Shallow Water Numerical Model Research Articles

GREENSURGE: AN EFFICIENT ADDITIVE MODEL TO ASSESS STORM SURGE INDUCED BY TROPICAL CYCLONES

Storm surge is one of the main components of coastal flooding induced by tropical cyclones (TCs), a big concern for Pacific Island Countries (PICs). It is well-known that storm surge levels can be accurately estimated using numerical models capable of considering both the inverse barometer effect and wind set-up. Therefore, dynamic simulations of a shallow water (SW) numerical model can be forced with the corresponding dynamic pressure and wind fields to accurately assess the storm surge induced by any TC at any spatial scale. However, this kind of dynamic simulations are a very computationally expensive task to be implemented in an operational inundation forecasting system, particularly for Small Island Developing States (SIDS) where computational resources are often limited. For this reason, in order to rapidly assess storm surge levels under the threat of occurrence of any TC, an additive model based on a library of pre-run cases has been developed.

Using Hydraulic Theory to Monitor Dense Overflows in a Parabolic Channel

Abstract Deep ocean passages are advantageous sites for long-term monitoring of deep transport and other physical properties relevant to climate. Rotating hydraulic theory provides potential for simplifying monitoring strategy by reducing the number of quantities that need to be measured. However, the applicability of these theories has been limited by idealizations such as restriction to zero or uniform potential vorticity (pv) and to channels with rectangular cross sections. Here the relationship between the flow characteristics in a canonical sea strait and its upstream condition is studied using uniform pv rotating hydraulic theory and a reduced-gravity shallow-water numerical model that allows for variation in pv. The paper is focused mainly on the sensitivity of the hydraulic solution to the strait geometry. We study the dynamics of channels with continuously varying (parabolic) cross sections to account for the rounded nature of sea-strait topographies and potentially improve monitoring strategies for realistic channel geometries. The results show that far enough from the channel entrance, the hydraulically controlled flow in the strait is insensitive to the basin circulation regardless of parabolic curvature. The controlled transport relation is derived for the case of uniform pv theory. Comparing the model to theory, we find that the measurement of the wetted edges of the interface height at the critical section can be used to estimate the volume flux. Based on this finding, we suggest three monitoring strategies for transport estimation and compare the estimates with the observed values at the Faroe Bank Channel. The results showed that the estimated transports are within the range of observed values. Significance Statement The paper investigates the relationship between the flow characteristics in an idealized sea strait and its upstream condition using rotating hydraulic theory and numerical modeling. We study the dynamics of channels with continuously varying (parabolic) cross sections to account for the rounded nature of sea-strait topographies and potentially improve monitoring strategies for realistic channel geometries. We suggest three monitoring strategies for transport estimation and apply the methods to the Faroe Bank Channel. Our estimates of dense water transport are within the range of observed values. This is significant, because the suggested monitoring strategies only require 1–3 measurements to estimate the transport at a given passage and can be used to guide observing systems.

High-resolution 2D shallow water modelling of dam failure floods for emergency action plans

High-resolution 2D shallow water modelling of dam failure floods for emergency action plans

Performance and limits of a shallow-water model for landslide-generated tsunamis: from laboratory experiments to simulations of flank collapses at Montagne Pelée (Martinique)

SUMMARYWe investigate the dynamics and deposits of granular flows and the amplitude of landslide-generated water waves using the HySEA depth-averaged shallow-water numerical model, both at laboratory and field scales. We evaluate the different sources of error by quantitatively comparing the simulations with (i) new laboratory experiments of granular collapses in different conditions (dry, immersed, dry flow entering water) and slope angles and (ii) numerical simulations made with the SHALTOP code that describes topography effects better than most depth-averaged landslide-tsunami models. For laboratory configurations, representing the limits of the shallow-water approximation in such models, we show that topography and non-hydrostatic effects are crucial. When topography effects are accounted for empirically—by artificially increasing the friction coefficient and performing non-hydrostatic simulations—the model is able to reproduce the granular mass deposit and the waves recorded at gauges located at a distance of more than two to three times the characteristic dimension of the slide with an error ranging from 1 to 25 per cent depending on the scenario, without any further calibration. Taking into account this error estimate, we simulate landslides that occurred on Montagne Pelée volcano, Martinique, Lesser Antilles as well as the generated waves. Multiple collapse simulations support the assumption that large flank collapses on Montagne Pelée likely occurred in several successive subevents. This result has a strong impact on the amplitude of the generated waves and thus on the associated hazards. In the context of the ongoing seismic volcanic unrest at Montagne Pelée volcano, we calculate the debris avalanche and associated tsunamis for two potential flank-collapse scenarios.

Wind-Forced Variability of the Zonal Overturning Circulation

AbstractThe mechanisms of wind-forced variability of the zonal overturning circulation (ZOC) are explored using an idealized shallow water numerical model, quasigeostrophic theory, and simple analytic conceptual models. Two wind-forcing scenarios are considered: midlatitude variability in the subtropical/subpolar gyres and large-scale variability spanning the equator. It is shown that the midlatitude ZOC exchanges water with the western boundary current and attains maximum amplitude on the same order of magnitude as the Ekman transport at a forcing period close to the basin-crossing time scale for baroclinic Rossby waves. Near the equator, large-scale wind variations force a ZOC that increases in amplitude with decreasing forcing period such that wind stress variability on annual time scales forces a ZOC ofO(50) Sv (1 Sv ≡ 106m3s−1). For both midlatitude and low-latitude variability the ZOC and its related heat transport are comparable to those of the meridional overturning circulation. The underlying physics of the ZOC relies on the influences of the variation of the Coriolis parameter with latitude on both the geostrophic flow and the baroclinic Rossby wave phase speed as the fluid adjusts to time-varying winds.Significance StatementThe purpose of this study is to better understand how large-scale winds at mid- and low latitudes move water eastward or westward, even in the deep ocean that is not in direct contact with the atmosphere. This is important because these currents can shift where heat is stored in the ocean and if it might be released into the atmosphere. It is shown that large-scale winds can drive rapid cross-basin transports of water masses, especially so at low latitudes. The present results provide a guide on what controls this motion and highlight the importance of large-scale ocean waves on the water movement and heat storage.

Optimal experiment design for a bottom friction parameter estimation problem

Calibration with respect to a bottom friction parameter is standard practice within numerical coastal ocean modelling. However, when this parameter is assumed to vary spatially, any calibration approach must address the issue of overfitting. In this work, we derive calibration problems in which the control parameters can be directly constrained by available observations, without overfitting. This is achieved by carefully selecting the ‘experiment design’, which in general encompasses both the observation strategy, and the choice of control parameters (i.e. the spatial variation of the friction field). In this work we focus on the latter, utilising existing observations available within our case study regions. We adapt a technique from the optimal experiment design (OED) literature, utilising model sensitivities computed via an adjoint-capable numerical shallow water model, Thetis. The OED method uses the model sensitivity to estimate the covariance of the estimated parameters corresponding to a given experiment design, without solving the corresponding parameter estimation problem. This facilitates the exploration of a large number of such experiment designs, to find the design producing the tightest parameter constraints. We take the Bristol Channel as a primary case study, using tide gauge data to estimate friction parameters corresponding to a piecewise-constant field. We first demonstrate that the OED framework produces reliable estimates of the parameter covariance, by comparison with results from a Bayesian inference algorithm. We subsequently demonstrate that solving an ‘optimal’ calibration problem leads to good model performance against both calibration and validation data, thus avoiding overfitting.

Modeling the Territorial Structure Dynamics of the Northern Part of the Volga-Akhtuba Floodplain

The subject of our study is the tendency to reduce the floodplain area of regulated rivers and its impact on the degradation of the socio-environmental systems in the floodplain. The aim of the work is to create a new approach to the analysis and forecasting of the multidimensional degradation processes of floodplain territories under the influence of natural and technogenic factors. This approach uses methods of hydrodynamic and geoinformation modeling, statistical analysis of observational data and results of high-performance computational experiments. The basis of our approach is the dynamics model of the complex structure of the floodplain. This structure combines the characteristics of the frequency ranges of flooding and the socio-environmental features of various sites (cadastral data of land use). Modeling of the hydrological regime is based on numerical shallow water models. The regression model of the technogenic dynamics of the riverbed allowed us to calculate corrections to the parameters of real floods that imitate the effect of this factor. This made it possible to use digital maps of the modern topography for hydrodynamic modeling and the construction of floods maps for past and future decades. The technological basis of our study is a set of algorithms and software, consisting of three modules. The data module includes, first of all, the cadastres of the territory of the Volga-Akhtuba floodplain (VAF, this floodplain is the interfluve of the Volga and Akhtuba rivers for the last 400 km before flowing into the Caspian Sea), satellite and natural observation data, spatial distributions of parameters of geoinformation and hydrodynamic models. The second module provides the construction of a multilayer digital model of the floodplain area, digital maps of floods and their aggregated characteristics. The third module calculates a complex territorial structure, criteria for the state of the environmental and socio-economic system (ESES) and a forecast of its changes. We have shown that the degradation of the ESES of the northern part of the VAF is caused by the negative dynamics of the hydrological structure of its territory, due to the technogenic influence the hydroelectric power station on the Volga riverbed. This dynamic manifests itself in a decrease in the stable flooded area and an increase in the unflooded and unstable flooded areas. An important result is the forecast of the complex territorial structure and criteria for the state of the interfluve until 2050.

Hydrokinetic Power Resource Assessment in a Combined Estuarine and River Region

The worldwide river and tidal hydrokinetic power potential is considerable. Harnessing such potential could allow the generation of a significant amount of sustainable electricity for local uses. To the present, most studies on hydrokinetic power have focused on large-scale commercial technology development, large tidal farms planning, and high-intensity resources assessment. Reduced attention was oriented towards investigating possibilities for small to medium-size hydrokinetic plants. However, given the characteristics of rivers and estuaries, in most cases, relevant hydrokinetic power exploitation possibilities exist regardless of the dimensions of the region considered. The planning of small to medium-size hydrokinetic plants for various aspects differs from larger developments. In the present work, a method for assessing the hydrokinetic resource is proposed and applied to the case study of the Douro waterway, which is characterized by moderate flow speeds and limited water depths. A high-resolution shallow-water numerical model is set up using ocean and river inflow boundary conditions. The flow velocities are estimated for the neap-spring period for different freshwater discharges. The spots presenting the highest annual hydrokinetic power average were identified, maximum flow speeds of about 1 m/s were found, and an annual mean power of 0.4 kW/m2 was estimated, indicating that prospects for hydrokinetic energy harvesting exist.

A Spatial Structure Variable Approach to Characterize Storm Events for Coastal Flood Hazard Assessment

Over the last decades, the evaluation of hazards and risks associated with coastal flooding has become increasingly more important in order to protect population and assets. The general purpose of this research was to assess reliable coastal flooding hazard maps due to overflow and wave overtopping. This paper addresses the problem of defining credible joint statistics of significant wave heights Hs and water levels ζ, focusing on the selection of the sample pair that characterizes each sea storm, to evaluate the occurrence probability of extreme events. The pair is selected maximizing a spatial structure variable, i.e., a linear combination of Hs and ζ, specific to each point of the area at risk. The structure variable is defined by the sensitivity of the flooding process to Hs and ζ, as found by analyzing a set of inundation maps produced through a Simplified Shallow-Water numerical model (SSW). The proposed methodology is applied to a coastal stretch in the Venetian littoral (Italy), by means of a 30 year-long time series recorded at the “Acqua Alta” oceanographic research tower, located in the Northern Adriatic Sea in front of the Venetian lagoon. The critical combination of Hs and ζ forming the structure variable is presented in a map, and it can be related to the topography and the presence of mitigation measures. The return period associated with the two recent large storms that occurred in this area in 2018 and 2019 is also investigated. The proposed procedure gives credible occurrence probabilities for these events, whereas other approaches would consider them extremely unlikely.

The exact solution to the Shallow water Equations Riemann problem at width jumps in rectangular channels

Riemann problems at geometric discontinuities are a classic and fascinating issue of hydraulics. In the present paper, the complete solution to the Riemann problem of the one-dimensional Shallow water Equations at monotonic width discontinuities is presented. This solution is based on the assumption that the relationship between the states immediately to the left and to the right of the discontinuity is a stationary weak solution of the one-dimensional variable-width Shallow water Equations. It is demonstrated that the solution to the Riemann problem always exists and it is unique, but there are cases where three solutions are possible. The appearance of multiple solutions is connected to a phenomenon, known as hydraulic hysteresis, observed for supercritical flow in contracting channel. The analysis of a Finite Volume numerical scheme from the literature (Cozzolino et al. 2018b) shows that the algorithm captures the solution with supercritical flow through the width discontinuity when multiple solutions are possible. Interestingly, the one-dimensional variable-width Shallow water Equations are formally identical to the one-dimensional Porous Shallow water Equations, implying that the exact solutions and the numerical scheme discussed in the present paper are relevant for two-dimensional Porous Shallow water numerical models aiming at urban flooding simulations. The exact solution presented here may be used not only as a benchmark, but also as a guide for the construction of new algorithms, and it can be even embedded in an exact solver.

Analysis of the Water Level Variation in the Polish Part of the Vistula Lagoon (Baltic Sea) and Estimation of Water Inflow and Outflow Transport through the Strait of Baltiysk in the Years 2008–2017

The Vistula Lagoon is located in both Poland and Russia along the southern coast of the Baltic Sea. It is connected to the Baltic Sea in the Russian part by the Strait of Baltiysk. The purpose of the paper is to identify the dominant factors underlying the water level variation mechanism at Tolkmicko in the Vistula Lagoon, revealed by a statistical analysis of the measured data and a discussion on the inflow and outflow transport variation through the strait, estimated by numerical modeling. Seawater transport is exceptionally valuable in terms of the hydrological water balance in the lagoon. Historical research on the hydrology of the lagoon shows that the water exchange in the lagoon is quite complex due to the presence of several different sources of water balance, such as seawater inflow, river inflow, groundwater inflow, precipitation, and evaporation. Unfortunately, there are no current data on seawater inflow and outflow through the Strait of Baltiysk due to the lack of continuous flow measurements in the strait. A novelty of the current work is an in-depth statistical analysis of the water level variation in the Polish part of the lagoon over a long time period and an estimation of water transport through the Strait of Baltiysk by use of a numerical model. The model reproduces well the water level variation responding to variations in the sea level outside the lagoon and the wind action over the lagoon. The years 2008–2017 were chosen as the analysis period. A two-dimensional free surface shallow water numerical model of the lagoon was adapted to simulate the water level variation in view of the wind over the lagoon and the sea level variation at one open boundary. Finally, it was concluded that the water level variation on the Polish side of the Vistula Lagoon is dominated by two factors: the water level in the Gulf of Gdańsk and the wind over the lagoon. The average annual marine water inflow into the Vistula Lagoon was estimated to be equal to 15.87 km3.

Salt-wedge dynamics in microtidal Neretva River estuary

The Neretva River estuary, located in Croatia, on the eastern coast of the Adriatic Sea, is a typical example of a micro-tidal salt-wedge estuary. Here, the salt-wedge dynamics was investigated based on continuous field measurements and numerical modeling for the period 2015-2018. A two-layer shallow-water numerical model proved to be an accurate and reliable tool for computing the salt-wedge dynamics in the Neretva River estuary. The simulations showed that the river inflow has the strongest impact on the salt-wedge dynamics, whereas sea levels and tides have a much smaller effect, mainly related to daily variations of the salt-wedge length and volume. A set of simple equations were derived, which link the salt-wedge intrusion length, salt-wedge volume, and salt-wedge spread to the river flow rate. It was shown that, during summer, the salt-wedge intrudes more than 20 km upstream from the mouth, exacerbating the salinization of aquifers and soils. The assessment of salt-wedge dynamics in the Neretva River estuary is thus a crucial element for planning, designing, and managing the irrigation system in this coastal region, for sustainable development of agriculture and protection of water resources. • A microtidal salt-wedge estuary in the Adriatic Sea is examined. • The salt wedge intrudes 25 km upstream from the river mouth in summer. • The salt wedge is completely flushed out from the estuary in winter. • A two-layer shallow water model is suitable for simulating the salt wedge dynamics. • Dependence was found between the salt wedge length, volume, and river flow rate.

Effects of forcing scale and intensity on the emergence and maintenance of polar vortices on Saturn and Ice Giants

We present numerical simulations to systematically explore the differences in the formation and maintenance of polar vortices under Saturnian (“S-Regime”) and Ice Giant (“I-Regime”) dynamical conditions. The wide variation of polar vortices observed on the gas giants Jupiter and Saturn by the Juno and Cassini spacecraft, respectively, and on the ice giants Uranus and Neptune by ground- and space-based telescopes, was recently captured in simulations by Brueshaber et al. (2019) (hereafter, ‘B19’) using the EPIC shallow-water numerical model. B19, expanding on a prior finding by O’Neill et al. (2015), reconfirmed this prior discovery that the dynamical regimes of giant planet polar vortices are controlled primarily by the planetary Burger number, B u = ( L d 0 ∕ a ) 2 , where L d 0 is the first-baroclinic deformation length at the pole, and a is the planetary radius. Small B u , matching estimates for Jupiter produce a Jupiter-like regime of multiple circumpolar cyclones (“J-Regime”). Larger B u , matching estimates of B u for Saturn and the Ice Giants, both produce a single cyclone over each pole; the resulting polar vortex has a larger diameter in the I-Regime than in the S-Regime. However, B19 found that the effect of B u alone was not sufficient to explain the differences in the polar vortices in the S- and I-Regimes. B19 speculated that the turbulent forcing scale and intensity had an impact on the size of the resulting polar vortices, which motivate the current study. Here, like in B19, we employ a shallow-water model forced by mass pulses that represent thunderstorms in which positive/negative mass pulses geostrophically adjust to form anticyclones/cyclones. We develop a new four-parameter experimental design to systematically test the role of (1) storm size, and (2) storm wind speed. In addition, we (3) investigate the role of the storm polarity fraction (the fraction of small-scale anticyclones to cyclones), using (4) B u values that sample the S- and I-Regimes. Our results provide new key insights into the dynamics of solitary polar cyclones that emerge on giant planets as a result of moist-convective forcing. We find that the wind speed of the polar cyclones within S- and I-Regimes is substantially influenced by storm size, storm wind speed, and storm polarity fraction. The radius of the polar cyclone is also influenced by the storm polarity fraction, but, is not influenced by the storm size or storm wind speed. Our new results clarify the role of storm forcing on the intensity and size of S- and I-Regime polar cyclones. Lastly, we resolve the conundrum found in B19 regarding polar cyclone circulations, providing a more dynamically consistent set of results of classifying polar cyclones into dynamical regimes based on B u . • Six key findings are presented for dynamic regimes that feature a solitary pole-centered cyclone on the giant planets. • The effects of turbulent forcing size and intensity on the resulting polar cyclones are investigated. • The polar cyclone’s winds are substantially influenced by storm size, storm wind speed, and storm polarity fraction. • The polar cyclone’s size is also influenced by the storm polarity fraction but not by the storm size or storm intensity.

Enhancing the resilience to flooding induced by levee breaches in lowland areas: a methodology based on numerical modelling

Abstract. With the aim of improving resilience to flooding and increasing preparedness to face levee-breach-induced inundations, this paper presents a methodology for creating a wide database of numerically simulated flooding scenarios due to embankment failures, applicable to any lowland area protected by river levees. The analysis of the detailed spatial and temporal flood data obtained from these hypothetical scenarios is expected to contribute both to the development of civil protection planning and to immediate actions during a possible future flood event (comparable to one of the available simulations in the database) for which real-time modelling may not be feasible. The most relevant criteria concerning the choice of mathematical model, grid resolution, hydrological conditions, breach parameters and locations are discussed in detail. The proposed methodology, named RESILIENCE, is applied to a 1100 km2 pilot area in northern Italy. The creation of a wide database for the study area is made possible thanks to the adoption of a GPU-accelerated shallow-water numerical model which guarantees remarkable computational efficiency (ratios of physical to computational time up to 80) even for high-resolution meshes (2.5–5 m) and very large domains (>1000 km2).

Numerical Investigations on the Instability of Boulders Impacted by Experimental Coastal Flows

Coastal boulders transported inland by marine hazards, such as tsunamis and storms, are commonly found worldwide. Studies on the transport process of coastal boulders contribute to the understanding of a wide range of phenomena such as high-energy flow events, fluid-structure interaction, and coastal sediments. Consequently, it is crucial to understand how boulders move, but even more important to determine the instability condition for boulder transport. The hydrodynamic formulas including drag and lift coefficients are widely used to predict the incipient motion of boulders while few studies are conducted to evaluate the capability of these formulas. Recently, a series of laboratory experiments carried out at the Hydraulic Engineering Laboratory (Italian acronym LIDR) of the University of Bologna, Italy, revealed that boulders can start moving when the flow height and flow velocity are lower than the theoretical threshold computed by hydraulic formulas. In this paper, we use a numerical shallow water model to reproduce these freely available laboratory data with the aim of testing the capability of the model in capturing the main evolution of the process, and of casting new light on the instability condition of coastal boulders.

Pohutukawa bio-shield on the coast of New Zealand as a tsunami mitigation strategy

New Zealand is vulnerable to both far-field and near-field tsunamis. The Pohutukawa tree (Metrosideros excelsa), a native tree to New Zealand, is commonly found in the New Zealand coastal environment. This tree has strong roots that grow deep into the ground, as well as have a wide spreading branching system. It is considered that these characteristics would enable the Pohutukawa tree to act effectively as a bio-shield against tsunamis in New Zealand. However, there is no research to show its capability in reducing the hydrodynamic force of a tsunami. Field investigation of the Pohutukawa tree in Maraetai Beach, and the use of a one-dimensional depth-integrated shallow water numerical model, was conducted to assess the capability of a Pohutukawa bio-shield against a tsunami wave. A Pohutukawa bio-shield of 35 m width against a tsunami wave of height of 3.5 m at shoreline with wave period of 20 min reduced the hydrodynamic force of a tsunami directly behind the bio-shield by approximately 21%. This study, therefore, elucidates the capability of a Pohutukawa bio-shield as a tsunami mitigation strategy.

Modelling the effect of suspended load transport and tidal asymmetry on the equilibrium tidal sand wave height

Abstract Tidal sand waves are rhythmic bed forms found in shallow sandy coastal seas, reaching heights up to ten meters and migration rates of several meters per year. Because of their dynamic behaviour, unravelling the physical processes behind the growth of these bed forms is of particular interest to science and offshore industries. Various modelling efforts have given a good description of the initial stages of sand wave formation by adopting a linear stability analysis on the coupled system of water movement and the sandy seabed. However, the physical processes causing sand waves to grow towards equilibrium are far from understood. We adopt a numerical shallow water model (Delft3D) to study the growth of sand waves towards a stable equilibrium. It is shown that both suspended load transport and tidal asymmetry reduce the equilibrium sand wave height. A residual current results in asymmetrical bed forms that migrate in the direction of the residual current. The combination of suspended load transport and tidal asymmetry results in predicted equilibrium wave heights comparable to wave heights found in the field.

A local time stepping algorithm for GPU-accelerated 2D shallow water models

Abstract In the simulation of flooding events, mesh refinement is often required to capture local bathymetric features and/or to detail areas of interest; however, if an explicit finite volume scheme is adopted, the presence of small cells in the domain can restrict the allowable time step due to the stability condition, thus reducing the computational efficiency. With the aim of overcoming this problem, the paper proposes the application of a Local Time Stepping (LTS) strategy to a GPU-accelerated 2D shallow water numerical model able to handle non-uniform structured meshes. The algorithm is specifically designed to exploit the computational capability of GPUs, minimizing the overheads associated with the LTS implementation. The results of theoretical and field-scale test cases show that the LTS model guarantees appreciable reductions in the execution time compared to the traditional Global Time Stepping strategy, without compromising the solution accuracy.

Hydrodynamics of long-duration urban floods: experiments and numerical modelling

Abstract. Flood risk in urbanized areas raises increasing concerns as a result of demographic and climate changes. Hydraulic modelling is a key component of urban flood risk analysis; yet, detailed validation data are still lacking for comprehensively validating hydraulic modelling of inundation flow in urbanized floodplains. In this study, we present an experimental model of inundation flow in a typical European urban district and we compare the experimental observations with predictions by a 2-D shallow-water numerical model. The experimental set-up is 5 m × 5 m and involves seven streets in each direction, leading to 49 intersections. For a wide range of inflow discharges, the partition of the measured outflow discharges at the different street outlets was found to remain virtually constant. The observations also suggest that the street widths have a significant influence on the discharge partition between the different streets' outlets. The profiles of water depths along the streets are mainly influenced by the complex flow processes at the intersections, while bottom roughness plays a small part. The numerical model reproduces most of the observed flow features satisfactorily. Using a turbulence model was shown to modify the length of the recirculations in the streets, but not to alter significantly the discharge partition. The main limitation of the numerical model results from the Cartesian grid used, which can be overcome by using a porosity-based formulation of the shallow-water equations. The upscaling of the experimental observations to the field is also discussed.

Planform evolution of two anabranching structures in the Upper Peruvian Amazon River

AbstractWe present a study to relate the sinuosity of the main channel and its effect on the dynamics of the secondary channels of anabranching structures. For this purpose, two locations of the Peruvian Amazon River were selected: (1) a site with a medium to high‐sinuosity main channel (MS site: Muyuy, Peru) and (2) a site with a low‐sinuosity main channel (LS site: at the triple boundary between Brazil, Colombia, and Peru). The main channels for both the MS and LS anabranching structures have freedom to migrate in the lateral direction, while at least one of their secondary channels is adjacent to the geological valley. For MS and LS sites, temporal analysis of planform evolution was carried out using 30 years of satellite imagery from which metrics such as width, sinuosity, and annual maximum migration rates of main and secondary channels were calculated. Additionally, detailed hydrodynamic and bed morphology field measurements were carried out, and a two‐dimensional shallow water numerical model was developed. For a medium to high‐sinuosity main channel anabranching structure, the secondary channels present a dominant mechanism for reworking the floodplain, while for the low‐sinuosity anabranching structure, the main channel planform dynamics is dominant. Flow velocities along the main and secondary channels for low, transition, and high‐flow discharges describe that for MS (LS) site, the velocities are much higher along the secondary (main) channels.