Roll Waves in Overland Flow

Roll waves are frequently observed in overland flow, especially in rill flow, which has an important effect on the development of soil erosion. Using one-dimensional St. Venant equations, this paper investigates the dynamics of periodic roll waves based on Dressler’s and Brock’s work. Under the assumption that the average flow depth equals the uniform flow depth, expressions of the roll-wave speed and roll-wave profile were obtained. Testing with the results observed by Brock (1970) for wave properties shows that these expressions can approximately describe the characteristics of periodic permanent roll waves. Numerical solutions of roll waves under specific conditions are found, which show that when a roll wave appears, the shear stress of flow increases, and the soil erosion accelerates.

Development of roll waves in open channels

This study is concerned with some of the properties of roll waves that develop naturally from a turbulent uniform flow in a wide rectangular channel on a constant steep slope . The wave properties considered were depth at the wave crest, depth at the wave trough, wave period, and wave velocity . The primary focus was on the mean values and standard deviations of the crest depths and wave periods at a given station and how these quantities varied with distance along the channel.

The wave properties were measured in a laboratory channel in which roll waves developed naturally from a uniform flow . The Froude number F (F = u_n/√gh_n, u_n = normal velocity , h_n = normal depth, g =acceleration of gravity) ranged from 3. 4 to 6. 0 for channel slopes S_o of . 05 and . 12 respectively . In the initial phase of their development the roll waves appeared as small amplitude waves with a continuous water surface profile . These small amplitude waves subsequently developed into large amplitude shock waves. Shock waves were found to overtake and combine with other shock waves with the result that the crest depth of the combined wave was larger than the crest depths before the overtake. Once roll waves began to develop, the mean value of the crest depths h_nmax increased with distance . Once the shock waves began to overtake, the mean wave period T_av increased approximately linearly with distance.

For a given Froude number and channel slope the observed quantities h^-_max/h_n , T' (T' = S_o T_av √g/h_n), and the standard deviations of h^-_max/h_n and T', could be expressed as unique functions of l/h_n (l = distance from beginning of channel) for the two-fold change in h_n occurring in the observed flows . A given value of h^-_max/h_n occurred at smaller values of l/h_n as the Froude number was increased. For a given value of h /hh^-_max/h_n the growth rate of δh^-_max/h^-_maxδl of the shock waves increased as the Froude number was increased.

A laboratory channel was also used to measure the wave properties of periodic permanent roll waves. For a given Froude number and channel slope the h^-_max/h_n vs. T' relation did not agree with a theory in which the weight of the shock front was neglected. After the theory was modified to include this weight, the observed values of h^-_max/h_n were within an average of 6.5 percent of the predicted values, and the maximum discrepancy was 13.5 percent.

For h^-_max/h_n sufficiently large (h^-_max/h_n > approximately 1.5) it was found that the h^-_max/h_n vs. T' relation for natural roll waves was practically identical to the h^-_max/h_n vs. T' relation for periodic permanent roll waves at the same Froude number and slope. As a result of this correspondence between periodic and natural roll waves, the growth rate δh^-_max/h^-_maxδl of shock waves was predicted to depend on the channel slope, and this slope dependence was observed in the experiments.

Roll waves evolution in high gradient channels to a non-Newtonian rheology

The criteria for the occurrence of roll wave phenomenon in the supercritical and turbulent Newtonian and non-Newtonian flows from the engineering point of view was analyzed. Imposing a constant discharge at the upstream of the canal and superposing a small perturbation, it was observed that roll waves can be developed more easily for small wave numbers and for high cohesions. Moreover, from the mathematical model used, it was demonstrated that the numerical viscosity was 10 times the physical viscosity.

Mitigação de riscos e catástrofes naturais: análise numérico-experimental de roll waves evoluindo em canais inclinados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Abordagem matemática de roll waves em escoamentos hiperconcentrados com superfície livre

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Um panorama sobre roll waves em escoamentos laminares e turbulentos com superfície livre

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estabilidade e controle dinâmico de roll waves

Pós-graduação em Engenharia Elétrica - FEIS

Implementação de aparato experimental para medição de instabilidades tipo Roll Waves em fluidos não- newtonianos

Pós-graduação em Engenharia Mecânica - FEIS

Experimental setup for measuring roll waves on laminar open channel flows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

可冲刷坡面滚波数值模拟研究

应用一维水沙耦合数学模型研究了可冲刷坡面上滚波的水动力学特性.模型的基本控制方程采用完整的、基于守恒定律的一维浅水动力学方程,运用能够捕捉激波和泥沙运动不连续性的WAF TVD二阶数值格式离散控制方程.通过复演定床滚波的运动特点,对模型进行了验证.可冲刷坡面的滚波数值模拟结果表明,床面形态对滚波水动力学特性有显著的影响.

纵波方位属性裂缝检测技术综合研究

Fractured oil and gas reservoir is an important type of oil and gas reservoir, which is taking a growing part of current oil and gas production in the whole world. Thus these technologies targeted at exploration of fractured oil and gas reservoirs are drawing vast attentions. It is difficult to accurately predict the fracture development orientation and intensity in oil and gas exploration. Focused on this problem, this paper systematically conducted series study of seismic data processing and P-wave attributes fracture detection based on the structure of ZX buried mountain, and obtained good results. This paper firstly stimulated the propagation of P-wave in weak anisotropic media caused by vertical aligned cracks, and analyzed the rule of P-wave attributes’ variation associated with observed azimuth, such as travel-time, amplitude and AVO gradient and so on, and quantitatively described the sensitive degree of these attributes to anisotropy of fracture medium. In order to further study the sensitive degree of these attributes to anisotropy of fractures, meanwhile, this paper stimulated P-wave propagation through different types and different intensity anisotropic medium respectively and summarized the rule of these attributes’ variation associated with observed azimuth in different anisotropic medium. The results of these studies provided reliable references for predicting orientation, extensity and size of actual complicated cracked medium by P-wave azimuth attributes responses. In the paper, amounts of seismic data processing methods are used to keep and recover all kinds of attributes applied for fracture detection, which guarantee the high accurate of these attributes, thus then improve the accurate of fracture detection. During seismic data processing, the paper adopted the three dimensional F-Kx-Ky field cone filter technique to attenuate ground roll waves and multiple waves, then enhances the S/N ratio of pre-stack seismic data; comprehensively applying geometrical spread compensation, surface consistent amplitude compensation, residual amplitude compensation to recover amplitude; common azimuth processing method effectively preserves the azimuthal characteristics of P-wave attributes; the technique of bend ray adaptive aperture pre-stack time migration insures to obtain the best image in each azimuth. Application of these processing methods guaranteed these attributes’ accuracy, and then improved the accuracy of fracture detection. After comparing and analyzing a variety of attributes, relative wave impedance (relative amplitude) attribute is selected to inverse the orientation of fracture medium; attenuation gradient and corresponding frequency of 85% energy are selected to inverse the intensity of fracture medium; then obtained the fracture distribution characteristics of lower Paleozoic and Precambrian in ZX ancient buried mountains. The results are good accord with the characteristics of faults system and well information in this area.

Control of instabilities in non-Newtonian free surface fluid flows

Free surface flows in inclined channels can develop periodic instabilities that are propagated downstream as shock waves with well-defined wavelengths and amplitudes. Such disturbances are called roll waves and are common in channels, torrential lava, landslides, and avalanches. The prediction and detection of such waves over certain types of structures and environments are useful for the prevention of natural risks. In this work, a mathematical model is established using a theoretical approach based on Cauchy's equations with the Herschel-Bulkley rheological model inserted into the viscous part of the stress tensor. This arrangement can adequately represent the behavior of muddy fluids, such as water-clay mixture. Then, taking into account the shallow water and the Rankine-Hugoniot's (shock wave) conditions, the equation of the roll wave and its properties, profile, and propagation velocity are determined. A linear stability analysis is performed with an emphasis on determining the condition that allows the generation of such instabilities, which depends on the minimum Froude number. A sensitivity analysis on the numerical parameters is performed, and numerical results including the influence of the Froude number, the index flow and dimensionless yield stress on the amplitude, the wavelength of roll waves and the propagation velocity of roll waves are shown. We show that our numerical results were in agreement with Coussot's experimental results (1994).

Rudder Roll Stabilisation of Ships

In this chapter, we present a case study of control system design for rudderbased stabilisers of ships using RHC. The rudder’s main function is to correct the heading of a ship; however, depending on the type of ship, the rudder may also be used to produce, or correct, roll motion. Rudder roll stabilisation consists of using rudder-induced roll motion to reduce the roll motion induced by waves. When this technique is employed, an automatic control system is necessary to provide the rudder command based on measurements of ship motion. The RHC formulation provides a unified framework to address many of the difficulties associated with this control system design problem.

Analysis of ship roll gyrostabiliser control

The use of dedicated spinning wheels that generate gyroscopic forces for reducing the roll motion of ships was considered and tested over 100 years ago. These devices, known as gyrostabilisers, presented a remarkable performance, but they fell into disuse due to their relatively large size and, primarily, due to the inability of the control systems to maintain performance over an extended envelope of sea states and sailing conditions (speed and heading relative to the waves). To date, advances in materials, mechanical design, electrical drives, and computer control systems have resulted in a revitalized interest in gyro-stabilisers for ships. This paper revisits the modelling of the coupled vessel-gyrostabiliser and delves into the associated gyrostabiliser control design problem. It also describes design trade-offs and potential performance limitations. A simulation study based on a navy patrol vessel is presented.