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Tidal flows around headlands with recirculations have long been of environmental importance and are now considered for tidal stream turbine deployment as flow accelerates around a headland tip, interacting with the recirculation zones, giving high kinetic energy. The 3D TELEMAC model with hydrostatic pressure and k-ε turbulence modelling where bed...
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... For demonstration purposes, we use a simple model geometry consisting of a conical headland on a beach in a straight channel, based on the setup of Stansby et al. (2016). The model geometry is shown in Fig. 2. The open ends of the channel can be forced with a constant or transient inflow to demonstrate transferability to real-world cases. ...
... Simple process model of conical headland across a beach, based onStansby et al. (2016). ...
Flow in coastal waters contains multi-scale flow features that are generated by flow separation, shear-layer instabilities, bottom roughness and topographic form. Depending on the target application, the mesh design used for coastal ocean modelling needs to adequately resolve flow features pertinent to the study objectives. We investigate an iterative mesh design strategy, inspired by hydrokinetic resource assessment, that uses modelled dynamics to refine the mesh across key flow features, and a target number of elements to constrain mesh density. The method is solver-agnostic. Any quantity derived from the model output can be used to set the mesh density constraint. To illustrate and assess the method, we consider the cases of steady and transient flow past the same idealised headland, providing dynamic responses that are pertinent to multi-scale ocean modelling. This study demonstrates the capability of an iterative approach to define a mesh density that concentrates mesh resolution across areas of interest dependent on model forcing, leading to improved predictive skill. Multiple design quantities can be combined to construct the mesh density, refinement can be applied to multiple regions across the model domain, and convergence can be managed through the number of degrees of freedom set by the target number of mesh elements. To apply the method optimally, an understanding of the processes being model is required when selecting and combining the design quantities. We discuss opportunities and challenges for robustly establishing model resolution in multi-scale coastal ocean models.
... In recent years, three-dimensional hydrodynamic models based on the assumption of hydrostatic pressure distribution have become popular in the study of water motion and material transport in rivers, lakes, and open seas [1][2][3]. Among these models, the three-dimensional discontinuous Galerkin (3D DG) hydrodynamic model is receiving increasing attention [4][5][6] due to its advantages of mesh flexibility, high precision, and local conservation. ...
A wetting and drying treatment for a three-dimensional discontinuous Galerkin hydrodynamic model without mode splitting (external and internal modes) was developed. In this approach, computing elements are classified into wet, dry, and semidry elements, which are treated differently. In a Runge–Kutta time step, the reconstruction of the semidry elements and the combined utilization of two- and three-dimensional limiters help the model maintain stability. Numerical results show that the wetting and drying method can achieve a well-balanced property under the condition of still-water equilibrium and can reasonably describe the variation process of wetting and drying regions during a long wave run-up on a uniform slope and a tidal cycle in a basin with a variable slope. Analysis of the role of the limiters in the model indicated that the robustness of the three-dimensional hydrodynamic model can be effectively maintained when the two- and three-dimensional limiters are jointly applied for wetting and drying process simulation. A three-dimensional discontinuous Galerkin hydrodynamic model was applied with the presented wetting and drying method to simulate the tidal current evolution of a spring tidal cycle in southwestern Laizhou Bay in the Bohai Sea, in November 2003, and the simulated results of the water surface elevation and vertical layered current velocities agreed well with the measured data.
... Alternatively, computational tools can be applied, with differing fidelity available. Two-dimensional shallow-water models are capable of estimating the depth-averaged velocity and flow direction with good accuracy [8], [9] unless there are recirculating wakes when accuracy is compromised [10], [11] and helping to inform layout optimisation [12], whilst have limited capabilities to resolve the turbulence in the flow as they are normally based on the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations that time-average the flow for small scales. These models have also been shown to predict deflected wakes for non-yawed turbines [9], [13]. ...
... Further progress has been done with expanding the shallowwater framework to three-dimensional models, e.g. Delft3D [8] or Telemac-3D [11], [14], allowing to partly account for the vertical variability of the flow that is introduced by bathymetry changes. These models can be considered as resource modelling tools as they have proven useful to quantify whether a site is deemed suitable depending on its power density [15]. ...
Micro-siting tidal stream turbines in a confined seabed area requires a extensive understanding of the flow dynamics over the water column at turbine deployment locations so that operating conditions are assessed, wake effects can be estimated to infer the energy yield [1], or bathymetry effects can be quantified. Tidal currents have the advantage of being highly predictable and mostly bidirectional but the uneven bathymetry found at most of sites introduces a high variability to the flow conditions within relatively short distances. Considering future tidal turbine arrays will comprise dozens of devices, deploying ADCPs at each turbine position would be very expensive or very time consuming, outlining the need for accurate modelling tools to be used as digital twins in micro-siting. Shallow-water models are widely adopted in preliminary design of tidal arrays but fail to capture the three dimensional nature of the flow and predict deflected wakes whose streamwise length is also over-predicted [2]. Thus, eddy-resolving method are required to fully capture the turbulence from the free-stream flow, induced by turbines and from bathymetry. \\ This study provides a real-project application of the state-of-the-art large-eddy simulation (LES) code DOFAS (Digital Offshore Farms Simulator) [3] to the six 100kW-turbine array deployed by NOVA Innovation Ltd. in the Shetlands, UK [4]. The bathymetry data has been obtained from EMODnet database with the velocity profiles set at the inlet condition of both ebb and flood tides imported from Macleod et al. (2019) [4]. The deployment site is characterised by steep slopes with a maximum depth of 45 m at the cross-section where turbines are located. The bathymetry has a downwards slope when the flow goes in the ebb tide direction whilst upstream during flood tide. The tidal rose indicated a slight deviation of about 20$^{\circ}$ between ebb and flood directions. The turbines have a diameter ($D$) of 9 m attached to a 10 m long hub whose diameter is 1 m. Three array configurations have been studied: (i) single row of three turbines, (ii) two rows of turbines spaced 8$D$, and (iii) two rows of turbines spaced 12$D$. The computational domain extends over 600 m by 300 m in the horizontal plane yielding 540 million cells, requiring 32,500 CPU hours to compute 30 min of physical time.\\ Results show that bathymetry effects at this site play a larger role when designing the location of the secondary row of turbines compared to wake effects from upstream turbines. During the ebb tide, the increase in water depth reduces the wake recovery far downstream so that the array with 12$D$ row spacing has a lower performance than the 8$D$ one with approx. 30\% decrease in energy yield. Conversely, the uphill shape of the bathymetry during the flood enables a fast wake recovery so that the downstream row experiences almost no energy yield loss due to wakes.
... A study by Stansby et al. (2016) employed a 3D Telemac model to investigate the oscillatory flow around a headland. This study is not directly connected to the tidal range modelling, however, the recirculating flow conditions resulting from flow around a headland closely resemble the large eddies induced by the high-velocity jets from a TRS. ...
... The NSE analysis showed slightly worse performance at site L1 with a value of 0.776, however, still within an acceptable range. This discrepancy can be attributed to the location of the site close to Mumbles headland which can have an impact on velocity predictions in numerical simulations (Stansby et al. 2016). The RMSE and SI were low in all cases and therefore of no concern. ...
... Streamwise flows moving around a headland or coastline point, result in a) streamwise flow acceleration, and b) an increase in centrifugal acceleration as flows separate from the headland (e.g., McCabe and MacCready, 2006;Stansby et al., 2016). Streamwise flow acceleration occurs within the radius of curvature of the headland and causes a drop in surface elevation. ...
We present an approach for estimating drag coefficients for depth-averaged tidal flows that uses the ratio of observed RMS velocities to the RMS velocities that would be observed without bottom friction. We find that this ratio, R, depends on a single non-dimensional number, P=CDCη0/ωH2, where CD is the drag coefficient, and C is the phase speed of a tidal wave with amplitude η0 and frequency ω, in water of depth h. The function R(P) can be inverted to solve for CD using measured values of R. Taking advantage of a unique multi-year record of tidal flows on Isla Nativdad, Baja California, Mexico, during which time the kelp forest there varied between non-existent and dense, we use this method to quantify the effect of kelp biomass on drag. This analysis shows that a maximum value of CD ≈ 0.04 is reached for relatively low values of kelp biomass, which may be an effect of sheltering (reductions in the velocity creating drag due to the close proximity of bundles of kelp stipes). However, values as large as 0.015 were observed when the water column experienced strong secondary flows in the presence of strong density stratification. Given that the long-term measurements were made near a coastal headland, we argue that this may reflect variations in secondary flow strength due to stratification. Lastly, our measurements show little evidence of enhancement of drag by surface waves.
... Streamwise flows moving around a headland or coastline point, result in a) streamwise flow acceleration, and b) an increase in centrifugal acceleration as flows separate from the headland (e.g., McCabe and MacCready, 2006;Stansby et al., 2016). Streamwise flow acceleration occurs within the radius of curvature of the headland and causes a drop in surface elevation. ...
Kelp forests affect coastal circulation but their influence on upwelling around headlands is poorly understood. Tidal-cycle surveys off two headlands with contrasting kelp coverage illustrated the influence of kelp forests on headland upwelling. Underway acoustic Doppler current and backscatter profiles were collected simultaneously to surface water temperature. Surveys occurred along three off-headland transects in July 25–29, 2018, off Isla Natividad, located midway on the western coast of the Baja California peninsula. Flows and water temperature distributions off the headland with no kelp coverage were consistent with headland upwelling. In contrast, the kelp around the headland with dense coverage: 1) attenuated the ambient flow; 2) favored an increase in effective radius of flow curvature; 3) promoted flow ducting, which consists of enhancing flow through channels unobstructed by kelp; and 4) suppressed headland upwelling. Kelp suppressed upwelling by channeling the flow away from the headland, keeping nearshore waters warmer than offshore.
Plain language abstract
This study documents a way in which biology can affect physics in coastal ocean environments. In particular, the study describes how a kelp forest suppresses the upward pumping of cool subsurface waters that is typically found around headlands. Such suppression of subsurface waters injection occurs via a process that we refer to as ‘flow ducting.’ In flow ducting, coastal flows are channelized through kelp gaps, concentrated in bands <30 m wide, and kept away from the morphological influences of a headland. This ducting is analogous to the tortuous flow through porous media.
... Increasing the number of layers results in greater accuracy; however, this increases computational time. Models were run with 10, 16, and 32 layers with the number of layers chosen by using a value of 10 layers from earlier research (Rahman and Venugopal, 2015;Chatzirodou et al., 2017;Stansby et al., 2016;Waldman et al., 2017) and from calculated y + values (Table 1). The y + value is a non-dimensional distance to describe the required resolution of a mesh near bottom for a particular flow pattern. ...
Areas around headlands often have higher tidal flow, making them important foraging locations for seabirds and marine mammals, as well as of interest for tidal energy extraction. Using in situ field measurements and hydrodynamic modelling, this study investigated tidal features around the most northerly promontory headland on the United Kingdom mainland. An acoustic wave and current (AWAC) instrument and an acoustic Doppler current profiler (ADCP) were deployed for 109 days in upward-facing configurations. These data were used to calibrate a hydrodynamic model developed using TELEMAC-MASCARET modelling suite. This study used a non-hydrostatic model with a vertical layer configuration to reproduce upwelling present in field data. Data showed complex hydrodynamics with occurrences of vertical water velocities of up to 0.219 m/s. Modelling suggests upwelling begins in association with headland eddy formation as a result of secondary circulation due to flow curvature, which occurs off the tip of the headland. Upwelling continues to develop as the eddy dissipates and forms an upwelling front which moves away from the headland as the tide starts to turn. The modelling work successfully reproduces upwelling recorded by field instruments. Models of sufficient complexity are required to resolve fine-scale hydrodynamics associated with such features, which is important for tidal stream renewable energy developments in these environments, as well as understanding foraging activity of seabirds and marine mammals.
... TELEMAC3D is a three-dimensional open-source finite element model that solves the Navier Stokes equations with or without hydrostatic pressure approximation (Guillou et al., 2016;Stansby et al., 2016). This study employs the hydrostatic pressure approximation due to the intense computational power demanded by non-hydrostatic pressure models (Botelho et al., 2009;Liu et al., 2016). ...
... This makes TELEMAC3D ideal for this study as sigma models are best suited for coastal regions (Chassignet et al., 2006;Mehra and Rivin, 2010) and unstructured mesh for resolving complex bathymetry and geometry commonly observed in rivers, tidal flats, estuaries and coast in a robust, efficient and adequate way (Zhang and Baptista, 2008;Wang and Shen, 2010). Furthermore, TELEMAC3D provides a wide variety of numerical options to solve various processes within the model (Stansby et al., 2016). The model was implemented with 5 equidistant σ-coordinate layers in the vertical and a time step of 45 seconds. ...
Crude oil is predicted to become one of the most detrimental sources of anthropogenic pollution to estuaries. A comprehensive survey of oil spill literature reveals that oil spill transport in estuaries presents a gap in academic knowledge and literature. To address this gap, we present the first detailed analysis of estuarine oil spill dynamics. We develop and analyse a range of simulations for the Humber Estuary, using TELEMAC3D; a coupled hydrodynamic and oil spill models. The river boundary of the Humber Estuary is forced by discharge data, while the offshore boundary is driven by tidal height data, including estuarine water temperature and salinity. The calibrated model shows good agreement with measured data during the validation process. Results show that: (a) the time of oil release within a tidal cycle significantly influences oil slick transport; and (b) the tidal range significantly influences oil slick impacted area and overall distance travelled, as oil slick released under spring tide is approximately double the oil slick size under neap tides and travels on average 71% farther. This study emphasises the need to: a) understand how the interaction of river discharge and tidal range influences oil slick transport; and (b) be aware of the time of release within a tidal cycle, to efficiently deal with oil spills. Findings should be useful for future operational oil spill response and could be equally applicable to other tide-dominated estuaries.
... TELEMAC3D, a three-dimensional open-source finite-element model that solves the Navier-Stokes equations with or without hydrostatic pressure approximation (Stansby et al., 2016) was used to compute the hydrodynamics of the Humber estuary. TELEMAC3D uses a sigma transformation to resolve the vertical direction and unstructured triangular grid in the horizontal direction (Moulinec et al., 2011;Villaret et al., 2013). ...
Oil spills in estuarine systems can strongly endanger habitats and water quality. However, the impacts of projected climatic conditions on oil spill transport in estuarine environments have received little attention. To address these key gaps, we analyse here a range of simulations for the Humber Estuary, UK, using coupled hydrodynamic and oil spill model. These simulations indicate that, for this well-mixed macro-tidal estuary: (a) the influence of projected sea level rise and river discharge on oil slick impacted area, slick length and overall distance travelled is relatively minor (<10%); (b) magnitude of currents determines differences in dynamics between oil slicks released along the estuary length; and (c) differences in lateral current speed and direction are key determinants of the differences in the dynamics of oil slicks released along the estuary width. The implications of these findings for operational oil spill response in estuaries similar to the Humber Estuary are: (i) the need to be aware of dominant current direction in different segments of the estuary; and (ii) the need take cognisance of the interaction between oil slicks and estuary bank and how it influences overall distance travelled by oil slicks.
... Conversely, wave dissipation and refraction impact on offshore marine engineering [8] and may help suppress coastal erosion during storm conditions around sandbanks [9]. Furthermore, the increased velocities caused by the geometric nature of these features make these desirable sites for the deployment of tidal current turbines [10,11]. Tidal flow in the lee of obstacles is affected by many factors, including the direction and speed of the tidal currents, the scale and bathymetry of island/headland and the influence of other obstacles located upstream [3]. ...
... For boundary conditions in Telemac-2D, there is no flow flux pass through solid, and for all velocity vectors tangential to a free stream boundary then a free slip condition is applied [41]. The Water 2020, 12, 1225 7 of 18 wave equation method, which has been widely used in turbulence studies, was used to solve the continuity and momentum equations in this study [11,32,42]. In this method, the velocity in the continuity equation is substituted from the momentum equation to generate a wave equation, in which the water depth is the only unknown. ...
Tidal flow can generate unsteady wakes, large eddies, and recirculation zones in the lee or around complex natural and artificial obstructions, such as islands, headlands, or harbours. It is essential to understand the flow patterns around such structures given the potential impacts they can have on sedimentation, the marine environment, ecology, and anthropogenic activities. In this paper, the wake around an island in a macro-tidal environment has been studied using a widely used hydro-environmental model, Telemac-2D. Current data collected using moored acoustic Doppler current profilers (ADCPs) were used to validate and refine the Telemac-2D model. Four different turbulence models and several different solver options for the k-ε model were tested in this study to assess which representation could best replicate the hydrodynamics. The classic k-ε model with the solver of conjugate residual was the most suitable method to simulate the wake in the lee of the island. The model results showed good correlation with measured data. The island wake parameter used to predict the wake behaviour and its predictions matched the model results for different tidal conditions, suggesting that the island wake parameter could be used to predict the wake behind obstacles in macro-tidal environments. The model predictions showed the development of a wake is similar between ebb and flood tides in the neap tide while showing more difference in spring tide. With the increase of velocity in the neap tide, two side-by-side vortices will appear and then changing to stable Karman Vortex Street. During the ebb phase of spring tide, the wake will develop from a stable vortex to an unstable Karman Vortex Street, while the wake remained stable with two vortices during an flood tide.
