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In this work, we study the generalized shallow water wave equation to obtain novel solitary wave solutions. The application of this nonlinear model can be found in tidal waves, weather simulations, tsunami prediction, river and irrigation flows. To obtain the new exact solutions of the considered model, we have applied a novel analytical technique namely ( G ′ G ′ + G + A) -expansion method. Using the aforementioned method and computational software, we have obtained different kinds of periodic and singular solitary wave solutions of the generalized shallow water wave equation. The obtained solutions are exponential function and trigonometric function solutions. Using 2D and 3D plots of the wave solutions, the dynamic behaviors of the developed solutions are displayed. The retrieved solutions validated the effectiveness and robustness of the proposed technique. [ABSTRACT FROM AUTHOR]

In this work, we develop a new framework to deal numerically with discontinuous solutions in nonconservative hyperbolic systems. First an extension of the MOOD methodology to nonconservative systems based on Taylor expansions is presented. This extension combined with an in‐cell discontinuous reconstruction operator are the key points to develop a new family of high‐order methods that are able to capture exactly isolated shocks. Several test cases are proposed to validate these methods for the Modified Shallow Water equations and the Two‐Layer Shallow Water system. [ABSTRACT FROM AUTHOR]

To study the water management of natural rivers, two-dimensional (2D) hydrodynamic models have become essential tools. The performance of five different hydrodynamic modelling packages, SRH 2D (developed by U.S. Bureau of Reclamation), Delft 3D (developed by Deltares), FESWMS (developed by Federal Highway Administration), MIKE 21 FM (developed by DHI), and Hec Ras 2D (developed by US Army Corps of Engineers) was evaluated in this study. Numerical solutions to shallow water equations were obtained using finite elements, finite differences, and finite volumes. This work aims to provide the most accurate and objective information that can help select two-dimensional models for different annual scenarios. This study focused on comparing annual flow cases in-channel rather than flood flow. A study area on the Nile River was selected for this study. A performance assessment has been conducted based on the calibration of the model, the representation of the channel flow, and the computing efficiency of the model. The results show that Delft 3D and SRH 2D models were the most compatible with the measured data. Delft 3D model outperforms SRH 2D in computational efficiency up to 66% times faster. [ABSTRACT FROM AUTHOR]

A large Courant–Friedrichs–Lewy (CFL) algorithm is presented for the explicit, finite volume solution of hyperbolic systems of conservation laws, with a focus on the shallow water equations. The Riemann problems used in the flux computation are determined using averaging kernels that extend over several computational cells. The usual CFL stability constraint is replaced with a constraint involving the kernel support size. This makes the method unconditionally stable with respect to the size of the computational cells, allowing the computational mesh to be refined locally to an arbitrary degree without altering solution stability. The practical implementation of the method is detailed for the shallow water equations with topographical source term. Computational examples report applications of the method to the linear advection, Burgers and shallow water equations. In the case of sharp bottom discontinuities, the need for improved, well‐balanced discretisations of the geometric source term is acknowledged. [ABSTRACT FROM AUTHOR]

Keywords: Regularity criterion; bootstrap argument; Green's function; global existence; decay rate of solution.GraphBy Jie Qi and Weike WangReported by Author; Author [Extracted from the article]

The second-order discontinuous Galerkin (DG2) solver of the shallow water equations in LISFLOOD-FP 8.0 is well-suited for predicting small-scale transients that emerge in rapid, multiscale floods caused by impact events like tsunamis. However, this DG2 solver can only be used for simulations on a uniform grid where it may yield inefficient runtimes even when using its graphics processing unit (GPU) parallelised version (GPU-DG2). To maximise runtime reduction, the LISFLOOD-FP 8.2 version integrates GPU parallelised dynamic (in time) grid resolution adaptivity of multiwavelets (MW) with the DG2 solver (GPU-MWDG2). The GPU-MWDG2 solver requires selecting a maximum refinement level, L , based on size and resolution of the Digital Elevation Model (DEM) and an error threshold, ε ≤ 10-3, to preserve similar accuracy as a GPU-DG2 simulation on a uniform grid. The accuracy and efficiency of dynamic GPU-MWDG2 adaptivity is assessed for four tsunami-induced flooding test cases involving increasingly complex tsunamis: from single-wave impact events to wave trains. At ε = 10-3, the GPU-MWDG2 simulations yield predictions similar to the GPU-DG2 simulations but using ε = 10-4 can improve the accuracy in velocity-related predictions. In terms of efficiency, the GPU-MWDG2 simulations show progressively larger speedups over the GPU-DG2 simulations from L ≥ 10, which become significant (≥ 3.3- and 4.5-fold at ε = 10-4 and 10-3 , respectively) for simulating a single-wave impact event. The LISFLOOD-FP 8.2 code is open source, DOI: 10.5281/zenodo.4073010 , as well as the simulation data and the input files and scripts to reproduce them, DOI: 10.5281/zenodo.13909072 , with additional documentation at https://www.seamlesswave.com/Adaptive (last accessed: 9 October 2024). [ABSTRACT FROM AUTHOR]

In order to study the supercritical flow in a curved channel of a rectangular cross section, the classical shallow water equations in a cylindrical coordinate system based on the mass and momentum laws that take into account the friction and bottom slope are used. The obtained mathematical model forms nonlinear partial differential equations of first-order. For simplification, a linearization of the partial differential equations (PDEs) set is performed using small perturbation approach valid for weak bends (axial curvature radius extremely larger than the channel width). The governing equations with well-posed initial and boundary conditions were solved for a rectangular bend channel flow by applying the method of characteristics that is capable of transforming the hyperbolic partial differential equations to a system of ordinary differential equations (ODEs). The proposed model is tested and validated by comparing the results with broad available experimental data reported in the literature, and particular attention was paid to the wave maximum and its location. Comparisons indicate a reasonable agreement between the results obtained for the maximum flow depth along the outer channel wall. However, the model prediction is only reliable for a small relative curvature. Despite the model limitations, the results show the reliability and accuracy of the proposed approach for practical design purposes. [ABSTRACT FROM AUTHOR]

Predicting flood wave propagation from reservoir failures is critical to practical flood hazard assessment and risk management. Flood waves are sensitive to topography, channel geometry, structures, and natural features along floodplain paths. Thus, the accuracy of flood wave modelling depends on how precisely those features are represented. This study introduces an enhancing approach to flood wave modelling by accurately representing three-dimensional objects in floodplains using the structure-from-motion (SfM). This method uses an unmanned aerial vehicle to capture topographic complexities and account for ground objects that impact flood propagation. Using the three-dimensional volume of fluid numerical approach significantly improves an enhanced representation of turbulent flow dynamics and computational efficiency, especially in handling large topography datasets. Reproductions from this enhanced three-dimensional approach were validated against recent reservoir failure observations and contrasted with traditional two-dimensional models. The results revealed that the suggested three-dimensional methodology achieved a significant 84.4% reproducibility when juxtaposed with actual inundation traces. It was 35.5%p more accurate than the two-dimensional diffusion wave equation (DWE) and 17.1%p more than the shallow water equation (SWE) methods in predicting flood waves. This suggests that the reproducibility of the DWE and SWE decreases compared to the three-dimensional approach when considering more complex floodplains. These results demonstrate that three-dimensional flood wave analysis with the SfM methodology is optimal for effectively minimising topographic and flood wave reproduction errors across extensive areas. This dual reduction in errors significantly enhances the reliability of flood hazard assessments and improves risk management by providing more precise and realistic predictions of flood waves. [ABSTRACT FROM AUTHOR]

Coastal restoration projects are significantly important in coastal ecosystems as wetland losses accelerate. This study investigates tidal hydrodynamics and the potential impacts of a waterway opening on an existing roadway to restore and revitalise salt marshes in a small estuarine system in Virginia, USA. A depth-integrated, discontinuous Galerkin shallow-water equations model (DG-SWEM) is applied for astronomic tide simulation. The model employs a high-resolution unstructured mesh with a minimum element size of less than one meter and resolves complex tidal flows in the entire barrier island system, including the existing culvert gate and canal system. Compared to the existing system, the water exchange increased dramatically (flushing time also dramatically decreased) under the opened scenarios regardless of the opening width (22.9-, 30.5-, and 38.1-m width). By increasing the opening width, peak velocity through the proposed opening decreased 30–40%, and the maximum shear stress was reduced by more than half. The high-resolution model represented complex tidal flows, including eddies, and assisted in striking a balance of water-exchange capability, opening stability, and minimising their potential erosions for the opening design. Besides, erosion and sediment transport potentials for suspended sediments were estimated using bed shear stress and a Lagrangian particle tracking module. Such proxy modelling approach allows for the impact assessment of civil engineering and ecological waterworks in complex and highly damped tidal flow areas and is readily transferrable to other like systems (e.g. causeway construction, causeway cutting, biota passageways, and inlet modification). [ABSTRACT FROM AUTHOR]

In this study, the nonlinear two-dimensional Kadomtsev–Petviashvili-modified equal width (KP-MEW) equation is under investigation, which is described as a nonlinear wave model in weakly restoring forces and shallow water waves in the way of ferromagnetic, solitary waves in two dimensions with short amplitude and long wavelength and are also helpful in the investigation of various behaviors in nonlinear sciences. We successfully found the interesting and novel solitary wave results in bright solitons, kink solitons, dark solitons, anti-kink solitons, periodic singular solitons for nonlinear two-dimensional KP-MEW equation on the base of extension of simple equation technique under symbolic computational software Mathematica. The created solitons play an important role in nonlinear engineering and physics such as nonlinear optics, nonlinear dynamics, soliton wave theory, optical fiber and communication system. We are sure that these constructed results are novel and interesting which does not exist in the previous literature works. The graphical representation of constructed results is shown by 2D, 3D and contour graphs. The investigated research work proved that utilized technique is more concise, straightaway and efficient for study of other nonlinear partial differential equations. [ABSTRACT FROM AUTHOR]

This work employs the sub-ODE method to compute new soliton solutions for the component generalization of (2 + 1) -dimensional Schwarz–Kortweg–de Vries (SKdV) equation in shallow water waves. The rational soliton solutions (RSS), Jacobian elliptic function (JEF), periodic solutions (PS), hyperbolic function solutions (HFS), positive solitons, dark soliton solutions (DSS) and bright soliton solutions (BSS) are constructed with this technique. Solitons-like solutions, HFS and trigonometric-function solutions (TFS) are also found as the JEF's parameter m approaches values of 1 and 0, respectively. The suggested approach for the nonlinear equations in mathematical physics is concise, simple, effective, and promising. [ABSTRACT FROM AUTHOR]

We establish the full justification of a "Whitham-Green-Naghdi" system modeling the propagation of surface gravity waves with bathymetry in the shallow water regime. It is an asymptotic model of the water waves equations with the same dispersion relation. The model under study is a nonlocal quasilinear symmetrizable hyperbolic system without surface tension. We prove the consistency of the general water waves equations with our system at the order of precision O (μ 2 (ε + β)) , where μ is the shallow water parameter, ε the nonlinearity parameter, and β the topography parameter. Then we prove the long time well-posedness on a time scale O (1 max ⁡ { ε , β }). Lastly, we show the convergence of the solutions of the Whitham-Green-Naghdi system to the ones of the water waves equations on the later time scale. [ABSTRACT FROM AUTHOR]

Shallow-buried cavities and underground structures are inevitably subjected to transient perturbation from earthquakes or engineering activities during their life circle, leading to the occurrence of dynamic failure. The investigation presented by this paper concentrates on the dynamic responses triggered by an aperiodic transient P wave around a circular lined tunnel with an imperfect interface in a half-space and the spring model is employed to describe the interface between rock mass and liner. Resorting to the wave function expansion scheme, the large arc assumption, the Graf's addition theorem and the numerical inversion algorithm of Laplace transformation, the dynamic responses around a circular shallow lined tunnel with an imperfect interface are evaluated theoretically. The good agreement of time–history curves and contour snapshots for stress between the theoretical solutions and the numerical counterparts validates the analytical scheme. The effect of disturbance direction, embedment depth, thickness of liner and interface coefficients on the dynamic responses around the shallow-buried lined tunnel is analyzed. The results indicate that the positions of peak hoop dynamic stress concentration factor (DSCF) are approximately perpendicular to the perturbation direction. The DSCF distributions converge to be stable when the ratio of embedment depth to excavation radius exceeds 10.0. The thickness of the liner mainly affects the dynamic responses around the interface. Increase of elastic coefficient induces a decreasing DSCF in rock mass and an increasing counterpart in the liner. The results may provide the theoretical basis for the transient responses and aseismic design of underground tunnels. [ABSTRACT FROM AUTHOR]

Numerical simulations were generated to investigate the response of a very large floating airport to an airplane takeoff, using the set of nonlinear shallow water equations of velocity potential for water waves interacting with a floating thin plate. We have proposed two methods to reduce persistent airport vibration: reflectance reduction by decreasing the flexural rigidity in airport edge parts and amplification reduction by decreasing the still water depth partially under airport runways. First, when the flexural rigidity is uniformly decreased in an airport edge part, the reflectance of the floating body waves due to a B737 was reduced because of the multiple reflections. However, the wave reflectance for a B747 increased, depending on the conditions. A too-long edge part was not effective in reducing the wave reflectance. Conversely, when the flexural rigidity is linearly decreased in an airport edge part, the wave reflectance was reduced for both airplanes. Second, when the still water depth under an airport runway is partially reduced at the location where floating body waves are amplified, the wave heights of floating body waves tended to decrease as the still water depth in the shallower area decreased. [ABSTRACT FROM AUTHOR]

In this manuscript, we survey a numerical algorithm based on the combination of the homotopy perturbation method and the Sadik transform for solving the time-fractional nonlinear modified shallow water waves (called Kawahara equation) within the frame of the Caputo–Prabhakar (CP) operator. The nonlinear terms are handled with the assistance of the homotopy polynomials. The stability analysis of the implemented method is studied by using S-stable mapping and the Banach contraction principle. Also, we use the fixed-point method to determine the existence and uniqueness of solutions in the given suggested model. Finally, some numerical simulations are illustrated to display the accuracy and efficiency of the present numerical method. Moreover, numerical behaviors are captured to validate the reliability and efficiency of the scheme. [ABSTRACT FROM AUTHOR]

This study proposes a novel framework of the lattice Boltzmann model for multilayer shallow water equations, considering the mass and momentum exchanges between layers (LABMSWE+). Compared with the original LABMSWE model consisting of N two-dimensional lattice Boltzmann method for shallow water equation (LABSWE) models, the new model includes 1+N LABSWE models. The singular LABSWE model with unit relaxation time is introduced to update the total water depth, and thus, the layer water depths can be obtained explicitly through the fixed layer ratios. The N-layer LABSWE models with the multiple-relaxation-time operator evolve the layer velocities. These two modules are coupled by the total water depth and depth-averaged velocities. The constructed model avoids the freely variable layer thicknesses, which is considered as the main source of the instability. In addition, the mass exchanges enable this model to simulate vertical circulation flows, which are beyond the application of the LABMSWE model. Several numerical tests are then conducted to validate the proposed model. The results show that it exactly satisfies the C-property. In addition, the central difference scheme is more stable and accurate than the upwind and nonequilibrium schemes in the computing of the mass exchanges. The numerical results have an excellent agreement with analytical solutions and reference data, while some unstable and nonphysical results are obtained by the original LABMSWE model. Moreover, the computational time is about 40%–60% of that for the MIKE3, a finite volume solver for the three-dimensional shallow water equations by the Danish Hydraulic Institute. [ABSTRACT FROM AUTHOR]

The present work focuses on the numerical approximation of the weak solutions of the shallow water model over a non-flat topography. In particular, we pay close attention to steady solutions with nonzero velocity. The goal of this work is to derive a scheme that exactly preserves these stationary solutions, as well as the commonly preserved lake at rest steady solution. These moving steady states are solution to a nonlinear equation. We emphasize that the method proposed here never requires solving this nonlinear equation; instead, a suitable linearization is derived. To address this issue, we propose an extension of the well-known hydrostatic reconstruction. By appropriately defining the reconstructed states at the interfaces, any numerical flux function, combined with a relevant source term discretization, produces a well-balanced scheme that preserves both moving and non-moving steady solutions. This eliminates the need to construct specific numerical fluxes. Additionally, we prove that the resulting scheme is consistent with the homogeneous system on flat topographies, and that it reduces to the hydrostatic reconstruction when the velocity vanishes. To increase the accuracy of the simulations, we propose a well-balanced high-order procedure, which still does not require solving any nonlinear equation. Several numerical experiments demonstrate the effectiveness of the numerical scheme. [ABSTRACT FROM AUTHOR]

Compound flooding, the concurrence of multiple flooding mechanisms such as storm surge, heavy rainfall, and riverine flooding, poses a significant threat to coastal communities. To mitigate the impacts of compound flooding, forecasts must represent the variability of flooding drivers over a wide range of spatial scales while remaining timely. One approach to develop these forecasts is through subgrid corrections, which utilize information at smaller scales to "correct" water levels and current velocities averaged over the model scale. Recent studies have shown that subgrid models can improve both accuracy and efficiency; however, existing models are not able to account for the dynamic interactions of hydrologic and hydrodynamic drivers and their contributions to flooding along the smallest flow pathways when using a coarse resolution. Here, we have developed a solver called CoaSToRM (Coastal Subgrid Topography Research Model) with subgrid corrections to compute compound flooding in coastal systems resulting from fluvial, pluvial, tidal, and wind-driven processes. A key contribution is the model's ability to enforce all flood drivers and use the subgrid corrections to improve the accuracy of the coarse-resolution simulation. The model is validated for Hurricane Eta 2020 in Tampa Bay, showing improved prediction accuracy with subgrid corrections at 42 locations. Subgrid models with coarse resolutions (R2 = 0.70, 0.73, 0.77 for 3-, 1.5-, 0.75-km grids) outperform standard counterparts (R2 = 0.03, 0.14, 0.26). A 3-km subgrid simulation runs roughly 50 times faster than a 0.75-km subgrid simulation, with similar accuracy. [ABSTRACT FROM AUTHOR]

This work examines tsunami run-up processes within a building array partially sheltered by a high-elevation, finite length, seawall. Work was performed using numerical modeling of 2D shallow water equations with varying seawall length, wave height, time scale, and structure size. Inundation depth and flow velocity were output at many locations of interest throughout the structural array. The most important influence on results when compared to the no-wall case was the sheltering or clearance angle as defined from the end of the wall. Behind the wall, inundation depth and cross-shore velocity declined significantly as sheltering angles increased (more sheltered). Alongshore inundation velocity (parallel to the seawall) increased strongly with increasing sheltering angle. A longer wave time scale resulted in significant increase in inundation depth and velocity especially at locations sheltered by the wall. Larger structure size or blockage ratio also led to increased inundation depth and flow velocity. However, varying wave height gave little change in inundation and velocity patterns. These results will serve to provide a better understanding of the wave inundation within a coastal urban region in a tsunami event when the seawall is breached, as well as the influence of coastal structure size and spacing on the tsunami inundation. [ABSTRACT FROM AUTHOR]

In this study, we propose a modified version of section-averaged Boussinesq equations of Winckler-Liu. The model is reformulated in conservative variables, allowing a decoupling of the Shallow-Water equations and the dispersive problem. An appropriate hybrid finite volume and finite element discretisations are performed and verified with a solitary wave solution derived for the typical case of prismatic channels with a trapezoidal cross-section. For the finite volume step we compare upwind and energy conservative numerical fluxes. The impact of this choice on the long time dynamics for Favre waves is thoroughly investigated. The proposed model and numerical approximations can accurately reproduce the main features of the wave train's free surface. The impact of the numerical dissipation introduced by upwind fluxes is discussed, emphasising the need for precaution in their applications to evaluate quantities of engineering interest such as maximum wave amplitudes. • A reformulation of Winckler and Liu's model is proposed to study wave propagation in channels with arbitrary cross-sections. • The model simplifies dispersive terms integration into existing shallow water solver, enhancing computational flexibility. • Hybrid discretization method, combining finite volume and finite element is proposed. • Two numerical flux formulations and their dissipative behaviours are investigated over long propagation times of Favre waves. • Comparing with Favre waves laboratory experiments, the numerical model captures key propagation phenomena. [ABSTRACT FROM AUTHOR]

Due to the complexity of terrain and climate in the mountain–plain transition zone, it is difficult to simulate and forecast the flow discharge of river basins accurately. The poor regularity of the river thus leads to uncertain flood control scheduling. Meanwhile, reservoirs and flood detention areas are constructed to store and divert water when severe floods threaten the safety of the basin. In order to improve the accuracy of flood forecasts and the effectiveness of flood control, a hydrological and 1D/2D hydrodynamic coupling model was developed to enable the joint computation of multiple objects, including mountainous streams, plains river networks, hydraulic control structures, and flood detention areas. For the hydrological component, the Xin'anjiang model with the Muskingum module is employed to simulate mountainous flow discharge. For the hydrodynamic component, the Saint–Venant equations and shallow water equations are applied to estimate flood processes in rivers and on land surfaces, respectively. The Dongtiaoxi River Basin in Zhejiang Province, China, serves as the case study, where river flow is influenced by both upstream mountainous floods and downstream backwater effects. Using the integrated model, flood routing and scheduling are simulated and visualized. Both the Xin'anjiang model and the 1D hydrodynamic model demonstrate over 80% acceptability in calibration and validation, confirming their robustness and reliability. Meanwhile, inundation in flood detention areas can be effectively estimated by coupling the 1D and 2D hydrodynamic models with a flood diversion scheduling model. The coupled model proves capable of simulating flood routing in complex river basins that include mountains, plains, and hydraulic control structures, accounting for the interactions between hydrological elements. These findings provide a new perspective on flood simulation in other similarly complex river basins. [ABSTRACT FROM AUTHOR]

In this article, the performances of the SPH method to solve Shallow Water Equations SWEs with three investigation parameters were studied, such as the type of kernel functions, namely: cubic spline, Gaussian and quintic spline kernels, the number of particles used and the stabilization terms injected, specifically: Lax Friedrichs flux, artificial viscosity and two shocks Riemann solver. Three benchmarking tests make the subject of unsteady free surface flow in this study. It is 1D typical dam-break on wet and dry bottom; 2D partial dam-break on a dry floodplain and 2D partial dam-break on channel with 90° bend. The analysis of the different errors between the numerical and analytical solutions and/or the experimental data shows that the SPH method gives reliable values with the selected optimal parameters which are the cubic kernel function and the artificial viscosity term. The increase in the number of particles increases the precision but also the calculation time. [ABSTRACT FROM AUTHOR]

Flash floods typically occur suddenly within hours of heavy rainfall. Accurate forecasting of flash floods in advance using the two-dimensional (2D) shallow water equations (SWEs) remains a challenge, due to the governing SWEs being difficult-to-solve partial differential equations (PDEs). Aiming at shortening the computational time and gaining more time for issuing early warnings of flash floods, constructing a new relationship between water storage and outflow in the rainfall–runoff process is attempted by assuming the catchment as a water storage system. Through numerical simulations of the diffusion wave (DW) approximation of SWEs, the water storage and discharge are found to be limited to envelope lines, and the discharge/water-depth process lines during water rising and falling showed a grid-shaped distribution. Furthermore, if a catchment is regarded as a semi-open water storage system, then there is a nonlinear relationship between the inside average water depth and the outlet water depth, namely, the water storage ratio curve, which resembles the shape of a plume. In the case of an open channel without considering spatial variability, the water storage ratio curve is limited to three values (i.e., the upper, the steady, and the lower limits), which are found to be independent of meteorological (rainfall intensity), vegetation (Manning's coefficient), and terrain (slope gradient) conditions. Meteorological, vegetation, and terrain conditions only affect the size of the plume without changing its shape. Rainfall, especially weak rain (i.e., when rainfall intensity is less than 5.0 mm h -1), significantly affects the fluctuations of the water storage ratio, which can be divided into three modes: Mode I (inverse S-shape type) during the rainfall beginning stage, Mode II (wave type) during the rainfall duration stage, and Mode III (checkmark type) during rainfall end stage. Results indicate that the determination of the nonlinear relationship of the water storage ratio curve under different geographical scenarios will provide new ideas for simulation and early warning of flash floods. [ABSTRACT FROM AUTHOR]

The rotating thermal shallow water (RTSW) equations is a model for studying thin layer fluids with horizontal variations in material properties. A mathematically rigorous framework is developed for deriving new reduced slow dynamics equations of the multiple-scale RTSW equations with both balanced and unbalanced initial data over the spatial periodic domain. It is rigorously proved that the reduced slow dynamics of the RTSW equations is the thermal quasi-geostrophic (thermal QG) equations by proper rescaling. Moreover, by introducing appropriate elliptic equations and using the time-averaging technique, we further obtained the convergence rates of the solutions with unbalanced initial data. [ABSTRACT FROM AUTHOR]

In this article, we propose a new path-conservative discontinuous Galerkin (DG) method to solve non-conservative hyperbolic partial differential equations (PDEs). In particular, the method here applies the one-stage ADER (Arbitrary DERivatives in space and time) approach to fulfill the temporal discretization. In addition, this method uses the differential transformation (DT) procedure rather than the traditional Cauchy–Kowalewski (CK) procedure to achieve the local temporal evolution. Compared with the classical ADER methods, the current method is free of solving generalized Riemann problems at inter-cells. In comparison with the Runge–Kutta DG (RKDG) methods, the proposed method needs less computer storage, thanks to the absence of intermediate stages. In brief, this current method is one-step, one-stage, and fully-discrete. Moreover, this method can easily obtain arbitrary high-order accuracy both in space and in time. Numerical results for one- and two-dimensional shallow water equations (SWEs) show that the method enjoys high-order accuracy and keeps good resolution for discontinuous solutions. [ABSTRACT FROM AUTHOR]

This paper presents simulations of dam-break flows of Herschel–Bulkley viscoplastic fluids over complex topographies using the shallow water equations (SWE). In particular, this study aims to assess the effects of rheological parameters: power-law index (n), consistency index (K), and yield stress ( τ c ), on flow height and velocity over different topographies. Three practical examples of dam-break flow cases are considered: a dam-break on an inclined flat surface, a dam-break over a non-flat topography, and a dam-break over a wet bed (downstream containing an initial fluid level). The effects of bed slope and depth ratios (the ratio between upstream and downstream fluid levels) on flow behaviour are also analyzed. The numerical results are compared with experimental data from the literature and are found to be in good agreement. Results show that for both dry and wet bed conditions, the fluid front position, peak height, and mean velocity decrease when any of the three rheological parameters are increased. However, based on a parametric sensitivity analysis, the power-law index appears to be the dominant factor in dictating fluid behaviour. Moreover, by increasing the bed slope and/or depth ratio, the wave-frontal position moves further downstream. Furthermore, the presence of an obstacle is observed to cause the formation of an upsurge that moves in the upstream direction, which increases by increasing any of the three rheological parameters. This study is useful for an in-depth understanding of the effects of rheology on catastrophic gravity-driven flows of non-Newtonian fluids (like lava or mud flows) for risk assessment and mitigation. [ABSTRACT FROM AUTHOR]

This study aims to employ the extended direct algebraic method (EDAM) to generate and evaluate soliton solutions to the nonlinear, space-time conformable Estevez Mansfield-Clarkson equation (CEMCE), which is utilized to simulate shallow water waves. The proposed method entails transforming nonlinear fractional partial differential equations (NFPDEs) into nonlinear ordinary differential equations (NODEs) under the assumption of a finite series solution by utilizing Riccati ordinary differential equations. Various mathematical structures/solutions for the current model are derived in the form of rational, exponential, trigonometric, and hyperbolic functions. The wide range of obtained solutions allows for a thorough analysis of their actual wave characteristics. The 3D and 2D graphs are used to illustrate that these behaviors consistently manifest as periodic, dark, and bright kink solitons. Notably, the produced soliton solutions offer new and critical insights into the intricate behaviors of the CEMCE by illuminating the basic mechanics of the wave's interaction and propagation. By analyzing these solutions, academics can better understand the model's behavior in various settings. These solutions shed light on complicated issues such as configuration dispersion in liquid drops and wave behavior in shallow water. [ABSTRACT FROM AUTHOR]

The wave motions of the initial discontinuities in the inviscid shallow water wave model governed by the bad Jaulent-Miodek system are explored by the Whitham modulation theory and dynamical analysis. The $ N $-phase algebro-geometric solutions along with the related genus-$ N $ Whitham equations are derived by algebro-geometric method and Flaschka-Forest-McLaughlin approach, respectively. The complete classification of solutions to the bad Jaulent-Miodek system is carried out by solving the Whitham equations both theoretically and numerically. Some exotic phenomena of nonlinear wave motions such as rarefaction waves and dispersive shock waves are found in the inviscid shallow water. Particularly, the nonlinear wave motions including the two-phase algebro-geometric solutions are found in the inviscid shallow water wave. It is shown that the results from Whitham modulation theory agree very well with the numerical calculations and dynamical analysis. [ABSTRACT FROM AUTHOR]

Storm surge is a natural process that causes flood disasters in coastal zones and results in massive casualties and property losses. Therefore, storm surge inundation is of major concern in formulating appropriate strategies for disaster prevention and mitigation. However, traditional storm surge hydrodynamic models have large limits with respect to computational efficiency and stability in practical applications. In this study, a novel storm surge inundation model was developed based on a wetting and drying algorithm established from a simplified shallow-water momentum equation. The wetting and drying algorithm was applied to a rectangular grid that iterates through a cellular automata algorithm to improve computational efficiency. The model, referred to as the Hydrodynamical Cellular Automata Flood Model (HCA-FM), was evaluated by comparing the simulations to regional field observations and to a widely used hydrodynamic numerical model. The comparisons demonstrated that HCA-FM can reproduce the observed inundation distributions and predict results that are consistent with the numerical simulation in terms of the inundation extent and submerged depth with much improved computational efficiency (predicting inundation within a few minutes) and high stability. The results reflect significant advancement of HCA-FM toward efficient predictions of storm surge inundation and applications at large spatial scales. [ABSTRACT FROM AUTHOR]

This article focuses on the design of semi-implicit schemes that are fully well-balanced for the one-dimensional shallow water equations, that is, schemes that preserve all smooth steady states of the system and not just water-at-rest equilibria. The proposed methods outperform standard explicit schemes in the low-Froude regime, where the celerity is much larger than the fluid velocity, eliminating the need for a large number of iterations on large time intervals. In this work, splitting and relaxation techniques are combined in order to obtain fully well-balanced semi-implicit first and second order schemes. In contrast to recent Lagrangian-based approaches, this one allows the preservation of all the steady states while avoiding the complexities associated with Lagrangian formalism. [ABSTRACT FROM AUTHOR]

We present an algorithm to solve the dispersive depth-averaged Serre--Green--Naghdi equations using patch-based adaptive mesh refinement. These equations require adding additional higher derivative terms to the nonlinear shallow water equations. This has been implemented as a new component of the open source GeoClaw software that is widely used for modeling tsunamis, storm surge, and related hazards, improving its accuracy on shorter wavelength phenomena. We use a formulation that requires solving an elliptic system of equations at each time step, making the method implicit. The adaptive algorithm allows different time steps on different refinement levels and solves the implicit equations level by level. Computational examples are presented to illustrate the stability and accuracy on a radially symmetric test case and two realistic tsunami modeling problems, including a hypothetical asteroid impact creating a short wavelength tsunami for which dispersive terms are necessary. [ABSTRACT FROM AUTHOR]

The Serre–Green–Naghdi equations of water wave theory have been widely employed to study undular bores. In this study, we introduce a modified Serre–Green–Naghdi system incorporating the effect of an artificial term that results in dispersive and dissipative dynamics. We show that the modified system effectively approximates the classical Serre–Green–Naghdi equations over sufficiently extended time intervals and admits dispersive–diffusive shock waves as traveling wave solutions. The traveling waves converge to the entropic shock wave solution of the shallow water equations when the dispersion and diffusion approach zero in a moderate dispersion regime. These findings contribute to an understanding of the formation of dispersive shock waves in the classical Serre–Green–Naghdi equations and the effects of diffusion in the generation and propagation of undular bores. [ABSTRACT FROM AUTHOR]

Impulse waves result from submarine or subaerial landslides colliding with water. To model this multiphase disaster, it is imperative to gain a comprehensive understanding of the complex processes and interactions involved. Achieving accurate simulations over a wide area is computationally demanding and presents a significant challenge. In this paper, we analyze the 1946 Aleutian tsunami to assess the effectiveness of various models: SNAKE (rigid landslide model), Ls-Rapid (progressive landslide model advocated by the International Consortium on Landslides), and the Cornell Multi-grid Coupled Tsunami model. We integrate these models using Fortran, presenting two approaches: RL-SWE (rigid landslide-shallow water equations) and PL-SWE (progressive landslide-shallow water equations). The RL-SWE model assumes a rigid semi-ellipsoid sliding mass, while the PL-SWE model considers progressive failure. We conducted computational simulations and validated the results using observed data. Significantly, the PL-SWE model outperformed LS-Tsunami (linked to Ls-Rapid) in simulating submarine landslide-generated waves. This demonstrates the practicality of using the PL-SWE model for large-scale landslide-generated impulse wave simulations. [ABSTRACT FROM AUTHOR]

Methods for stabilising the turbulent cascade of potential enstrophy are analysed and compared for a compatible finite element discretisation of the rotating shallow water equations. These different approaches to upwinding the potential vorticity include the well-known anticipated potential vorticity method (APVM), streamwise upwind Petrov-Galerkin (SUPG) method, and a more recent method where the trial functions are evaluated downstream within the reference element. In all cases the upwinding scheme conserves both potential vorticity and energy, since the antisymmetric structure of the equations is preserved. The APVM leads to a symmetric definite correction to the potential enstrophy that is dissipative and inconsistent. The SUPG scheme introduces a consistent correction to the APVM scheme that acts as a backscatter term ensuring a richer depiction of turbulent dynamics. The downwinded trial function formulation results in the advection of downwind corrections, which analysis and numerical experiments show to be quantitatively similar to the SUPG scheme for a turbulent shear flow. The main difference between the SUPG and downwinded trial function schemes is in the energy conservation and residual errors. If just two nonlinear iterations are applied then the energy conservation errors are improved for the downwinded trial function formulation, reflecting a smaller residual error than for the SUPG scheme. We also present new temporal formulations by which potential enstrophy is exactly integrated across each time level. Results using these formulations are observed to be stable in the absence of any dissipation, despite the aliasing of grid scale turbulence. Using such a formulation and the APVM with a coefficient O (100) times smaller that its regular value leads to turbulent spectra that are greatly improved at the grid scale over the SUPG and downwinded trial function formulations with unstable potential enstrophy errors. [ABSTRACT FROM AUTHOR]

To improve computational efficiency while maintaining numerical accuracy, coupled hydrologic–hydrodynamic models based on non-uniform grids are used for flood inundation prediction. In these models, a hydrodynamic model using a fine grid can be applied to flood-prone areas, and a hydrologic model using a coarse grid can be used for the remaining areas. However, it is challenging to deal with the separation and interface between the two types of areas because the boundaries of the flood-prone areas are time dependent. We present an improved Multigrid Dynamical Bidirectional Coupled hydrologic–hydrodynamic Model (IM-DBCM) with two major improvements: (1) automated non-uniform mesh generation based on the D-infinity algorithm was implemented to identify the flood-prone areas where high-resolution inundation conditions are needed and (2) ghost cells and bilinear interpolation were implemented to improve numerical accuracy in interpolating variables between the coarse and fine grids. A hydrologic model, the 2D nonlinear reservoir model, was bidirectionally coupled with a 2D hydrodynamic model that solves the shallow-water equations. Three cases were considered to demonstrate the effectiveness of the improvements. In all cases, the mesh generation algorithm was shown to efficiently and successfully generate high-resolution grids in those flood-prone areas. Compared to the original M-DBCM (OM-DBCM), the new model had lower root-mean square errors (RMSEs) and higher Nash–Sutcliffe efficiencies (NSEs), indicating that the proposed mesh generation and interpolation were reliable and stable. It can be adequately adapted to the real-life flood evolution process in watersheds and provide practical and reliable solutions for rapid flood prediction. [ABSTRACT FROM AUTHOR]

Summary: Many environmental phenomena, such as flows in rivers or in coastal region can be characterised by means of the 'shallow approach'. A multi‐layer scheme allows to extend it to density layered shallow water flows (e.g., gravity currents). Although a variety of models allowing numerical investigation of single and multi‐layer shallow water flows, based on continuum and particle approaches, have been widely discussed, there are still some computational aspects that need further investigation. Focusing on the Lattice Boltzmann models (LBM), available multi‐layer models generally use the standard linear collision operator (CO). In this work we adopt a multi relaxation time (MRT) cascaded collision operator to develop a two‐layered liquid Lattice‐Boltzmann model (CaLB‐2). Specifically, the model solves the shallow water equations, taking into account two separate sets of particle distribution function (PDF), one for each layer, solved separately. Layers are connected through coupling terms, defined as external forces that model the mutual actions between the two layers. The model is validated through comparisons with experimental and numerical results from test cases available in literature. First results are very promising, highlighting a good correspondence between simulation results and literature benchmarks. [ABSTRACT FROM AUTHOR]

We derive a new quasilinear nonlocal shallow water equation of Camassa-Holm type with higher-order nonlinearities from the governing equations for large-amplitude gravity water waves, which incorporates an ambient underlying linear shear flow and can be recognized as the higher-order generalization of the compressible hyper-elastic rod model in the material science. The mathematical modeling is implemented for the rotational water flow in the general form compared with the known models. Moreover, the local well-posedness in Besov spaces of the corresponding Cauchy problem is studied. [ABSTRACT FROM AUTHOR]

The water hammer phenomenon, commonly acknowledged in pressurized pipe-flows is relevant to various water distribution systems. This phenomenon constitutes a major concern for hydraulic researchers and designer, given the dramatic consequences of this phenomenon on hydraulic structures and human life. This study aimed at expanding research on the water hammer waves in the free-surface flow framework. The main objective was to address a comprehensive simulation of the free-surface wave behavior caused by the abrupt closure of sluice-gate in prismatic open channel. The one-dimensional Saint-Venant equations embedding the Boussinesq add-on was used to predict the free-surface wave behavior; which was discretized using the (2–4)-dissipative scheme. Results evidenced the analogy between the water hammer wave behavior in free-surface and pressurized pipe flows. Furthermore, results illustrated that the water hammer maneuver produced a sudden depth rise, about three times of the normal depth value in the cross section adjacent to the gate. From a computational point of view, the proposed solver provided simplicity and accuracy attributes in simulating shock-waves in free-surface-flow. This solver also consumed low computational time compared with the conventional or multiple grid technique – based Finite Element Algorithm. [ABSTRACT FROM AUTHOR]

This research delves into the comprehensive study of the mathematical model governing the propagation of tsunami waves along ocean coastlines in imprecise or uncertain environment. The model is based on the widely used shallow-water assumption, which can be represented by a system of non-linear fuzzy partial differential equations. Utilizing fuzzy numbers to represent the problem's uncertainty may have distinct advantages from a certain perspective. As such, this work employs the homotopy perturbation method (HPM) to obtain fuzzy approximate analytical solutions for the governing model under various coastal slopes and ocean depths. The addition of uncertainty to the model may add complexity to the methodology. Therefore, a double parametric approach has been integrated into the HPM procedure. This approach allows us to analyze the impact of coastal slope and sea depth on tsunami wave characteristics, specifically wave velocity and run-up height, in uncertain environments. Furthermore, the numerical results obtained for fuzzy tsunami wave velocity and wave height resemble the real behavior of tsunamis. These can be seen through the given fuzzy plots, both in 2D and 3D forms. Finally, to validate the obtained solutions, a comparison has been made between the special case of the present fuzzy solutions and the existing precise (crisp) solutions. [ABSTRACT FROM AUTHOR]

As water flow erodes bed sediment in a steep channel, a partly saturated debris flow, which has an unsaturated layer in its upper part, develops while interacting with a subsurface flow in the bed sediment; however, this interaction remains unclear. This study developed a numerical model that links the shallow water equation representing surface flows (i.e., fully and partly saturated, hyperconcentrated, and turbulent flows) with the depth-averaged Richards equation representing subsurface flows. The shallow water equation incorporates a new resistance equation, which accurately reproduces previous experimental results on steady uniform fully and partly saturated flows. The numerical model successfully replicated our experimental results on the evolution of a partly saturated flow. The sensitivity analysis of the numerical model demonstrated that the front velocity of a debris flow over the 4.0-m-thick bed is 28% smaller than that over the 0.6-m-thick bed and that over the unsaturated bed sediment is 22% smaller than that over bed sediment saturated through the entire layer. The decreases in front velocities are due to water seeping through the bed surface. Additionally, the analysis revealed that water infiltrating through a bed surface triggers the transition of a debris flow front from fully to partly saturated flow when the channel gradient ranges from 18 to 19°. We concluded that the interaction between the process of infiltration in the bed sediment and the development of a debris flow should be considered for accurate prediction of debris flow development processes in a steep channel. [ABSTRACT FROM AUTHOR]

On 18 March 2021 an earthquake of magnitude M w = 6.0 occurred offshore the Algerian coasts and generated a tsunami with offshore amplitudes smaller than a few millimetres crossing the western Mediterranean Sea. The objective of this study is threefold: first, to determine whether seismic sources calculated in the context of tsunami early warning are relevant; secondly, to determine whether tsunami simulations are able to reproduce tide-gauge observations and thirdly, to define the sensitivity of simulations to the grid resolutions and tsunami parameters. In the Mediterranean Sea, a very small number of available coastal tide gauges recorded the tsunami. Among them, a few French tide gauge stations recorded water waves with amplitudes smaller than a few centimetres and with periods ranging from 5 to 20 min associated to harbour or bay resonances. Numerical simulations of the tsunami are performed by the operational code Taitoko for seven different source fault models. Three of them allow for a rapid source detection and characterization in the framework of tsunami warning at CENALT (Centre National d'Alerte aux Tsunamis, France). The integrated code Taitoko uses a system of multiple nested grids. Standard Boussinesq equations are solved in the Mediterranean grid, whereas non-linear shallow water equations are solved in coastal and harbour grids with 25 and 5 m resolutions, respectively. Whatever the fault model, the observed time-series of water heights are reproduced satisfactorily both in phase and amplitude by the model at Nice and Monaco but poorly at Port Mahon (Minorca) and Toulon. [ABSTRACT FROM AUTHOR]

The objective of this study is to propose and investigate two new forms of generalized variable coefficients within multi-dimensional equations describing shallow-water waves. We employ the Mathematica program to rigorously establish Painlevé's integrability for these two nonlinear equations. Subsequently, we constructed their bilinear forms and utilized Hirota's bilinear method to examine the dispersion relations and phase shifts of these two models that enable the derivative of multi-soliton solutions. Furthermore, diverse forms of lump-wave solutions are also considered. To illustrate the physical characteristics of these two models, we establish several graphical representations of the discovered solutions. These visualizations offer insights into the behavior, shape, and dynamics of both the multi-soliton, Peregrine soliton, lump wave, and rogue wave, enhancing our understanding of their physical significance. The two soliton solutions effectively replicate the shallow water waves, encompassing the T-, X-, and Y-types, along with other intricate interactions. Additionally, the lump and rogue wave structures are displayed to visually represent their spatial structures. These graphical representations offer a comprehensive view of the diverse wave phenomena observed in shallow water systems, aiding in the understanding of their spatial characteristics and interactions. Therefore, our findings indicate that the introduction of the two newly proposed integrable nonlinear evolution equations enhances the repertoire of integrable system models and aids in comprehending the distinctive characteristics of nonlinear dynamics in real-world applications. [ABSTRACT FROM AUTHOR]

A nondispersive, conservative regularisation of the inviscid Burgers equation is proposed and studied. Inspired by a related regularisation of the shallow water system recently introduced by Clamond and Dutykh, the new regularisation provides a family of Galilean-invariant interpolants between the inviscid Burgers equation and the Hunter–Saxton equation. It admits weakly singular regularised shocks and cusped traveling-wave weak solutions. The breakdown of local smooth solutions is demonstrated, and the existence of two types of global weak solutions, conserving or dissipating an H 1 energy, is established. Dissipative solutions satisfy an Oleinik inequality like entropy solutions of the inviscid Burgers equation. As the regularisation scale parameter ℓ tends to 0 or ∞ , limits of dissipative solutions are shown to satisfy the inviscid Burgers or Hunter–Saxton equation respectively, forced by an unknown remaining term. [ABSTRACT FROM AUTHOR]

A theory of large-scale flows in a rotating astrophysical plasma under conditions of non-trivial properties of the physical medium, which are not described by the classical hydrodynamic theory of plasma, is developed. As a first step, the theory is developed within a neutral fluid model to describe astrophysical plasma, with a subsequent generalization in mind to take into account magnetic effects. Such a model is of independent importance for studying turbulent dynamo in star-forming regions in galaxies and hydrodynamic instabilities in poorly ionized disks, for describing meridional flows below convective zones in low-mass stars and on the Sun, as well as for studying oscillations of the Sun and stars. Therefore, the results obtained have a wider application, e.g., for describing geophysical currents. The theory is based on two key ideas developed in plasma astrophysics: the use of a shallow water model with large-scale compressibility and the use of a two-layer shallow water model. Equations for two-layer shallow water are derived taking into account rotation and the effect of flow sphericity on rotation, in which the effects of large-scale compressibility are taken into account in the upper layer. For a rotating system, dispersion relations are obtained for Poincaré waves in two-layer shallow water, taking into account large-scale compressibility; similar dispersion relations for Poincaré waves are obtained in the high-frequency limit taking into account the effect of sphericity on rotation; in the low-frequency limit, a dispersion relation is obtained for Rossby waves. It is shown that the dispersion relations for Poincaré waves, taking into account the sphericity of the flow, have a qualitatively different form, which leads to three-wave interactions of Poincaré waves and the interaction of two Poincaré waves with a Rossby wave, which are not observed in a single-layer flow of a compressible fluid. All types of three-wave interactions for the flows under consideration are studied using the method of multiscale expansions. [ABSTRACT FROM AUTHOR]

For flood discharge structures with high water heads, aeration facilities are usually installed in engineering to promote water flow aeration and prevent cavitation damage to the overflow surface. Actual engineering has shown that as the slope of the discharge channel bottom decreases or water level changes lead to a decrease in the Froude number, the cavity morphology after conventional aeration facilities or allotype aerators is poor. This article proposes a curved aeration facility scheme based on the idea of locally increasing the bottom slope to reduce the impact angle, which is formed by the convex parabolic bottom plate and concave parabolic bottom plate. The convex parabolic bottom plate is tangent to a flat bottom plate behind the offset, and the concave parabolic bottom plate is tangent to the downstream. The jet landing point is controlled at the junction of the convex parabolic bottom plate and the concave parabolic bottom plate, and the lower jet trajectory is in line with the parabolic bottom plate. The corresponding parabolic bottom plate calculation formulas were theoretically derived, and the design method of the shape parameters of the aeration facility was provided. Through specific engineering case studies, it was found that: (1) As the ZAC/ZAG value increases, point C becomes closer to point G, the slope of the water tongue landing point C becomes steeper, and the cavity is less likely to return water. (2) When the position of the water tongue landing point is 0.5–0.8 times the height of the water tongue impact point, there is almost no water accumulation in the calculated cavity. At this time, the platform length LAB = 0.5LAF, the convex parabolic section length LBC = (0.45–0.6) LAG, the concave parabolic section length LCD = (0.43–0.11) LAG, the convex parabolic section calculation formula is z (x) = −A1x2 (A1 = 0.0059–0.00564), and the concave parabolic section calculation formula is A2x2 − B2x2 (A2 = 0.003347–0.01927).This solved the problem of aeration and corrosion reduction under small bottom slope, large-unit discharge, and low Froude number engineering conditions. [ABSTRACT FROM AUTHOR]

Landslide is a frequent geological hazard in the Three Gorges reservoir area of China. Impulse waves could be created and cause substantial damage if the landslide collides with a water body. A nonlinear shallow water equation in combination with a progressive landslide model is proposed to simulate this catastrophic disaster. The proposed approach is distinguished by rapid calculation, less computational burden, and high practical value. By simulating the 2008 Three Gorges Reservoir Gongjiafang landslide and the subsequent impulse waves, we illustrated and validated this methodology. The initiation and motion processes of the landslide, as well as the generation, propagation, and run-up processes of impulse waves, were thoroughly performed. The simulation results were in good agreement with the field survey data, demonstrating the viability of the proposed approach for simulating the impulse waves triggered by landslide events. This numerical approach is beneficial for engineers to perform a preliminary estimation of landslide-generated waves and further facilitate the prevention and mitigation of geological hazards. [ABSTRACT FROM AUTHOR]

The east coast of India is highly prone to devastating winds, torrential rainfall, and storm surges caused by tropical cyclones. The storm surge is affected by ocean basin characteristics involving the width and slope of the continental shelf. The bed roughness plays a major role in surge formation. The east coast of India is characterized by a broader shelf in the north and a narrow shelf in the south. This paper uses a hybrid Finite Volume Method–Finite Element Method based Shallow water equation (SWE) solver to predict the storm surges during different cyclone events, and the roughness parameter Manning's n is used in bed friction calculations. The bottom friction coefficient parameterization involving bed roughness is used to calibrate the resistance to flow in the numerical model. The calibration exercises are carried out with different values of n for each surge simulations for different cyclones to predict the surface elevation. Different statistical parameters against the measured values are used to analyze the impact of varying n values on predicted surge levels, and the most suitable n value is carefully chosen. The relationship between n and the bed slope is established as an expression, to replace the formulations involving Manning's n, thereby minimizing the usual computational efforts. The performance of the novel bed friction formulation involving the physical parameter in bed slope is demonstrated through statistical evaluations. [ABSTRACT FROM AUTHOR]

Transient, synoptic-scale vortices produce a large fraction of total rainfall in most monsoon regions and are often associated with extreme precipitation. However, the mechanism of their amplification remains a topic of active research. For monsoon depressions, which are the most prominent synoptic-scale vortex in the Asian–Australian monsoon, recent work has suggested that meridional gradients in zonal wind in the vortex environment may produce growth through barotropic instability, while meridional gradients in environmental humidity have also been proposed to cause amplification through coupling with precipitating convection. Here, a two-dimensional shallow water model on a sphere with parameterized precipitation is used to examine the relative role played by these two environmental gradients. By systematically varying the meridional moisture gradient and meridional wind shear for both weak, quasi-linear waves and finite-amplitude isolated vortices, we show that rotational winds in the initial vortex are amplified most strongly by meridional shear of the environmental zonal wind, while vortex precipitation rates are most sensitive to environmental moisture gradients. The growth rate in the presence of both gradients is less than the sum of growth rates in the presence of isolated gradients, as the phase relation between moisture and vorticity anomalies becomes distorted with increasing shear. These results suggest that background meridional gradients in both zonal wind and environmental humidity can contribute to the amplification of vortices to monsoon depression strength, but with some degree of decoupling of the dry rotational flow and the moist convection.

In this paper, we propose a new 3D model for vertical-axis tidal turbines (VATTs) embedded in the shallow-water code SHYFEM. The turbine model is based on the Blade-Element∖Momentum (BEM) theory and, therefore, is able to predict turbine performance based on the local flow conditions and the geometric characteristics of the turbine. It is particularly suitable for studying turbine arrays, as it can capture the interactions between the turbines. For this reason, the model is used to test a tidal farm of 21 devices with fluid dynamic simulations. In particular, we deploy the farm at Portland Bill, which is a marine site characterised by a wide spread in the direction of the tidal currents during a flood-ebb tide cycle. We optimised the lateral and longitudinal spacing of the turbines in a fence using computational fluid dynamics simulations and then performed a sensitivity analysis by changing the distance between the fences. The results show that the greater the distance between the fences, the higher the power output. The increase in power generation is around 16%, but this implies a huge increase in the horizontal extent of the farm. Further assessments should be carried out, as the expansion of a marine area dedicated to energy exploitation may conflict with other stakeholder interests. [ABSTRACT FROM AUTHOR]

This research aims to develop an efficient and accurate model for simulating tuned liquid dampers (TLDs) with sloped beds. The model, based on nonlinear shallow water equations, is enhanced by introducing new terms tailored to each specific case. It employs the central upwind method and Minmod limiter functions for flux and interface variable assessment, ensuring both high accuracy and reasonable computational cost. While acceleration, slope, and dissipation are treated as explicit sources, an implicit scheme is utilized for dispersion discretization to enhance the model's stability, resulting in matrix equations. Time discretization uses the fourth-order Runge–Kutta scheme for precision. The performance of the model has been evaluated using several test cases including dam-breaks on flat and inclined beds and run-up and run-down simulations over parabolic beds, which are relevant to sloshing in tanks with sloped beds. It accurately predicts phenomena such as asymmetric sloshing waves, especially in sloped beds, where pronounced waves occur. Dispersion and dissipation terms are crucial for capturing these effects and maintaining stable wave patterns. An initial perturbation method assesses the tank's natural period and numerical diffusion. Furthermore, the model integrates with a single-degree-of-freedom (SDOF) system to create a TLD model, demonstrating enhanced damping effects with sloped beds. [ABSTRACT FROM AUTHOR]