Depth-averaged Numerical Model Research Articles

Peeling fingers in an elastic Hele-Shaw channel

Using experiments and a depth-averaged numerical model, we study instabilities of two-phase flows in a Hele-Shaw channel with an elastic upper boundary and a non-uniform cross-section prescribed by initial collapse. Experimentally, we find increasingly complex and unsteady modes of air-finger propagation as the dimensionless bubble speed $Ca$ and level of collapse are increased, including pointed fingers, indented fingers and the feathered modes first identified by Cuttle et al. (J. Fluid Mech., vol. 886, 2020, A20). By introducing a measure of the viscous contribution to finger propagation, we identify a $Ca$ threshold beyond which viscous forces are superseded by elastic effects. Quantitative prediction of this transition between ‘viscous’ and ‘elastic’ reopening regimes across levels of collapse establishes the fidelity of the numerical model. In the viscous regime, we recover the non-monotonic dependence on $Ca$ of the finger pressure, which is characteristic of benchtop models of airway reopening. To explore the elastic regime numerically, we extend the depth-averaged model introduced by Fontana et al. (J. Fluid Mech., vol. 916, 2021, A27) to include an artificial disjoining pressure that prevents the unphysical self-intersection of the interface. Using time simulations, we capture for the first time the majority of experimental finger dynamics, including feathered modes. We show that these disordered states evolve continually, with no evidence of convergence to steady or periodic states. We find that the steady bifurcation structure satisfactorily predicts the bubble pressure as a function of $Ca$ , but that it does not provide sufficient information to predict the transition to unsteady dynamics that appears strongly nonlinear.

Unconfined fishway design, implementation, and assessment for the emerald Shiner (Notropis atherinoides) in the Upper Niagara River, New York

An engineered seawall in need of repair along the Upper Niagara River in Buffalo, NY, was previously identified as a hydrodynamic barrier to the migration of a small but important prey fish, the emerald shiner (Notropis atherinoides), and its connection to the upstream environs of Lake Erie. This study proposed a novel unconfined fishway design to be incorporated into existing plans for rehabilitation of the seawall at Broderick Park. The proposed fishway was developed using a two-dimensional depth-averaged numerical model, it was explored by placing the target fish into a physical model, and the constructed demonstration project was assessed using field measurements and observations. The numerical model showed that modular baffles attached to the seawall reduced the nearshore flow velocities to about 0.4 to 0.6 m s−1, which was within the acceptable range of velocities for the upstream migration of the emerald shiners. The physical experiments demonstrated that most emerald shiners chose to swim toward, within, or close to the proposed fishway in the presence of higher flow velocities within the main channel region. The proposed fishway design was integrated into the seawall repair as part of a demonstration project supervised by the US Army Corps of Engineers-Buffalo District. Post-construction assessment of the installation showed that (1) the modular baffles reduced time-averaged flow velocities near the seawall and water surface, (2) while very few shiners were observed swimming along the pre-construction seawall, large numbers were observed swimming upstream within this reduced flow velocity corridor created by the baffles, and (3) the structural integrity of the installation proved to be durable and resilient to extremely harsh environmental conditions. This study explored a new approach to fishway design for the passage of relatively small fish in large rivers, and it effectively melded fishway requirements into seawall restoration in concert with the expectations of multiple stakeholders.

IMEX_SfloW2D v2: a depth-averaged numerical flow model for volcanic gas–particle flows over complex topographies and water

Abstract. We present developments to the physical model and the open-source numerical code IMEX_SfloW2D (de' Michieli Vitturi et al., 2019). These developments consist of a generalization of the depth-averaged (shallow-water) fluid equations to describe a polydisperse fluid–solid mixture, including terms for sedimentation and entrainment, transport equations for solid particles of different sizes, transport equations for different components of the carrier phase, and an equation for temperature/energy. Of relevance for the simulation of volcanic mass flows, vaporization and entrainment of water are implemented in the new model. The model can be easily adapted to simulate a wide range of volcanic mass flows (pyroclastic avalanches, lahars, pyroclastic surges), and here we present its application to transient dilute pyroclastic density currents (PDCs). The numerical algorithm and the code have been improved to allow for simulation of sub- to supercritical regimes and to simplify the setting of initial and boundary conditions. The code is open-source. The results of synthetic numerical benchmarks demonstrate the robustness of the numerical code in simulating transcritical flows interacting with the topography. Moreover, they highlight the importance of simulating transient in comparison to steady-state flows and flows in 2D versus 1D. Finally, we demonstrate the model capabilities to simulate a complex natural case involving the propagation of PDCs over the sea surface and across topographic obstacles, through application to Krakatau volcano, showing the relevance, at a large scale, of non-linear fluid dynamic features, such as hydraulic jumps and von Kármán vortices, to flow conditions such as velocity and runout.

Realistic visualization of debris flow type landslides through virtual reality

Immersive media technologies, such as virtual and augmented reality, have recently enabled a more holistic way to comprehend natural hazards. In this work, we aim at visualizing the temporal and spatial evolution of a debris flow in a virtual reality environment. We develop a framework to integrate the output results obtained from a debris flow numerical model into virtual reality. To guide the framework, a real debris flow event, which happened in Hunnedalen (Norway) in 2016 and blocked a road network, is considered as a case study. The debris flow is back-calculated using a depth-averaged numerical model and the simulation results are imported into a dedicated game engine to construct a digital model of the debris flow event. The debris flow is visualized using a Head-Mounted Display. We therefore discuss a wide range of potential applications of virtual reality to manage and grasp landslide phenomena: training for rescue operations; improving decision-making; studying early warning systems, and educating communities affected by natural hazards. We finally provide a quantitative evaluation of the hazard perception for a road user. We show that the debris flow movement is perceived at variable delayed times from the triggering of the landslide, depending on the position along the road where the debris flow is observed. Evaluating the realistic perception time of the natural hazard may be fundamental to designing more effective road networks, signs, and mitigation measures.

Sea-level extremes of meteorological origin in the Red Sea

Severe weather events and the resulting sea-level extremes are considered among the greatest threats to coastal environments. Understanding this coastal hazard is vital for various coastal developments and planning activities. This study examines the sea-level extremes of meteorological origin in the Red Sea. A high-resolution (approximately 500 m) depth-averaged numerical ocean model forced by 5 km dynamically downscaled meteorological fields was implemented to hindcast the sea level of the Red Sea over 37-year, 1980–2016. The model was first validated with observations, showing good agreement with available data. The hindcast model outputs were then analyzed to describe the spatiotemporal features of the sea-level extremes in the Red Sea. The sea-level extremes in the Red Sea developed in response to wind variability over the southern Red Sea and exhibited a basin-wide impact. The magnitudes of the maximum sea levels reached approximately 0.30–0.50 m inside the Red Sea basin, with the highest values (0.85 m) in the Gulf of Suez. The seasonal distribution of the extremes suggests that these are frequent during the winter months (January–March). Assessment of long-term changes in the annual maxima, 99th and 95th percentiles of hourly sea levels indicate no significant trends over the study period.

Interplay of induced charge electroosmosis and electrothermal flow in insulator-based dielectrophoresis

A depth-averaged numerical model is developed to understand the experimentally observed interplay of induced charge electroosmosis and electrothermal flow in an insulator-based dielectrophoresis microdevice. The experimentally measured nonlinear fluid velocity matches asymptotically the predicted velocity of the electroosmotic flow in a low-concentration buffer and that of electrothermal flow in a high-concentration buffer. This agreement is consistent with a scaling analysis.

Rainfall-triggered debris flows: triggering-propagation modelling and application to an event in Southern Italy

Debris flows are high-speed and unpredictable phenomena, considered among the main sources of hazard worldwide, since they can affect structures, the economy, and human lives. Rainfall typically triggers these events, causing the flowing of the unconsolidated soil downslope. This work focuses on debris-flow events characterized by multiple triggering areas, which are extremely complex since they involve a spatial sequence of numerous triggers in a relatively small portion of the slope. Numerical modelling of this type of phenomenon can contribute to hazard and risk assessment, which is key to designing effective mitigation structures. In this article, two different models are applied for triggering and propagation, respectively. The former computes the transient pore-pressure changes and the consequent factor of safety variation caused by rainfall infiltration, inducing the triggering of the event. The latter is a depth-averaged numerical model that simulates the event runout, and whose parameters are calibrated through back-analysis. The applicability of the two combined approaches is tested through modelling of an historical event in Southern Italy, which was characterized by large mass releases from multiple triggering zones. Residential areas were hit, suffering serious consequences. Two rheologies are compared to individuate the most suitable propagation model for the study case and obtained results are commented.

Movement process analysis of the high-speed long-runout Shuicheng landslide over 3-D complex terrain using a depth-averaged numerical model

Flow-like landslide is one of the most catastrophic types of natural hazards due to its high velocity and long travel distance. In 2019, a large catastrophic landslide was triggered by heavy rainfall and occurred in Shuicheng County, Guizhou, China. The Shuicheng landslide was characterized by a short slip time, high speed, and long sliding distance, causing significant damages to the downstream communities and properties. Depth-averaged models have been widely used to predict the velocity and runout distance of flow-like landslides. However, most of the existing depth-averaged models have various shortcomings for application in real-world simulations. In this study, a high-performance depth-averaged model taking into account the effects of topography-related vertical acceleration and centrifugal force was used to examine the influence of complex 3-D terrain on the landslide movement process. The simulation results were in satisfactory agreement with the field observations. This work reveals the landslide movement process at different stages, including acceleration, diversion, secondary acceleration, impact, and deposition. The maximum average velocity was predicted to be 35 m/s, with a local maximum velocity exceeding 50 m/s. The seismic records obtained from the adjacent seismic stations and the predicted kinetic energy and velocity of the landslide event revealed a dual acceleration and obstruction process. It was also found that the movement process and final deposit morphology were strongly influenced by the complex terrain and were sensitive to the surface friction coefficient. This may also be the reason for the survival of some houses in the middle of the slope during the event. This study provides a reference for investigating long-runout, high-speed, flow-like landslides.

Non-Hydrostatic Transitional Open-Channel Flows from a Supercritical to a Subcritical State

Abstract In this study, a depth-averaged numerical model was employed to investigate the two-dimensional flow features of transitional open-channel flows from a supercritical to a subcritical state. Compared to a shallow-water model, the proposed model incorporates supplementary terms to account for the effects of non-uniform velocity and non-hydrostatic pressure distributions. The model equation was solved numerically by means of the Adams–Bashforth–Moulton scheme. A wide variety of transitional open-channel flow problems such as hydraulic jumps was considered for assessing the suitability of the numerical model. The results of the model for the free-surface profile, pressure distribution, and characteristics of the first wave of an undular jump were compared with the experimental data, and the agreement was found to be satisfactory. Despite the effects of the three-dimensional characteristics of the flow and the bulking of the flow caused by air entrainment, the model performed reasonably well with respect to the simulations of the mean flow characteristics of the curvilinear turbulent flow problems. Furthermore, the results of this investigation confirmed that the model is more suitable for analyzing near-critical turbulent flow problems without cross-channel shock waves.

Two-Dimensional Numerical Modeling of Flow in Physical Models of Rock Vane and Bendway Weir Configurations

While there are a wide range of design recommendations for using rock vanes and bendway weirs as streambank protection measures, no comprehensive, standard approach is currently available for design engineers to evaluate their hydraulic performance before construction. This study investigates using 2D numerical modeling as an option for predicting the hydraulic performance of rock vane and bendway weir structure designs for streambank protection. We used the Sedimentation and River Hydraulics (SRH)-2D depth-averaged numerical model to simulate flows around rock vane and bendway weir installations that were previously examined as part of a physical model study and that had water surface elevation and velocity observations. Overall, SRH-2D predicted the same general flow patterns as the physical model, but over- and underpredicted the flow velocity in some areas. These over- and underpredictions could be primarily attributed to the assumption of negligible vertical velocities. Nonetheless, the point differences between the predicted and observed velocities generally ranged from 15 to 25%, with some exceptions. The results showed that 2D numerical models could provide adequate insight into the hydraulic performance of rock vanes and bendway weirs. Accordingly, design guidance and implications of the study results are presented for design engineers.

Hydrodynamics of a hyper-tidal estuary influenced by the world's second largest tidal power station (Rance estuary, France)

The Rance estuary is a relatively small low-discharge steep-sided ria, located along the Brittany coast in northern France, with a maximum spring tidal range of 13.5 m. Taking advantage of this hyper-tidal regime, the first and currently the second largest operational tidal power station in the world was built at the estuary's mouth and has been in operation since the 1960s. Despite the well-known effect of damping of estuarine water levels, little attention has been given to quantifying the influence of the plant on the propagation and asymmetry of the tidal wave inside the estuary. In this study, hydrodynamics and tidal wave patterns were analyzed in this anthropogenically influenced estuarine system. A two-dimensional depth-averaged numerical model of the Rance estuary was developed. Two scenarios without the tidal power plant involving the dam's pre- and post-construction bathymetry (1957 and 2018 respectively) and present-day conditions scenarios were designed, to highlight the impact of bed evolution and the tidal power station on hydrodynamics and tidal asymmetry. Numerical results showed that, without the structure, bathymetric evolution did not substantially influence estuarine hydrodynamics. Nevertheless, on the estuary-side of the dam, the presence of the tidal power plant induced (i) a decrease in both tidal range and tidal prism, (ii) an increase of low water levels, and (iii) a decrease in both flood and ebb currents. Contrastingly, the region close to the structure reacted differently to plant operating modes, with an increase in flood currents (ebb currents) upstream of the sluice gates (downstream of the turbines). For both the natural condition and the artificially-induced hydrodynamic forcing due to the presence of the plant, numerical results showed that the Rance estuary mainly exhibits flood-dominant behavior, with a longer duration of falling than rising water and stronger peak flood currents than ebb currents. Spanning a period of approximately 60 years, this study presents a quantitative analysis of the influence of the tidal power station on the hydrodynamics in the Rance estuary, and its possible consequences for sediment dynamics. This approach is novel for this particular enclosed water body, characterized by the presence of a dam at its mouth and a lock at its uppermost limit.

Joule heating effects on electrokinetic flows with conductivity gradients.

Instability occurs in the electrokinetic flow of fluids with conductivity and/or permittivity gradients if the applied electric field is beyond a critical value. Understanding such an electrokinetic instability is significant for both improved transport (via the suppressed instability) and enhanced mixing (via the promoted instability) of liquid samples in microfluidic applications. This work presents the first study of Joule heating effects on electrokinetic microchannel flows with conductivity gradients using a combined experimental and numerical method. The experimentally observed flow patterns and measured critical electric fields under Joule heating effects to different extents are reasonably predicted by a depth-averaged numerical model. It is found that Joule heating increases the critical electric field for the onset of electrokinetic instability because the induced fluid temperature rise and in turn the fluid property change (primarily the decreased permittivity) lead to a smaller electric Rayleigh number.

Joule heating-enabled electrothermal enrichment of nanoparticles in insulator-based dielectrophoretic microdevices.

Insulator-based dielectrophoresis (iDEP) exploits the electric field gradients formed around insulating structures to manipulate particles for diverse microfluidic applications. Compared to the traditional electrode-based dielectrophoresis, iDEP microdevices have the advantages of easy fabrication, free of water electrolysis, and robust structure, etc. However, the presence of in-channel insulators may cause thermal effects because of the locally amplified Joule heating of the fluid. The resulting electrothermal flow circulations are exploited in this work to trap and concentrate nanoscale particles (of 100nm diameter and less) in a ratchet-based iDEP microdevice. Such Joule heating-enabled electrothermal enrichment of nanoparticles are found to grow with the increase of alternating current or direct current electric field. It also becomes more effective for larger particles and in a microchannel with symmetric ratchets. Moreover, a depth-averaged numerical model is developed to understand and simulate the various parametric effects, which is found to predict the experimental observations with a good agreement.

Modification of tidal resonance in the Severn Estuary by a barrage and lagoon

The Bristol Channel/Severn Estuary has some of the largest tides in the world with a mean spring tidal range of 12.2 m. Numerous proposals have been made to exploit this for energy extraction. However, the large tidal range is partially driven by tidal resonance and such systems can be sensitive to small changes. Thus, it is important to understand the impact of a barrage on the resonance of the system which in turn leads to an understanding of the environmental impact of building a barrage. In this paper, we examine the resonant response of the Bristol Channel system, with and without a barrage structure deployed, using a depth-averaged numerical model. We find that the barrage can alter the response of the Bristol Channel to excitation with higher frequencies than 12 h. However, the barrage causes very little change to the resonant response for longer periods including for the semi-diurnal periods which dominate the tides in the region. We also briefly examine the Swansea Lagoon scheme and find that this is too small to have a significant impact on the resonant response of the channel.

Improved Modeling of Subaerial and Subaqueous Muddy Debris Flows

AbstractIn this note, a two-dimensional depth-averaged numerical model (MassFlow2D) previously developed to simulate subaerial and subaqueous muddy debris flows is further improved. The retarding e...

2D Numerical Modeling on the Transformation Mechanism of the Braided Channel

This paper investigates the transformation mechanism between different channel patterns. A developed 2D depth-averaged numerical model is improved to take into account a bank vegetation stress term in the momentum conservation equation of flow. Then, the extended 2D model is applied to duplicate the evolution of channel pattern with variations in flow discharge, sediment supply and bank vegetation. Complex interaction among the flow discharge, sediment supply and bank vegetation leads to a transition from the braided pattern to the meandering one. Analysis of the simulation process indicates that (1) a decrease in the flow discharge and sediment supply can lead to the transition and (2) the riparian vegetation helps stabilize the cut bank and bar surface, but is not a key in the transition. The results are in agreement with the criterion proposed in the previous research, confirming the 2D numerical model’s potential in predicting the transition between different channel patterns and improving understanding of the fluvial process.

The impact of a tidal barrage on coastal flooding due to storm surge in the Severn Estuary

The proposed Severn Barrage is a controversial but widely discussed proposal to generate clean and renewable energy. A key concern with this technology is that such structures may cause other environmental problems. However, such structures might also have beneficial environmental effects in some areas, such as mitigating coastal flooding from storm surges. In this paper, we model the hydrodynamics of the Severn Barrage and surrounding area using a depth-averaged numerical model. We simulate a storm surge event based on realistic meteorological conditions coinciding with a spring tide. We find that to the east of the barrage the peak water level is significantly reduced by the barrage. To the west of the barrage, on the ocean side, the presence of the barrage leads to a small increase in the water levels during a surge event despite the reduction in the tidal amplitude. We examine different operational strategies for the barrage during a storm event—these make a small but perhaps significant difference. Overall, a barrage can help to mitigate the impact of storm surges on coastal flooding.

The impact of spring-neap tidal-stream cycles in tidal energy assessments in the Chilean Inland Sea

The Chilean Inland Sea (CIS) has natural conditions for marine tidal energy development. Recent studies show that lunar variability in the tides should be considered, because the practical power generation varies considerably when large differences exist between spring and neap tides. Using a high resolution (∼1 km) 2D depth-averaged numerical model, we investigate the effect of lunar cycle variability in the CIS and this impact on tidal energy evaluation by validating a 30 days simulation. There are two highly energetic areas where currents exceed 2 m/s 50% of the time: the Chacao and Desertores Channels. Both zones are dominated by semi-diurnal tides, and tidal current amplitude shows large changes during spring and neap tides. Due to these changes power density can vary considerably in a period of 2 weeks. In the Chacao Channel, tidal-stream power is four times as large during spring tide (40 kW/m2) compared to neap tide (10 kW/m2). Tidal-stream power is only significant during spring tide in the Desertores Channel (8 kW/m2). This work is a contribution to understanding the tidally driven flows in an inland sea and the importance of considering the variations between spring and neap tides in tidal-stream energy assessment.

Modelling of hyperconcentrated flow in steep-sloped channels

ABSTRACTAn unsteady two-dimensional depth-averaged numerical model for hyperconcentrated flows in steep-sloped alluvial channels is developed and applied to the Zhuoshui River in Central Taiwan. In this model, the suspended load and bed load are both included to reproduce actual sediment transport characteristics of steep-sloped channels in the chosen study river reaches. A rheological relationship for Bingham fluid and the formula for the sediment carrying capacity, established through laboratory experiments, are used to describe the hyperconcentrated flow behaviour in the model. At peak discharge during Typhoon Morakot, bed shear stress from the hyperconcentrated flow model can be 150% larger than that from the clear water model. According to the simulation for Tung-Pu-Rey Creek, an upstream tributary of Zhuoshui River, the temporal evolution of bed changes obtained from the model can be used to provide plausible explanations for the reasons behind levee failure during Typhoon Toraji.

Unified Integral Model for Fluvial and Aeolian Sediment Transport

The commonly used three-dimensional mathematical model in aeolian sediment transport modeling could inevitably turn out to be very costly and time consuming when applied to large scale simulation. In this study, a depth-averaged numerical model which is widely applied to fluvial sediment transport numerical simulation is introduced to aeolian sediment transport modeling. Model validity has been assessed using experimental data of aeolian saltation cases, and the results have shown that the major features of aeolian sediment transport can be well captured by the proposed model.