a pattern of anastomosing branches that probably evolved by head ward extension of low-angle tribu taries to the original sinuous channel, and its branches are at different stages of development. Several hundred bottom photographs show well-indurated rocks on channel walls and floors, with such flysch-like characteristics as cyclic graded bedding, clastic dikes, and syndepositional deformation. The lower-channel branches have been eut by turbidity currents with speeds of 5- 12 rn/sec., and combined discharges exceeding 1 x 106 m3 /sec. Bedrock erosion in and around the channels bas proceeded by intense corrasion and fluid stressing, and is marked by such small-scale effects as rock polishing, fluting, pot-holing and ledge recession. Rockfalls have caused retreat of steep channel walls, and conglomerate or pcbbly mudstone deposits suggest that debris flows have been locally active. Sorne coarse debris delivered by these processes and clay halls torn from semi-lithifled outcrops remain in the channels, but the channel f1ll is generally thin, with a patch y veneer of pelagie mud that bas accumulated since the last major turbidity current event. The surfaces of the unconsolidated s~diment have been smoothed and lineated, or moulded into seo ur moats and occasional fields of ripples, by thermohaline currents

Energy extraction from shallow tidal flows

Over the past decade within the renewable energy sector a strong research and development focus has resulted in the growth of an embryonic tidal stream energy industry. Previous assessments of the tidal stream resource appear to have neglected shallow tidal flows. This resource located in water depths of 10-30m is significant because it is generally more accessible for energy extraction than deeper offshore tidal sites and hence a good location for first generation tidal stream arrays or fences. The close proximity to shore may lead to improvements in construction feasibility and economic prospects. The objective of this project is to investigate several aspects concerning the exploitation of shallow tidal flows for energy extraction. Fundamental to this project is the importance of developing research alongside and in conjunction with industrial shallow water prototype projects. The key objectives are: (1) The development and understanding of the use of artificial flow constraint structures in the form of specifically-shaped foundations (herein described as “rampfoundations”) that constrain the flow leading to an increase in the magnitude and quality of power from marine current energy convertors (MCEC) operating in shallow tidal flows. (2) The investigation of seabed and free-surface proximity effects on the downstream wake structure of a MCEC. (3) Commercial shallow water device optimisation; utilising project results to aid with the design and development of full-scale commercial demonstrators.Through theoretical and scaled experimental modelling, and commercial collaboration the project has concluded ramp foundations could be utilised to locally increase tidal flow velocities and increase MCEC output across a tidal cycle in shallow flows. Predicted power benefits are in the region of 5-22% depending on lateral and vertical ramp channel blockage ratios. The ramp width or overall array width must therefore be tuned to the channel width to maximise power benefits. Rampfoundations will thus only be technically viable in relatively narrow channels or ideally in MCEC arrays or tidal fences. Results have shown that the downstream wake length is dependent on and varies with the vertical flow constraint and it is critical that the downstream array spacing of MCECs are tuned to the local flow depth. An optimum device height to flow depth ratio to minimise wake length has been identified. It is hoped that this ramp-foundation concept and the relationship between boundary proximity and wake length will continue to help with the development of a niche shallow tidal energy marke

A high resolution scheme for flows in open channels with arbitrary cross-section

The aim of this paper is to present a numerical scheme to simulate unsteady, one dimensional flows in open channels with arbitrary cross-section. This scheme is fully conservative of volume and momentum and preserves the non-negativity of the water depth. The finite difference method derived is semi-implicit in time and based on a space staggered grid. A high resolution technique, the flux limiter method, is implemented to control the accuracy of the proposed scheme. Our purpose is to achieve the precision and the stability of the method with respect to the regularity of the data. A few computational examples on classical test cases are given to illustrate the properties of the present method in terms of stability, accuracy and efficiency