Inertial Equations Research Articles

Quantifying Compound and Nonlinear Effects of Hurricane‐Induced Flooding Using a Dynamically Coupled Hydrological‐Ocean Model

AbstractWe recently developed a dynamically coupled hydrological‐ocean modeling system that provides seamless coverage across the land‐ocean continuum during hurricane‐induced compound flooding. This study introduced a local inertial equation and a diagonal flow algorithm to the overland routing of the coupled system’s hydrology model (WRF‐Hydro). Using Hurricane Florence (2018) as a test case, the performance of the coupled model was significantly improved, evidenced by its enhanced capability of capturing backwater and increased water level simulation accuracy and stability. With four model experiments, we present a framework to detangle, define, and quantify compound and nonlinear effects. The results revealed that the flood peaks in the lower Cape Fear River Basin and the coastal waters were contributed by inland flooding and storm surge, respectively. These two processes had comparable contributions to the flooding in the Cape Fear River Estuary. The compound effect was identified when the flood levels resulting from the combination of land and ocean processes surpassed those caused by an individual process alone. The compound effect during Hurricane Florence exhibited limited impact on flood peaks, primarily due to the time lag between the peaks of the storm surge and the inland flooding. In the period between the two peaks, the compound effect was salient and significantly impacted the magnitude and variation of the flood level. The nonlinear effect, defined as the difference between the compound flood level and the superposition of storm surge and inland flooding water levels, reduced flood levels in the river channels while increasing flood levels on the floodplain.

Multi-pursuer pursuit differential game for an infinite system of second order differential equations

We study a pursuit differential game of many pursuers and one evader. The game is described by the infinite systems of $m$ inertial equations. By definition, pursuit in the game is completed if the state and its derivative of one of the systems are equal to zero at some time. In the literature, such a condition of completion of pursuit is also called soft landing. We obtain a condition in terms of energies of players which is sufficient for completion of pursuit in the game. The pursuit strategies are also constructed.

Analyzing the kinematics and longitudinal aerodynamics of a four-wing bionic aircraft

This paper designs a bionic aircraft model equipped with multiple degrees of freedom to study the inertial force equation and the aerodynamic interaction between its forewings and hindwings. Each wing’s phase difference angle (PDA) and stroke plane angle (SPA) are independently adjustable. Employing the kinematic equation of a single wing, we establish a model for the inertial force of the four-wing aircraft, validating its accuracy through experimental comparisons. Furthermore, we analyze various combinations of PDA and SPA parameters for the fore- and hindwings to ascertain the most efficient aerodynamic motion modes. Our findings reveal that aerodynamic interference between the fore- and hindwings tends to be unfavorable, predominantly due to the hindwings being exposed to the wake generated by the forewings, hindering their lift-capturing ability. Nevertheless, a specific PDA = 270° (forewing ahead of hindwing 270°) helps mitigate this interference across a wider range of SPA. Interestingly, when the stroke plane aligns parallel to the horizontal direction, asynchronous flapping of the fore- and hindwings, forming a lift mechanism akin to clap-and-fling wings, positively impacts lift. Consequently, staggered flapping of the fore- and hindwings reduces fuselage jitter and alleviates aerodynamic interference through specialized PDA, resulting in a temporary lift enhancement. The purpose of this study is to provide theoretical support for the longitudinal attitude control of four-wing aircraft.

An improved subgrid channel model with upwind-form artificial diffusion for river hydrodynamics and floodplain inundation simulation

Abstract. An accurate estimation of river channel conveyance capacity and the water exchange at the river–floodplain interfaces is pivotal for flood modelling. However, in large-scale models limited grid resolution often means that small-scale river channel features cannot be well-represented in traditional 1D and 2D schemes. As a result instability over river and floodplain boundaries can occur, and flow connectivity, which has a strong control on the floodplain hydraulics, is not well-approximated. A subgrid channel (SGC) model based on the local inertial form of the shallow water equations, which allows utilization of approximated subgrid-scale bathymetric information while performing very efficient computations, has been proposed as a solution, and it has been widely applied to calculate the wetting and drying dynamics in river–floodplain systems at regional scales. Unfortunately, SGC approaches to date have not included the latest developments in numerical solutions of the local inertial equations, and the original solution scheme was reported to suffer from numerical instability in low-friction regions such as urban areas. In this paper, for the first time, we implement a newly developed diffusion and explicit adaptive weighting factor in the SGC model. Adaptive artificial diffusion is explicitly included in the form of an upwind solution scheme based on the local flow status to improve the numerical flux estimation. A structured sequence of numerical experiments is performed, and the results confirm that the new SGC model improved the model performance in terms of water level and inundation extent, especially in urban areas where the Manning parameter is less than 0.03 m-1/3 s. By not compromising computational efficiency, this improved SGC model is a compelling alternative for river–floodplain modelling, particularly in large-scale applications.

Experimental Investigation of Wave-Induced Forces on a Large Quasi-Elliptical Cylinder during Extreme Events

Large quasi-elliptical cylinders are extensively used in ocean engineering. To enhance a better understanding of the hydrodynamic wave force on such quasi-elliptical cylinders during extreme events, a series of experiments on extreme wave interaction with a quasi-elliptical cylinder were conducted. A series of waves with various wave heights, wave periods, and wave incident directions were tested to investigate the wave parameter effect and wave directionality effect on the wave forces on the quasi-elliptical structure. The experimental results indicate that the extreme wave-induced forces on the quasi-elliptical cylinder are strongly correlated to the wave period and wave incident direction. The peak forces on the quasi-elliptical model do not vary monotonically with the increasing wave period but show an increase followed by a decrease. Both the longitudinal and transversal forces are significantly increased when the wave incident direction changes from 0° to 45° and the wave directionality effect is enhanced when the wave period is decreased. Additionally, the inertial force equation was applied to the wave force estimation for such quasi-elliptical cylinders, and the inertia coefficient CM was fitted based on the experimental results of α = 0°.

Magnetization switching in the inertial regime

We have numerically solved the Landau-Lifshitz-Gilbert (LLG) equation in its standard and inertial forms to study the magnetization switching dynamics in a $3d$ thin film ferromagnet. The dynamics is triggered by ultrashort magnetic field pulses of varying width and amplitude in the picosecond and Tesla range. We have compared the solutions of the two equations in terms of switching characteristic, speed and energy analysis. Both equations return qualitatively similar switching dynamics, characterized by regions of slower precessional behavior and faster ballistic motion. In case of inertial dynamics, ballistic switching is found in a 25 % wider region in the parameter space given by the magnetic field amplitude and width. The energy analysis of the dynamics is qualitatively different for the standard and inertial LLG equations. In the latter case, an extra energy channel, interpreted as the kinetic energy of the system, is available. Such extra channel is responsible for a resonant energy absorption at THz frequencies, consistent with the occurence of spin nutation.

On the well-posedness and decay characterization of solutions for incompressible electron inertial Hall-MHD equations

In this paper, by using the properties of decay character and the Fourier splitting method, we establish the time decay rates of solutions for three-dimensional incompressible electron inertial Hall-MHD equations. In particular, the optimal decay rates of the mixed space-time derivatives of the solution are obtained.

Radar-Updated Inertial Landing Navigation With Online Initialization

This article focuses on the employment of an inertial measurement unit (IMU) and a radar altimeter and velocimeter as navigation sensors for Mars landing navigation. At the beginning of the parachute descent phase, high dynamic oscillatory motion may saturate the gyroscope and produce large attitude estimation errors, thereby producing a high landing risk. To address this problem, an online navigation initialization algorithm is presented by combining data from the IMU and the radar. By defining a new inertial frame, attitude, and Mars-related velocity are conveniently initialized. A key contribution of this article is the computation of gravitational acceleration using IMU and velocimeter's measurements for the approximation of the nadir vector. Given the nadir vector, the inertial position is initialized in conjunction with the altimeter's measurement, the gravitational acceleration is modeled such that the inertial navigation equation can be propagated and the propagated altitude and velocity can be corrected by radar radar-derived measurements.

Investigation of the dynamics of the manipulator drive with a stepper motor

A mathematical model of the manipulator drive with a stepper motor is developed in the form of inductance equations, which is a source of reactive moment, inertial moment equation and angular velocity. Stepper motors work in the drives of manipulators with continuous movement, when the control action is given by a sequence of electrical pulses. The block diagram of the speed and current control loop of the stepper motor, given by the operator, is calculated in the computer (full step, direction, correction value for reverse speed, acceleration braking), the data is sent to the controller, in the controller the signals pass through the hard logic circuits and are sent to the driver. The stepper motor driver board generates a signal that is fed to the stator windings of the stepper motor. The results of mathematical modeling in MATLAB & Simulink are presented. The dependences of the oscillatory process of the system in the transients of the stepper motor, which are oscillatory in nature, are obtained. A comparison of the results of theoretical modeling of the operation of a step drive with experimental studies is given. As a result of the simulation, additional dynamics arise in the armature current circuit, however, at the point of the nominal mode, it does not significantly affect the angular velocity regulation processes, that is, the speed regulator provides its astatic regulation under the action of a constant load moment.

Solving the inertial particle equation with memory

The dynamics of spherical particles in a fluid flow is governed by the well-accepted Maxey–Riley equation. This equation of motion simply represents Newton’s second law, equating the rate of change of the linear momentum with all forces acting on the particle. One of these forces, the Basset–Boussinesq memory term, however, is notoriously difficult to handle, which prompts most studies to ignore this term despite ample numerical and experimental evidence of its significance. This practice may well change now due to a clever reformulation of the particle equation of motion by Prasath, Vasan & Govindarajan (J. Fluid Mech., vol. 868, 2019, pp. 428–460), who convert the Maxey–Riley equation into a one-dimensional heat equation with non-trivial boundary conditions. Remarkably, this reformulation confirms earlier estimates on particle asymptotics, yields previously unknown analytic solutions and leads to an efficient numerical scheme for more complex flow fields.

Allocation of distributed generation and capacitor banks in distribution system

<p>Voltage profile and power losses on the distribution system is a function of real and imaginary power loading condition. This can be effectively managed through the controlled real and reactive power flow by optimal placement of capacitor banks (CB) and distributed generators (DG). This paper presents adaptive Particle Swarm Optimization (MPSO) to efficiently tackle the problem of simultaneous allocation of DG and CB in radial distribution system to revamp voltage magnitude and reduce power losses. The modification to the conventional PSO was achieved by replacing the inertial weight equation (W) in the velocity update equation base on the particle best experience in the previous iteration. The inertial weight equation is designed to vary with respect to the iteration value in the algorithm. The proposed method was investigated on IEEE 30-bus, 33-bus and 69-bus test distribution systems. The results shows a significant improvement in the rate of convergence of APSO, improved voltage profile and loss reduction.</p>

Road profile reconstruction using connected vehicle responses and wavelet analysis

Practitioners analyze the elevation profile of a roadway to detect localized defects and to produce the international roughness index. The prevailing method of measuring road profiles uses a specially instrumented vehicle and trained technicians, which usually leads to a high cost and an insufficient measurement frequency. The recent availability of probe data from connected vehicles provides a method that is cost-effective, continuous, and covers the entire roadway network. However, no method currently exists that can reproduce the elevation profile from multi-resolution features of the vehicle inertial response signal. This research uses the wavelet decomposition of the vehicle inertial responses and a nonlinear autoregressive artificial neural network with exogenous inputs to reconstruct the elevation profile. The vehicle inertial responses are a function of both the vehicle suspension characteristics and its speed. Therefore, the authors normalized the vehicle response models by the traveling speed and then numerically solved their inertial response equations to simulate the vehicle dynamic responses. The results demonstrate that applying the artificial neural network to the wavelet decomposed inertial response signals provides an effective estimation of the road profile.

An Integrated Hydrological-Hydraulic Model for Simulating Surface Water Flows of a Shallow Lake Surrounded by Large Floodplains

An integrated hydrological-hydraulic model employing the 2-D local inertial equation as the core is established for effective numerical simulation of surface water flows in a great lake and its floodplain. The model is a cascade of validated hydrological and hydraulic sub-models. The model was applied to simulating the surface water flows of the Tonle Sap Lake and its floodplain in Cambodia using the roughness coefficient value calibrated comparing with a remote-sensing data set. The resulting model reasonably handles backwater flows during the rainy season and simulates the propagations of wet and dry interfaces without numerical instability, owing to a proper setting of time step supported by a novel numerical stability analysis. Sensitivity analysis of the surface water dynamics focusing on the setting of roughness coefficient and the backwater effect was also carried out. Overall, utilizing the 2-D local inertial equation in the assessment of lake water dynamics is a new modelling approach, which turns out to be an efficient simulation tool.

Characteristics of Process of Surmounting Obstacles by Downhole Tractors in Horizontal Shafts

A downhole tractor is a quick and efficient means of transporting logging devices and its obstacle performance directly influences the quality of the tractor’s work and is a critical element in studies of the tractor over-obstacle process. The construction of a faithful tractor over-obstacle model comprises (1) studies of the over-obstacle statics of the downhole tractor, including the relationship between the driving force of the motor, tractor resistance, and the height of the obstacle, along with the derivation of the static balance equation of the tractor over-obstacle process; (2) a dynamic analysis of the downhole tractor over-obstacle process, including compilation of the system of dynamic D’Alembert initial force equations and the system of D’Alembert inertial moment equations, and a more detailed description of the downhole tractor over-obstacle process, along with a more accurate calculation of the driving force required by the downhole tractor. It was found that matches downhole tractor prototype test data matches the data calculated by the analytic method. The use of the dynamic equations can increase the over-obstacle success rate of the downhole tractor in a horizontal well and solves the technical problems involved in overcoming obstacles.

Wetting and drying numerical treatments for the Roe Riemann scheme

ABSTRACTAccurate characterization of wetting-drying fronts in free surface flows is challenging because it is difficult and computationally demanding to track the exact position of the interface. This work presents a novel numerical treatment of the wetting-drying fronts applied to an approximate Roe Riemann solver and compares it to four other approaches. The numerical treatments were implemented both for the shallow water equations and for the local inertial equations. The results of this comparison overall showed a good agreement. For the tests conducted it was verified that element removal numerical treatments with global distributing of water can introduce errors and degenerate the solution introducing or displacing water upstream. Local correction and flux restricting numerical treatments show the best results. The negative depth numerical treatments provided similar results to the local correction and flux restricting numerical treatment, although with mass conservation errors.

A comparison of three dual drainage models: shallow water vs local inertial vs diffusive wave

In this study we compared three overland flow models, a full dynamic model (shallow water equation), a local inertial equations model (gravity wave model), and a diffusive wave model (parallel diffusive wave model). The three models are coupled with the same full dynamic sewer network model (SIPSON). We adopted the volume exchange between sewer and overland flow models, and the hydraulic head and discharge rates at the linked manholes to evaluate differences between the models. For that purpose we developed a novel methodology based on RGB scale. The test results of a real case study show a close agreement between coupled models in terms of the extents of flooding, depth and volume exchanged, despite highly complex flows and geometries. The diffusive wave model gives slightly higher maximum flood depths and a slower propagation of the flood front when compared to the other two models. The local inertial model shows to a slight extent higher depths downstream as the wave front is slower than the one in the fully dynamic model. Overall, the simplified overland models can produce comparable results to fully dynamic models with less computational cost.

Numerical stability analysis of the local inertial equation with semi- and fully implicit friction term treatments: assessment of the maximum allowable time step

Numerical stability analysis of the local inertial equation with semi- and fully implicit friction term treatments: assessment of the maximum allowable time step

Influence of sewer network models on urban flood damage assessment based on coupled 1D/2D models

One of the main steps in assessing flood risk in urbanised areas is the quantification of damage costs. Damage is often estimated based on depth‐damage curves for which depth maps are obtained (ideally) from coupled flood models. While the comparative analysis of flood damage models has been extensively researched in the literature, the influence of the underlying sewer network model has not been investigated. In this study, a 2D locally inertial equations flood risk analysis model (GWM) is coupled with two stormwater models (SWMM, tested with three different configurations, and SIPSON). The assessment of the network performance is made through the total exchanged volume between the surface and stormwater system, the surcharged conduits and manholes, maximum overland inundation and costs using a stepped version of the multi‐coloured manual depth‐damage curves for continuous urban fabric. The models behave similarly; however, they do show differences in the head pressures, number of surcharged manholes and maximum depth in some locations. The case study results show that despite the good agreement in damage between the four configurations (≈6% maximum disagreement), some localised high differences in maximum depth observed [0.25 (m)] exist. It was also shown that SWMM needs to be calibrated in order to perform similarly to Preissmann slot models.

Perturbed soliton excitations of Rao-dust Alfvén waves in magnetized dusty plasmas

We investigate the propagation dynamics of the perturbed soliton excitations in a three component fully ionized dusty magnetoplasma consisting of electrons, ions, and heavy charged dust particulates. We derive the governing equation of motion for the two dimensional Rao-dust magnetohydrodynamic (R-D-MHD) wave by employing the inertialess electron equation of motion, inertial ion equation of motion, the continuity equations in a plasma with immobile charged dust grains, together with the Maxwell's equations, by assuming quasi neutrality and neglecting the displacement current in Ampere's law. Furthermore, we assume the massive dust particles are practically immobile since we are interested in timescales much shorter than the dusty plasma period, thereby neglecting any damping of the modes due to the grain charge fluctuations. We invoke the reductive perturbation method to represent the governing dynamics by a perturbed cubic nonlinear Schrödinger (pCNLS) equation. We solve the pCNLS, along the lines of Kodama-Ablowitz multiple scale nonlinear perturbation technique and explored the R-D-MHD waves as solitary wave excitations in a magnetized dusty plasma. Since Alfvén waves play an important role in energy transport in driving field-aligned currents, particle acceleration and heating, solar flares, and the solar wind, this representation of R-D-MHD waves as soliton excitations may have extensive applications to study the lower part of the earth's ionosphere.

Analytical Solution of the Classical Dam-Break Problem for the Gravity Wave–Model Equations

AbstractSaint-Venant Equations (SVE) are often simplified for the sake of practicality, faster computational times, or physical representation. The Gravity Wave Model (GWM), or Local Inertial Equations, is a simplification of the SVE whereby the convective terms are neglected. The aim of this work is to present an analytical solution for the dam-break problem based on the GWM set of equations without source terms using the method of characteristics (MOC) and compare it with the analytical solution of SVE. The formulas for the depth and velocity are derived and explained along with the wave propagation characteristics. Conclusions are drawn about the propagation and analytical solution.