Velocity Potential Research Articles

Land-Use-Change-Driven Erosion and Sediment Transport in the Yaqui River Sub-Basin (Mexico): Insights from Satellite Imagery and Hydraulic Simulations

Soil erosion and sediment transport are significant concerns in the Yaqui River sub-basin in northwest Mexico, driven by land use changes and environmental degradation. This study aims to evaluate erosion processes between 2000 and 2020 using a combination of satellite imagery and numerical simulations with Iber software (Version 2.5.2). The primary objective is to assess the impacts of land use changes, particularly the conversion of forest to grassland, on erosion rates and sediment transport. Satellite images from 2000 and 2020 were analyzed to detect land cover changes, while Iber’s sediment transport module was used to simulate erosion patterns based on the Meyer–Peter and Müller equation for bedload transport. Hydrological and topographical data were incorporated to provide accurate simulations of flow velocity, depth, and erosion potential. The results reveal a 35.3% reduction in forest cover, leading to increased erosion and sediment transport in steep areas. Simulation predictions highlighted areas with high future erosion potential, which are at risk of further soil loss if current trends continue. Flow velocity increased, contributing to riverbank destabilization and higher sediment yield, posing a risk to infrastructure such as the Álvaro Obregón Dam. This study underscores the need for targeted erosion control measures and sustainable land management practices to mitigate future risks and protect vital infrastructure in the Yaqui River Basin.

Water wave radiation by an array of bottom-mounted surface-piercing concentric cylinders

This paper develops a wave radiation analysis model in horizontal oscillation mode for concentric cylindrical arrays with arbitrary numbers and arrangements within the framework of linear potential flow theory. The concentric cylinders have solid inner cylinders and porous outer cylinders, and they are both bottom-mounted and surface-piercing. The porous boundary conditions of the outer cylinders are treated using Darcy's law, and the flow field is divided into one outer region and N (number of cylinders) inner regions with the outer cylinders as the boundary. Employing eigenfunction expansion and region-matching methods, expressions for the radiation velocity potential of each region are obtained, and then expressions of the added mass and damping coefficient of each cylinder are obtained. Following a rigorous verification of the results against published literature, this paper proceeds to analyze the impact of various parameters, including oscillation modes, outer cylinder permeability, radius ratio, spacing, and the number of cylinders, on the wave radiation characteristics of tandem-arranged cylindrical arrays. The research reveals that when the oscillation direction of the structure is parallel with its arrangement direction, the hydrodynamic coefficient curves exhibit significant spikes, attributed to the influence of the Dirichlet trapped mode. Outside the peak regions, the hydrodynamic coefficient curves display regular fluctuations, which are attributed to the alternating occurrence of constructive and destructive interference effects within the wave field.

Hydroelastic responses of a multi-modular very large floating structure on a flexible bottom with lateral stress in a two-layer fluid

Based on the small-amplitude water wave theory, an analytical investigation is performed for the interaction between incident waves and a multi-modular very large floating structure (VLFS) in a two-layer fluid with a flexible seabed. A vertical porous flexible plate is fixed in the center of each floating plate to suppress the hydroelastic response. A key innovation is the modeling of both the VLFSs and the seabed as thin elastic plates with the lateral stress. The analytical expressions for dispersion relationships and vertical eigenfunctions are exactly derived in the water regions with a flexible seabed. The series solution of the velocity potential is obtained through the combination of inner product and the least squares approximation method. The study uniquely illustrates the impact of lateral stress and flexible seabeds on wave propagation, revealing that at low frequencies, waves in both open water and plate-covered regions with a flexible seabed exhibit the similar propagation characteristics. At higher frequencies, however, the propagation characteristics of the waves in the open water regions remain unaffected by the presence of a flexible seabed. The lateral stress has significant effects on the roots of dispersion relationships and the hydroelastic responses. The influences of other physical parameters of the fluid and structures are also displayed graphically. The results demonstrate that the increasing number of modules and extending the vertical plates effectively suppress hydroelastic responses and reduce wave transmission. The porous barriers can reduce the stress on the vertical plates and weaken the effect of barriers for suppressing hydroelastic response.

Theory of quasi-ballistic FET: steady-state regimeand low-frequency noise.

Abstract We present the theoretical analysis of steady state regimes and lowfrequency
noises in quasi-ballistic FETs. The noise analysis is based on the Langevin
approach, which accounts for the microscopic sources of fluctuations originated from
intrachannel electron scattering. The general formulas for local fluctuations of the
carrier concentration, velocity and electrostatic potential as well, as their distributions
along the channel are found as functions of applied voltage/current. Two circuit
regimes with stabilized current and stabilized voltage are considered. The noise
intensities for the devices with different electron ballisticity in the channel are
compared.
We suggest that the presented analysis makes better comprehension of physics of
electron transport and fluctuations in quasi-ballistic FETs, improves their theoretical
description and can be useful for device simulation and design.

Effect of step bottom and waterway on flexural gravity wave scattering

Flexural gravity wave scattering by two semi-infinite non-identical ice sheets, which are separated by a clean water surface, is investigated in the presence of a step bottom topography. The problem is investigated in the cases of (i) intermediate water depth and (ii) shallow water. The effect of two edge conditions, (i) simply supported edge and (ii) free edge, on wave scattering is also analyzed. Employing linear velocity potential theory, the problem is studied in the frequency domain. The physical phenomenon is modeled as a boundary value problem having the Laplace equation as the governing equation, and it is solved using the eigenfunction expansion method. Considering the bottom topography and upper boundary, the fluid domain is divided into three regions, and in each region, velocity potential is expressed in terms of infinite Fourier series. Velocity and pressure are matched at the intermediate surface of two regions, and a system of algebraic equations with unknown coefficients is obtained. The complete solution of the present problem is recognized by solving the system of equations numerically. The energy relation is derived using Green's theorem. The reflection and transmission coefficients are computed and compared with the energy relation to check the accuracy of the present method. For different parameters (depth ratio, clean waterway, and different ice properties), reflection coefficient and transmission coefficient are computed and presented as a function of angular frequency. The value of the reflection coefficient ranges from zero to unity, whereas at certain frequencies, the transmission coefficient attends value more than unity.

Струйный эффект при возникновении присоединенной каверны от системы импульсивных давлений

We consider the plane problem of the emergence of an attached cavity caused by the sudden action of impulsive pressures at some initial time. It is assumed that these pressures are distributed on the upper part of the boundary of a stationary circular cylinder immersed in liquid. A problem with unilateral constraints is formulated, on the basis of which the flow of liquid at the initial moment of time and the initial zone of separation of liquid particles are determined. At the next moments of time, an attached cavity is formed, the shape of which is determined based on the solution of the dynamic initial-boundary value problem of the theory of potential flows of an ideal incompressible fluid with free boundaries. The main unknowns in it are the velocity potential, the shape of the cavity, the dynamics of the separation points, and the perturbation of the external free boundary of the liquid. It is required to study the posed problem at short times, focusing on the behavior of the internal free boundary of the liquid near the separation points. When studying this problem, pressure in the cavern, which is created artificially, plays an important role. At low pressures, the internal free boundary of the liquid near the separation point is located on opposite sides of this point. In this case, the end part of the cavity resembles a stream of gas directed along the boundary of the cylinder towards the liquid.

Probing the effect of time conformal factor on the particle dynamics around AdS Reissner–Nordström black hole

This study entails the effect of time on particle dynamics (both charged and uncharged) in the surrounding of the Reissner–Nordström AdS black hole in light of a general time conformal factor by acquiring Noether symmetry relation using the Lagrangian of the considered black hole spacetime. Upon acquiring the required time conformal spacetime as well as the Noether and approximated Noether symmetries along with their respective laws of conservation, the study further aims at investigating different parameters, like effective potential, effective force, and trajectories of escape velocity for the particle dynamics of the specified black hole. Additionally, in order to investigate orbit stability, the study employs the Lyapunov exponent.

Modeling of Filtration and Heat and Mass Transfer Processes in Groundwater

Purpose. The method of mathematical modeling is an important tool for solving complex problems involving the analysis of groundwater dynamics and heat and mass transfer processes in them when studying their contamination from various anthropogenic sources in the event of accidental spills of chemically hazardous substances, etc. The main purpose of the article is to develop a set of mathematical models for calculating the process of filtration of non-pressure groundwater, mass transfer of impurities and the process of heat transfer in groundwater. Methodology. The two-dimensional Boussinesq equation of filtration was used to predict the dynamics of groundwater. The two-dimensional equation of convective-diffusive transport of impurities was used to model the processes of mass transfer in groundwater. The process of freezing of individual sections of the groundwater flow is modeled using the Laplace equation for the velocity potential (calculation of the flow velocity field in a time-varying geometry) and the two-dimensional equation of heat transfer in groundwater. Finite difference schemes were used to solve the modeling equations of groundwater dynamics and heat and mass transfer. Findings. A set of mathematical models has been developed to calculate the process of filtration of non-pressure groundwater and its chemical contamination. The experiment has confirmed the adequacy of the constructed numerical model of filtration of a non-pressure groundwater flow. An effective mathematical model was developed that allows determining the temperature fields in groundwater during the operation of a well used to freeze certain sections of the flow. The results of computer modeling indicate the effectiveness of the developed mathematical models. Originality. Effective mathematical models for predicting the level of chemical contamination of groundwater, its dynamics and thermal regime are proposed. The constructed mathematical models make it possible to determine the dynamics of changes in the temperature regime of groundwater during the operation of wells through which refrigerant is supplied to freeze individual areas. A computer program has been developed that allows for a comprehensive assessment of groundwater conditions. Practical value. A set of computer programs has been developed to conduct a computational experiment to study the processes of filtration, chemical contamination of groundwater and heat transfer processes in them. This set of programs can be used for the scientific substantiation of engineering solutions aimed at protecting groundwater.

A novel variable-coefficient extended Davey–Stewartson system for internal waves in the presence of background flows

We propose a novel variable-coefficient Davey–Stewartson type system for studying internal wave phenomena in finite-depth stratified fluids with background flows, where the upper- and lower-layer fluids possess distinct velocity potentials, and the variable-coefficient terms are primarily controlled by the background flows. This realizes the first application of variable-coefficient DS-type equations in the field of internal waves. Compared to commonly used internal wave models, this system not only describes multiple types of internal waves, such as internal solitary waves, internal breathers, and internal rogue waves, but also aids in analyzing the impact of background flows on internal waves. We provide the influence of different background flow patterns on the dynamic behavior and spatial position of internal waves, which contribute to a deeper understanding of the mechanisms through which background flows influence internal waves. Furthermore, the system is capable of capturing variations in the velocity potentials of the upper and lower layers. We discover a connection between internal waves under the influence of background flows and velocity potentials. Through the variations in velocity potentials within the flow field, the dynamic behaviors of internal waves can be indirectly inferred, their amplitude positions located, and different types of internal waves distinguished. This result may help address the current shortcomings in satellite detection of internal wave dynamics and internal rogue waves.

Inverse problem for wave equation of memory type with acoustic boundary conditions

In this article, for the direct problem, which consists of finding the velocity potential and the displacement of boundary points in the wave equation of memory type with initial and boundary acoustic conditions, the inverse problem of determining the memory kernel by the integral overdetermination condition is studied. By introducing a new function, the problem is reduced to a problem with homogeneous boundary conditions. Using the technique of estimating integral equations and the contraction mappings principle in Sobolev spaces, the existence and uniqueness theorem for the inverse problem is proved.

Cellular Stress in Dry Eye Disease-Key Hub of the Vicious Circle.

Disturbance or insufficiency of the tear film challenges the regulatory systems of the ocular surfaces. The reaction of the surfaces includes temporary mechanisms engaged in the preservation of homeostasis. However, strong or persisting challenges can lead to the potential exhaustion of the coping capacity. This again activates the vicious circle with chronic inflammation and autocatalytic deterioration. Hence, the factors challenging the homeostasis should be addressed in time. Amongst them are a varying osmolarity, constant presence of small lesions at the epithelium, acidification, attrition with mechanical irritation, and onset of pain and discomfort. Each of them and, especially when occurring simultaneously, impose stress on the coping mechanisms and lead to a stress response. Many stressors can culminate, leading to an exhaustion of the coping capacity, outrunning normal resilience. Reaching the limits of stress tolerance leads to the manifestation of a lubrication deficiency as the disease we refer to as dry eye disease (DED). To postpone its manifestation, the avoidance or amelioration of stress factors is one key option. In DED, this is the target of lubrication therapy, substituting the missing tear film or its components. The latter options include the management of secondary sequelae such as the inflammation and activation of reparative cascades. Preventive measures include the enhancement in resilience, recovery velocity, and recovery potential. The capacity to handle the external load factors is the key issue. The aim is to guard homeostasis and to prevent intercellular stress responses from being launched, triggering and invigorating the vicious circle. Considering the dilemma of the surface to have to cope with increased time of exposure to stress, with simultaneously decreasing time for cellular recovery, it illustrates the importance of the vicious circle as a hub for ocular surface stress. The resulting imbalance triggers a continuous deterioration of the ocular surface condition. After an initial phase of the reaction and adaption of the ocular surface to the surrounding challenges, the normal coping capacity will be exhausted. This is the time when the integrated stress response (ISR), a protector for cellular survival, will inevitably be activated, and cellular changes such as altered translation and ribosome pausing are initiated. Once activated, this will slow down any recovery, in a phase where apoptosis is imminent. Premature senescence of cells may also occur. The process of prematurization due to permanent stress exposures contributes to the risk for constant deterioration. The illustrated flow of events in the development of DED outlines that the ability to cope, and to recover, has limited resources in the cells at the ocular surface. The reduction in and amelioration of stress hence should be one of the key targets of therapy and begin early. Here, lubrication optimization as well as causal treatment such as the correction of anatomical anomalies (leading to anatomical dry eye) should be a prime intent of any therapy. The features of cellular stress as a key hub for the vicious circle will be outlined and discussed.

Boussinesq model for two-fluid system with surface- and interfacial tension

A Boussinesq model associated with surface and internal waves with surface tension and interfacial tension in a two-layer fluid is presented in the application range of weakly dispersive nonlinear. The nonlinear form of model definitions in terms of surface and interfacial tensions along with velocity potentials are provided. Based on the perturbation technique, the Boussinesq equations for both layers are derived. The present Boussinesq result is validated against existing published results and it has a good level of agreement. Further, the present model results of crests of surface and interface displacements are compared with existing published numerical OpenFOAM simulations. The dispersion relations for fast- and slow modes are derived in the quadratic form of wave frequencies in the presence of surface and interfacial tensions. The second-order surface and internal wave displacements along with velocity potentials for upper- and lower-layer fluids are presented. The effects of surface and interfacial tensions on dispersion characteristics, harmonic transfer functions, and shoaling gradients on different physical parameters associated with the present model are studied by analyzing several numerical results. In the end, a real physical problem is demonstrated in the application of surface tension with solvents in the gas-liquid interface.

Dynamic response in a transversely isotropic and layered nonlocal poroelastic seabed subjected to vertical P-waves

A novel model is put forward to characterize the seismic response excited by vertical P-waves in a transversely isotropic and layered nonlocal poroelastic seabed. The proposed model integrates nonlocal parameter, anisotropy, and stratification to accurately examine wave propagation behavior. The fundamental equations for the underlying seabed are formulated using Biot's poroelastodynamic theory and Eringen's nonlocal theory. The wave equation for the overlying water is expressed in terms of the velocity potential. General solutions in both the poroelastic seabed and water layer are derived by solving the involved ordinary differential equations. Employing the newly devised and unconditionally stable propagator matrix scheme, semi-analytical solutions are derived for the time-harmonic response in a layered poroelastic seabed subjected to vertical P-wave excitation within the frequency domain. The validity of the proposed solutions is confirmed through rigorous comparison with the previously established analytical solutions. The influence of key material properties of seabed on the velocities of P-waves and free-field response in the poroelastic seabed is estimated in detail, along with the free-field response in a nonhomogeneous poroelastic seabed.

Investigation on the oblique water entry of the flared cavity

An experimental study of the oblique water entry of a flared cavity is reported in this paper. A numerical model is established that takes gas compressibility into account. This model effectively captures the additional flow phenomena that occur due to gas expansion and contraction within the cavity. There is a significant fluctuation phenomenon during the oblique water entry of the flared cavity, which is reflected not only in the movement of the water entry bubble but also in the slamming pressure. This fluctuation phenomenon is caused by the bottom cavity of the flared cavity, which adds the additional processes of external fluid inflow and internal fluid outflow compared with the closed-bottom structure, leading to additional flow due to conventional flow separation. When the external liquid flows into the cavity, the additional flow reduces the velocity potential of the fluid near the flow separation point, causing the bubble diameter near the flow separation point to contract. At the same time, the external liquid inflow causes the gas in the cavity to compress and the slamming pressure to increase. When the liquid flows out of the cavity, the additional flow increases the velocity potential of the fluid near the flow separation point, causing the bubble diameter near the flow separation point to expand. Meanwhile, the internal fluid outflow causes the gas in the cavity to expand and the slamming pressure to decrease.

A novel approach for using submerged structure as wave-trapping zone

Entrapment of waves is a hydrodynamic phenomenon that occurs under certain incident wave circumstances. The present article, based on potential flow theory, deals with the phenomena of waves interacting with a proposed submerged structure. Focus of this study is on the frequencies for which the wave trapping occurs in the region of the proposed structure. The frequencies presented correspond to significantly higher values of velocity potential in the region. We refer this region as a wave-trapping zone. In scattering problem the reflection coefficient is also investigated with respect to submergence depth, water depth, length and rigidity of the structure and other physical parameters. The optimum values of the structural parameters are also proposed for zero transmission and trapping frequencies. The investigation establishes that for a suitable configuration we can achieve a range of frequencies for which such a geometry can be used as breakwater with total reflection and at certain frequencies also for trapping of waves.

Effect of Flexible Tank Wall on Seismic Response of Horizontal Storage Tank

Horizontal storage tanks are integral to the petrochemical industry but pose significant risks during earthquakes, potentially causing severe secondary disasters. Current seismic designs predominantly assume rigid tank walls, which can lead to an underestimation of seismic responses. This study introduces a novel analysis method for assessing the dynamic response of flexible-walled horizontal storage tanks. By separating the liquid velocity potential into convective and impulsive components and integrating these with beam vibration theory, we developed a simplified mechanical model. A parameter analysis and dynamic response research were conducted using numerical methods. Results indicate that flexible tank walls amplify seismic responses, including liquid dynamic pressure peaks, base shear, and overturning bending moments, compared to rigid walls. Additionally, the impact of flexible walls is more pronounced in tanks with larger radii, aspect ratios, diameter–thickness ratios, and H/R ratios. These findings highlight the necessity for revised seismic design approaches that consider wall flexibility to enhance the safety and resilience of horizontal storage tanks.

Interaction of short-crested waves with cylinder and concentric segmented arc breakwaters

Using the outer breakwater of Palm Jumeirah in Dubai as a physical geometric model, the diffraction problem of short-crested waves interacting with concentric segmented arc structures was theoretically investigated using linear water wave theory. In this study, the watershed was partitioned into two regions, and a unique coordinate system was established to describe the velocity potential function within each region. The interface between the two regions connects the velocity potentials across them using the matching eigenfunction expansion technique. By accounting for the boundary conditions, the integral equation was streamlined into a series of algebraic equations, which were subsequently resolved to determine an unidentified function. The precision of the model was validated through a comparison with findings from the literature. Numerical investigations have elucidated the correlation between changes in wave force, cylinder run-up, and parameters such as the spacing between adjacent arcs, opening angle, and porous coefficient. The numerical results indicated that the impermeable segmented arcs structure provides better protection against short-crested and plane waves, whereas the permeable segmented arc structure provides better protection against standing waves. Interestingly, for a segmented three-arc structure, when the segments are moderately spaced, the protection of the interior region is superior to that of an unsegmented arc structure.

Kinematics of nonlinear waves over variable bathymetry. Part I: Numerical modelling, verification and validation

Fluid particle kinematics due to wave motion (i.e. orbital velocities and accelerations) at and beneath the free surface is involved in many coastal and ocean engineering applications, e.g. estimation of wave-induced forces on structures, sediment transport, etc. This work presents the formulations of these kinematics fields within a fully nonlinear potential flow (FNPF) approach. In this model, the velocity potential is approximated with a high-order polynomial expansion over the water column using an orthogonal basis of Chebyshev polynomials of the first kind. Using the same basis, original analytical expressions of the components of velocity and acceleration are derived in this work. The estimation of particle accelerations in the course of the simulation involves the time derivatives of the decomposition coefficients, which are computed with a high-order backward finite-difference scheme in time. The capability of the numerical model in computing the particle kinematics is first validated for regular nonlinear waves propagating over a flat bottom. The model is shown to be able to predict both the velocity and acceleration of highly nonlinear and nearly breaking waves with negligible error compared to the corresponding stream function wave solution. Then, for regular waves propagating over an uneven bottom (bar-type bottom profile), the simulated results are confronted with existing experimental data, and very good agreement is achieved up to the sixth-order harmonics for free surface elevation, velocity and acceleration.

Error analysis of a fully discrete projection method for Cahn–Hilliard Inductionless MHD problems

This article investigates the fully discrete finite element approximation and error analysis for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn–Hilliard equations, Navier–Stokes equations and Poisson equations, which are nonlinearly coupled through convection, stresses, and Lorentz forces. To address this highly nonlinear and multi-physics system, we propose a fully discrete energy stable scheme with the finite element projection method for spatial discretization, in which the velocity and pressure are decoupled. The temporal discretization is a combination of the first-order Euler semi-implicit scheme and a convex splitting energy strategy. We show that the proposed scheme is mass-conservative, charge-conservative and unconditional energy stable. The error estimates for the phase variable, chemical potential, velocity, pressure, current density and electric potential are rigorously established. Finally, several three-dimensional numerical experiments are performed to illustrate the features of the proposed numerical method and verify the theoretical conclusions.

A High-Efficiency Theorical Model of Von Karman–Generalized Wagner Model–Modified Logvinovich Model for Solving Water-Impacting Problem of Wedge

The water-impacting behavior of a wedge is often studied in the slamming phenomenon of ships and aircraft. Many scholars have proposed theoretical models for studying the water-impacting problem of a wedge, but these models still have some shortcomings. This study combines Von Karman’s method, the Generalized Wagner Model (GWM), and Modified Logvinovich Model (MLM) to establish a converged theoretical Von Karman-GWM-MLM (VGM) model. The VGM model utilizes added mass to replace the fluid influence, which is derived from the velocity potential and boundary conditions. Considering the influence of impulse, the velocity is determined by the momentum theorem. Subsequently, the pressure, resultant force, and acceleration of the wedge can be calculated. By comparing with the published test data of other scholars, it is found that the velocity, acceleration, pressure, and force of the wedge obtained by the VGM model reached a consensus with experiments. The validity and accuracy of the VGM model are also verified. The efficiency and accuracy of problem-solving are both balanced when using the VGM model. The establishment of the VGM model is significant for solving water-impacting problems related to wedges.