Depth-averaged Shallow Water Model Research Articles

Tidal turbine array modelling using goal-oriented mesh adaptation

To examine the accuracy and sensitivity of tidal array performance assessment by numerical techniques applying goal-oriented mesh adaptation. The goal-oriented framework is designed to give rise to adaptive meshes upon which a given diagnostic quantity of interest (QoI) can be accurately captured, whilst maintaining a low overall computational cost. We seek to improve the accuracy of the discontinuous Galerkin method applied to a depth-averaged shallow water model of a tidal energy farm, where turbines are represented using a drag parametrisation and the energy output is specified as the QoI. Two goal-oriented adaptation strategies are considered, which give rise to meshes with isotropic and anisotropic elements. We present both fixed mesh and goal-oriented adaptive mesh simulations for an established test case involving an idealised tidal turbine array positioned in a channel. With both the fixed meshes and the goal-oriented methodologies, we reproduce results from the literature which demonstrate how a staggered array configuration extracts more energy than an aligned array. We also make detailed qualitative and quantitative comparisons between the fixed mesh and adaptive outputs. The proposed goal-oriented mesh adaptation strategies are validated for the purposes of tidal energy resource assessment. Using only a tenth of the number of degrees of freedom as a high-resolution fixed mesh benchmark and lower overall runtime, they are shown to enable energy output differences smaller than 2% for a tidal array test case with aligned rows of turbines and less than 10% for a staggered array configuration.

Modeling the impacts of climate extremes and multiple water uses to support water management in the Icó-Mandantes Bay, Northeast Brazil

Abstract The hydropower production, water supply and aquaculture services of the Itaparica Reservoir are of immense importance for the Brazilian Northeast. Uncontrolled water resources consumption (e.g. irrigation, water supply), climate and land use change effects deteriorated the water quantity and quality in the reservoir, leading to socio-economic and environmental problems. In this work, a depth-averaged shallow water model was set up for the Icó-Mandantes Bay, one major branch of the reservoir, using the open TELEMAC-MASCARET system. The aim was to assess the impacts of the newly built water diversion channel, as well as the effects of a flood and tracer transport from an intermittent tributary, both located in the bay. An alternative approach to estimate the water retention times was additionally implemented. The simulations showed that though the diversion channel did not significantly influence the hydrodynamics of the bay, it is necessary to continuously monitor water quality parameters in the withdrawal, especially during rainy periods after droughts, because of the nutrient inputs from the tributary and the overflows of the nearby drainage systems. Management measures adapting to the continuously changing natural conditions and anthropogenic impacts are thus indispensable and the model presented can be a valuable supporting tool for this purpose.

Numerical Study of Monsoon Effect on Green Island Wake

ABSTRACT Hsu, T.-W.; Doong, D.-J.; Hsieh, K.-J., and Liang, S.-J., 2015. Numerical study of monsoon effect on Green Island wake. The wind effect on Kuroshio-induced island wake downstream of Green Island, Taiwan, is studied using a depth-averaged shallow-water model. The seasonal monsoon effect on spatial–temporal scales, such as the aspect ratio, dimensionless width, and Strouhal number, as well as the relative propagation speed of Green Island vortices, is studied. It is found that a NE monsoon has a more pronounced effect on wake characteristics than a SW monsoon does in terms of net speed and vorticity, aspect ratio, and dimensionless width. Vortices are pushed back and packed close to the north of the island with a smaller area of recirculation when Kuroshio flows against the NE monsoon; vortices are pushed farther downstream with a larger area of recirculation when Kuroshio flows in favor of the SW monsoon. However, the wind effect on temporal variation of island wake seems less significant. The per...

Spatial-temporal scales of Green Island wake due to passing of the Kuroshio current

The Kuroshio current-induced island wake downstream of Green Island, Taiwan, is studied using satellite imagery and a depth-averaged shallow-water model. Spatial–temporal scales, such as aspect ratio, dimensionless width, and Strouhal number, as well as propagation speed of the vortices, are quantified for Reynolds numbers 100, 200, and 500, respectively. It is found that the aspect ratio is between 1.76 and 2.72 obtained from satellite images and between 3.50 and 3.72 from numerical simulations. The dimensionless width is in the range of 1.84 to 1.92 from satellite images, and 1.29 to 1.33 from numerical modelling. The Strouhal number is between 0.17 and 0.20 from numerical simulations. Computed results are compared with theory, available satellite imagery, and in situ measurements, and show reasonable agreement. The magnitude of the propagation speed of the vortices is found to be of the same order as that of the Kuroshio, implying non-linearity as well as interactions of vortices, and the Kuroshio is strong. The Coriolis force affects the free-surface distribution, but its effect on vortices and flow field is insignificant.

Tracer dynamics in two-layer density-stratified estuarine flow

This paper considers tidal-driven particle motion in Tampa Bay, Florida, USA under fully stratified conditions with riverine inflow. The flow field is modelled by means of the two-layer shallow-water equations solved on an adaptive quadtree grid using a second-order Roe-type finite-volume scheme. Tracer dynamics are then obtained through Lagrangian particle tracking. The results show that the effect of external forcing is concentrated primarily in the upper layer, with particles in the lower layer less mixed and exhibiting relatively longer residence time in the semi-enclosed tidal bay. Particle flushing from Old Tampa Bay into the open sea is particularly hindered by the narrow inlet, whereas particles in Hillsborough Bay experience rapid transport seaward due to the large influx of river discharge. Particle patches are typically stretched in Middle Tampa Bay and may be trapped in the shallow Lower Tampa Bay region. The study reveals interesting underlying mixing features that cannot be produced by a single-layer depth-averaged shallow-water model.

Tidal stream energy resource assessment of the Anglesey Skerries

Many candidate sites for tidal stream power devices can be classified as headlands. This paper analyses one such site, off Anglesey. In order to investigate the disturbance to the local flow field due to the operation of tidal arrays and evaluate the extractable power at the site, a two-dimensional depth-averaged shallow water model of the naturally occurring tidal dynamics of the south-west UK and Irish Sea has been developed and validated. In the model, the effect of tidal arrays is represented by line discontinuities where upstream and downstream heads are related by Linear Momentum Actuator Disk Theory. A parametric study to investigate the importance of array locations, the connectivity of the arrays and local blockage effects on the available power has been undertaken. General conclusions from this analysis are that it is usually advantageous to arrange tidal turbines in long rows rather than as a number of rows in series, and that arrays with higher local blockage outperform arrays with lower blockage.

Overland flow computations in urban and industrial catchments from direct precipitation data using a two-dimensional shallow water model

This paper presents the experimental validation and the application to a real industrial catchment of a two-dimensional depth-averaged shallow water model used for the computation of rainfall-runoff transformation from direct precipitation data. Instead of using the common approach in flood inundation modelling, which consists in computing the water depth and velocity fields given the water discharge, in this study the rainfall intensity is imposed directly in the model, the surface runoff being generated automatically. The model considers infiltration losses simultaneously with flow simulation. Gullies are also included in the model, although the coupling between the surface runoff and the sewer network is not considered. Experimental validation of the model is presented in several simplified laboratory configurations of urban catchments, in which the surface runoff has been measured for different hyetographs. The application to a real industrial catchment includes a sewer network flow component, which is solved with the SWMM model. The numerical predictions of the discharge hydrograph generated by a 12 hours storm event are compared with field measurements, providing encouraging results.

Modelling flash flood propagation in urban areas using a two-dimensional numerical model

This paper reports on the numerical modelling of flash flood propagation in urban areas after an excessive rainfall event or dam/dyke break wave. A two-dimensional (2-D) depth-averaged shallow-water model is used, with a refined grid of quadrilaterals and triangles for representing the urban area topography. The 2-D shallow-water equations are solved using the explicit second-order scheme that is adapted from MUSCL approach. Four applications are described to demonstrate the potential benefits and limits of 2-D modelling: (i) laboratory experimental dam-break wave in the presence of an isolated building; (ii) flash flood over a physical model of the urbanized Toce river valley in Italy; (iii) flash flood in October 1988 at the city of Nimes (France) and (iv) dam-break flood in October 1982 at the town of Sumacarcel (Spain). Computed flow depths and velocities compare well with recorded data, although for the experimental study on dam-break wave some discrepancies are observed around buildings, where the flow is strongly 3-D in character. The numerical simulations show that the flow depths and flood wave celerity are significantly affected by the presence of buildings in comparison with the original floodplain. Further, this study confirms the importance of topography and roughness coefficient for flood propagation simulation.

Winter-Spring flushing of Bass Strait, South-Eastern Australia: a numerical modelling study

This study investigates winter-spring flushing of Bass Strait with a two dimensional non-linear depth-averaged shallow-water model. The model is driven with a 180-day wind time-series. An advection-diffusion scheme for several tracers is used to reveal the flushing pattern/timescale of the region. The study considers how external water masses flush strait waters. It shows that shelf-water entering the strait through the passage between King Island and Cape Grim makes the largest contribution to strait waters. Results show that the central area of the strait is a stagnation-area of weak currents and long flushing times (>160 days). The influence of external water masses on the stagnation-area is estimated. The findings have implications for marine ecosystems, residence times, air-sea modifications of water mass properties and dense water formation in the region.

Surf zone wave overtopping a trapezoidal structure: 1-D modelling and PIV comparison

Experiments have been undertaken on surf zone waves, with a surf similarity parameter of about 0.3, overtopping a trapezoidal obstacle with 1:2 side slopes, on a beach of 1:20 slope. Particle image velocimetry (PIV) investigation has shown complex vortical structures resulting from shoreward propagating bores interacting/colliding with bores partially reflected from the obstacle, before overtopping the obstacle. A 1-D depth-averaged shallow-water model captures qualitatively much of the wave dynamics. However, the marked turbulent air entrainment in the collision zone appears significant in raising mean water level relative to the model and causing a phase lag in the model relative to the experiment. Peak overtopping levels are overpredicted by about 100% with this phase lag.

MODELLING SHALLOW WATER FLOW AROUND PILE GROUPS.

The velocity vector fields and far wake instabilities associated with flow through pile groups is shallow water were measured in physical models using particle tracking velocimetry. The piles were in a staggered arrangement with spacings of two, four and eight diameters. The flow structure showed similar large scale features in all cases. A stagnant near wake zone was formed with a length that increased as the pile spacing increased. Wake oscillation occurred downstream, with a remarbly constant Strouhal number of about 0.22 based on upstream velocity and pile group width. However, wake oscillation was intermittent for the eight-diameter spacing, suggesting that it might die away for greater spcings. The results could be broadly reproduced in a depth-averaged shallow water model by using suitably increased values of bed friction (Manning's n is used), a very simple modelling strategy. However, the n values required are about twice the magnitude that is calculated from straightforward drag representation based on single piles. Based on the results, a methodology for including effects due to pile groups in shallow water computer models of rivers and marine environments is suggested.