Kinematic Wave Research Articles

Dislocation Etching Morphology on the A Plane of Sapphire Crystal

AbstractIn this work, the dislocation etching pit morphology and etching kinetics on the A‐{110} plane of sapphire crystal (α‐Al2O3) are studied experimentally. The results show that the etch pit exhibits a subrhombic 3D morphology, which is consistent with the atom arrangement symmetry of the A plane. Further analysis shows that the two adjacent sides of the rhombic etch pits correspond to the directions [30] and [302], respectively; both of them are in the atomic close‐packing direction of A plane. The etch pits are controlled by a chemical reaction between Al2O3 and potassium hydroxide (KOH) with the reaction activation energy of 51.7 kJ mol−1, which is developed in a manner of kinematic wave by the step moving with a constant speed.

Stable local dynamics for day-to-day departure time choice

Existing dynamical systems for day-to-day departure time choice are either unstable, or stable but assuming drivers to possess complete information and make decisions on both arrival and departure times. In this paper, we present a new dynamical system with local shifting of departure times, such that a driver only defers or advances his/her departure time to a time interval later or earlier with lower costs. We establish the asymmetrical upper bounds of the deferral and advance coefficients for the discrete model to be well-defined. We then derive the continuous version as a kinematic wave model and present some examples of symmetrical deferral and advance coefficients. We demonstrate that the stationary state of the dynamical system is the same as the user equilibrium, and the user equilibrium is proved with Lyapunov's second method to be stable for the symmetrical deferral and advance coefficients. With numerical examples, we verify the analytical results and examine the model's sensitivity to different factors with different combinations of heuristic asymmetrical coefficients and theoretically stable symmetrical coefficients. Both analytical and numerical results confirm that the new dynamical system is asymptotically stable in a stability region. This study provides some guidelines on how to derive new day-to-day dynamical system models of departure time user equilibrium. Such a dynamical system can potentially be applied to solve the general dynamic traffic assignment problem in the future.

Applicability of Diffusive model for mud-flows: An unsteady analysis

Simplified versions of the Shallow Water Equations, known as Kinematic and Diffusive models, are commonly applied to the analysis of debris- and mud- flow dynamics. For this reason, the study of their applicability conditions represents an important concern. The present work investigates on the applicability conditions of the Diffusive Wave Model (DWM) for the prediction of mud-flows of shear-thinning fluid represented by a power-law rheology. The study has been carried out through the numerical solution of the DWM and the Full Wave Model (FWM) in unsteady conditions with hydrographs of different durations assigned at the channel inlet. The analysis has considered different rheological indexes, several values of the Froude (F) and of the Kinematic Wave (K) numbers. Predictions of DWM and FDM have been compared considering the mean value of dimensionless errors on maximum flow depth,εh*, and maximum discharge εq*. Positive (negative) error leads to an overestimation (underestimation) of the maximum flow depth and flow discharge in the prediction of the DWM. In the present analysis the DWM is considered safely applicable in case of underestimation, i.e. for positive values of εh* and εq*. Negative errors are acceptable if their absolute value is smaller than 5%. For all the investigated values of the governing parameters, the performance of the DWM has been found to strongly depend on the value of the rheological index, worsening as the fluid rheology becomes more shear-thinning. Regardless of the hydrograph duration, and for fixed power-law exponent (n) and F values, results indicate the existence of limiting values of the kinematic wave numberK-h and K-q above which the DWM is applicable in terms of maximum depth and discharge, respectively. For K values smaller than K-h and K-q, the DWM applicability depends also on the hydrograph duration. In these conditions and for several values of the (F, n) pair, the threshold values of the hydrograph duration necessary for DWM applicability have been identified. The presented applicability criteria represent a useful guideline for the practical application of the DWM in assessing the hazard of a mud flood.

Уравнения кинематической волны для размываемых русел

The mathematical model of kinematic wave, that is widely used in hydrological calculations, is generalized to compute processes in deformable channels. Self-similar solutions to the kinematic wave equations, namely, the discontinuous wave of increase and the “simple” wave of decrease are generalized. A numerical method is proposed for solving the kinematic wave equations for deformable channels. The comparison of calculation results with self-similar solutions revealed a good agreement.

Kinematic Wave Equations for Movable Riverbeds

Kinematic Wave Equations for Movable Riverbeds

Adaptive network traffic control with an integrated model-based and data-driven approach and a decentralised solution method

This paper presents an adaptive traffic controller for stochastic road networks with an integrated model-based and data-driven solution framework. The model-based optimisation component operates based upon an underlying kinematic wave model driven by stochastic demand within a prediction horizon. The data-driven optimisation component operates based upon an approximate dynamic programming (ADP) formulation which approximates the state-control interactions over future stages with a parametric approximator. The approximator reduces the computational complexity of the adaptive control problem by parameterising the state and decision space. The parametric approximator is to be iteratively updated with online feeding of realisations of traffic states via a temporal difference (TD) learning process. Our results reveal that incorporation of the model-based component facilitates the training of the ADP-based state approximator, and hence improve the overall performance of the control system. We further develop a decentralised solution approach in which individual intersections are allowed to derive their own control policies in an asynchronous manner. The data-driven ADP approximator would serve as a central agent coordinating the control policies derived at individual intersections in the network. This is shown to be able to improve and stabilise the performance of the overall control system even under congested conditions. This is a significant progress in adaptive control system design with use of decentralised optimisation techniques. The present study contributes to the adaptive network traffic control with uncertainties through use of advanced modelling and optimisation methods.

Space and Time Fractional Governing Equations of Unsteady Overland Flow

AbstractCombining fractional continuity and motion equations, the space and time fractional governing equations of unsteady overland flow were derived. The kinematic and diffusion wave approximatio...

Reconstruction of the MPD system parameters at the gas kicks into well with the measured surface data in situ by the mathematical modeling

One of the main problems of managed pressure drilling (MPD) is detection and monitoring of gas kicks from the formation to the annulus. The model is proposed to estimate the parameters of the gas kick and gas-liquid flow in a well during MPD process based on measurements performed only at the surface. A gas-liquid flow is described by the kinematic wave model. The ability of gaseous hydrocarbon to dissolve in mud, when drilling on an oil based mud (OBM), is taken into account. The hydrodynamic parameters of the flow are estimated by numerically solving the equations of fluid motion jointly with measured input data: the flowrate of the mud at inlet, the flowrate of gas-liquid mixture at outlet, and the surface back pressure (SBP). The control parameters are the change in mass gas and void fraction over the well depth and on time, as well as BHP. To verify the proposed model, the calculation of gas-liquid flow parameters is conducted on base of the detailed measured data of field test during drilling of 16,000-ft deep well using a water based mud (WBM). The pattern of the gas kick into the well from the formation is reconstructed, the change in void fraction during gas rising was traced until it was kicked to the surface, and the total mass of gas entering the well is determined. The error is estimated by comparing deviations of the measured and calculated bottomhole pressure (BHP) value.

A New Probabilistic Wave Breaking Model for Dominant Wind‐Sea Waves Based on the Gaussian Field Theory

AbstractThis study presents a novel method for obtaining the probability of wave breaking (Pb) of deep water, dominant wind‐sea waves (i.e., waves made of the energy within ±30% of the peak wave frequency) derived from Gaussian wave field theory. For a given input wave spectrum, we demonstrate how it is possible to derive a joint probability density function between wave phase speed (c) and horizontal orbital velocity at the wave crest (u) from which a model for Pb can be obtained. A nonlinear kinematic wave breaking criterion consistent with the Gaussian framework is further proposed. Our model would allow, therefore, the application of the classical wave breaking criterion (i.e., wave breaking occurs if u/c > 1) in spectral wave models which, to the authors' knowledge, has not been done to date. Our results show that the proposed theoretical model has errors in the same order of magnitude as six other historical models when assessed using three field data sets. With optimization of the proposed model's single free parameter, it can become the best performing model for specific data sets. Although our results are promising, additional, more complete wave breaking data sets collected in the field are needed to comprehensively assess the present model, especially in regards to the dependence on phenomena such as direct wind forcing, long wave modulation, and wave directionality.

Jam-Absorption Driving Strategy for Improving Safety Near Oscillations in a Connected Vehicle Environment Considering Consequential Jams

This article proposes an optimal jam-absorption driving (JAD) strategy, which not only prevents the occurring traffic oscillation but also avoids the consequential jam caused by the JAD vehicle. We first conducted a theoretical analysis to estimate the relationship between velocity and space headway within kinematic waves. Then an optimization function was formed to minimize the system travel delay. A procedure for specifying the absorbing vehicle was proposed. The performance of the JAD strategy was validated in a simulation model developed for the connected and automated driving environment. The results showed that by reaching a balance between the space headways in the “slow in” and “fast out” JAD execution stages, our optimal JAD strategy can successfully eliminate the oscillation without causing consequential jams. The collision risks measured by surrogate safety measures were reduced by 14.63% to 44.22% during the oscillation. Our strategies outperformed some previous ones in the same traffic condition. The proposed JAD strategy can effectively improve the safety situation on the freeway by eliminating traffic oscillations.

Simulating Flash Floods in Small Rivers of the Northern Caucasus with the Use of Data of Automated Hydrometeorological Network

Examples are given for numerical modeling of rain-induced flash floods in mountain areas based on actual and forecast data on precipitation. The calculated hydrographs are compared with the data of hydrometeorological network and calculations of other authors. Two hydrological models were applied: STREAM 2D CUDA, based on numerical solution of the shallow water equations in a two-dimensional (horizontal) formulation using an original algorithm, and KW-GIUH―a Geomorphological Instantaneous Unit Hydrograph model, based on kinematic wave equation. The direct numerical simulation of level regimes at the passage of flood wave and the incorporation of the accumulation of a part of flood flow by reservoirs–traps in the dynamic regime are new scientific results in hydrology. It is concluded that both models can be effectively used to forecast rain floods, in case reliable data on precipitation are available.

A synthetic equation for storage function model parameter estimation based on kinematic wave approximation

ABSTRACT The storage function model (SFM) is a rainfall–runoff model widely used in Korea for flood forecasting and warning systems. The traditional equations for parameter estimation are based on observed data under limited conditions, and so it is difficult to sensitively consider the factors affecting actual runoff. The aim of this study is to develop synthetic equations for SFM parameter estimation that are useful for ungauged watersheds, through 35 000 applications of the distributed kinematic wave model (KWM) for virtual watersheds. The parameter estimation equation developed in this study was applied to 101 observed events of 16 basins in Korea. We obtained satisfactory results from the application of a synthetic equation to actual basins. That is to say, the peak flood volume simulated by the equation was comparable with the observed volume. The relative error (RE), mean absolute percent error (MAPE), and percent bias (PBIAS) were used as criteria to evaluate the performance of the equation. For the results, RE and MAPE were within 10%, and PBIAS was within 15%.

A Diffusion-Based Analysis of a Multiclass Road Traffic Network

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows based on conservation laws that incorporate the macroscopic fundamental diagram (a functional relationship between vehicle density and flow). Our setup is capable of handling multiple types of vehicle densities, with general macroscopic fundamental diagrams, on a network with arbitrary topology. Interpreting our system as a spatial population process, we derive, under natural scaling, fluid, and diffusion limits. More specifically, the vehicle density process can be approximated with a suitable Gaussian process, which yield accurate normal approximations to the joint (in the spatial and temporal sense) vehicle density process. The corresponding means and variances can be computed efficiently. Along the same lines, we develop an approximation to the vehicles’ travel time distribution between any given origin and destination pair. Finally, we present a series of numerical experiments that demonstrate the accuracy of the approximations and illustrate the usefulness of the results.

Comparing Five Kinematic Wave Schemes for Open-Channel Routing for Wide-Tooth-Comb-Wave Hydrographs

AbstractDue to its simplicity, the kinematic wave is commonly applied to open-channel routing in watershed hydrologic modeling. However, these applications must fulfill certain conditions, such as ...

Overland Flow Characteristics Using Kinematic Wave Formulation.(Dept.C)

The characteristics of overland flow resulting from a uniform rainfall intensity on an impervious sloping plane are investigated. The characteristic solution of the one dimensional unsteady nonuniform flow equations with the kinematic wave approximation applied to the momentum equation is used. The influence of the different overland flow parameters on the synthesized hydrograph, the peak runoff discharge, and the time taken to reach equilibrium is studied for the case of turbulent flow. The overland flow parameters include the slope and the length of the plane, the surface resistance, and the uniform rainfall intensity. A dimensionless peak runoff hydrograph is determined and compared with both Izzard's experimental dimensionless hydrograph and the dimensionless hydrograph determined by the finite difference solution of the full dynamic form of the momentum equation.

Multiclass Traffic Flow Dynamics: An Endogenous Model

Vehicles on roads can be distinguished, each defined by its own set of properties (e.g., fleet length and free-flow speed). The traffic states on roads can be attributed to the longitudinal heterogeneity in vehicles. Vehicles slower than prevailing vehicles are defined as moving bottlenecks. On a multilane road section with multiple vehicle types, slower vehicles create moving bottlenecks and induce overtaking by faster vehicles so as to maintain their higher desired speed. The influence of single-class moving bottlenecks has been studied in the past. However, the impacts of multiple classes of moving bottlenecks have not yet been fully explored. This paper categorizes vehicles into passenger cars, medium trucks, and heavy trucks. By defining medium trucks and heavy trucks as moving bottlenecks, we develop analytical formulas for the fundamental diagram on a multilane road section with heterogeneous moving bottlenecks. The formula confirms that the composition of traffic and the longest truck platoon length influence the fundamental diagram. We then conduct simulations using a first-order kinematic wave model in Lagrangian coordinates to validate the fundamental diagram developed with the analytical formula and obtain promising results. This study provides fundamental knowledge for multiclass traffic modeling and multilane traffic operations.

Observing traveling waves in glaciers with remote sensing: new flexible time series methods and application to Sermeq Kujalleq (Jakobshavn Isbræ), Greenland

Abstract. The recent influx of remote sensing data provides new opportunities for quantifying spatiotemporal variations in glacier surface velocity and elevation fields. Here, we introduce a flexible time series reconstruction and decomposition technique for forming continuous, time-dependent surface velocity and elevation fields from discontinuous data and partitioning these time series into short- and long-term variations. The time series reconstruction consists of a sparsity-regularized least-squares regression for modeling time series as a linear combination of generic basis functions of multiple temporal scales, allowing us to capture complex variations in the data using simple functions. We apply this method to the multitemporal evolution of Sermeq Kujalleq (Jakobshavn Isbræ), Greenland. Using 555 ice velocity maps generated by the Greenland Ice Mapping Project and covering the period 2009–2019, we show that the amplification in seasonal velocity variations in 2012–2016 was coincident with a longer-term speedup initiating in 2012. Similarly, the reduction in post-2017 seasonal velocity variations was coincident with a longer-term slowdown initiating around 2017. To understand how these perturbations propagate through the glacier, we introduce an approach for quantifying the spatially varying and frequency-dependent phase velocities and attenuation length scales of the resulting traveling waves. We hypothesize that these traveling waves are predominantly kinematic waves based on their long periods, coincident changes in surface velocity and elevation, and connection with variations in the terminus position. This ability to quantify wave propagation enables an entirely new framework for studying glacier dynamics using remote sensing data.

Harnessing connected and automated vehicle technologies to control lane changes at freeway merge bottlenecks in mixed traffic

This paper proposes three control strategies for lane-changing (LC) at a merge bottleneck to improve bottleneck throughput by mitigating voids and speed disturbances in mixed traffic using connected and automated vehicle (CAV) technologies. Strategy 1 is ‘gap closure’ control, where an LC vehicle and its follower are controlled to close the void (extra time gap ahead) induced by the LC and prevent a backward-propagating speed disturbance. Strategy 2 is ‘batch LC’, where a group of LC vehicles are controlled to line up along a kinematic wave to minimize the total voids. Strategy 3 is ‘gap redistribution’ control, where extra gaps of vehicles are redistributed to periodically create large enough gaps for disturbance-free insertions. In a general control framework, the three strategies are integrated in different combinations exploiting their complementary nature. A numerical analysis shows that certain combinations, such as Strategy 2 and 3, can be very effective for improving bottleneck throughput. The analysis reveals insights on leveraging CAVs to develop traffic management strategies and/or policies and therefore improve system performance.

Macroscopic model of multidirectional pedestrian network flows

Pedestrian flow models are useful for the design and operation of pedestrian spaces. This article describes a macroscopic model of pedestrian flows through networks composed of bidirectional corridors that are connected by multidirectional intersections. The proposed model builds on an existing pedestrian bidirectional fundamental diagram to define bidirectional sending and receiving flows, and it relies on the incremental transfer principle to model bidirectional flows across nodes with an arbitrary number of adjacent links. The model is solved in a cell-transmission formulation that is in all of its unidirectional properties consistent with the kinematic wave model.

A Link Queue Model of Network Traffic Flow

Fundamental to many transportation network studies, traffic flow models can be used to describe traffic dynamics determined by drivers’ car-following, lane-changing, merging, and diverging behaviors. In this study, we develop a deterministic queueing model of network traffic flow, in which traffic on each link is considered as a queue. In the link queue model (LQM), the demand and supply of a link queue are defined in the queue size (number of vehicles), and its in- and out-flows are computed from junction flux functions corresponding to macroscopic merging and diverging rules. The new model is a system of ordinary differential equations that is mathematically tractable and computationally efficient and can capture queue spillbacks and interactions among links. We further demonstrate that the LQM is fundamentally different from the cell transmission model (CTM) and link transmission model (LTM) for a road segment, a signalized ring road, and a diverge-merge network, with respect to the shock and rarefaction waves, network fundamental diagram, and stability property. In a sense, the new model is a space-continuous approximation of the kinematic wave model and can be a useful addition to the multiscale modeling framework of network traffic flow. The model has been applied to formulate and solve network traffic control and observation problems.