Propagation of shallow water waves in an open parabolic channel using the WKB perturbation technique

Bautista, E.; Méndez, F.; Bautista, O.; Mora, A.

doi:10.1016/j.apor.2011.03.002

Cited by 8 publications

(3 citation statements)

References 22 publications

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“…: newtonian fluid), the solution of the Linearized Saint-Venant Equations (LSVE) has been deduced by different techniques [37,11,23,64,38,39,57,14,20] and it has been variously applied. For instance, the knowledge of its analytical expression allowed to enlighten some peculiar flow features of the waves [37,57,16], to design automatic controllers for water distribution in openchannel systems [38,39,42], to assess the applicability of simplified methods for flood routing [64], to predict the propagation of long ocean waves into channels [9], to conceptually support semi-empirical criteria aimed to predict roll-waves occurrence [43,34,17,19]. The effectiveness of these semi-empirical criteria also for frictional granular flows [18] corroborates the validity of linearized analysis for media characterised by a more sophisticated behaviour.…”

Section: Introductionmentioning

confidence: 99%

Waves dynamics in a linearized mud-flow Shallow model

Cristo¹,

Iervolino²,

Vacca³

2013

ams

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The study of formation and evolution of waves in mud-flows is strongly motivated by their destructive power. The rheology of these flows, which involve massive solid transport, is often described using linear or non-linear viscoplastic models. The paper analyzes the wave dynamics of mud-flows, presenting the linearized response of the 1D uniform flow of a viscoplastic fluid with yield stress, i.e. Herschel & Bulkley fluid, to a pointwise impulsive forcing term. The solution in either linearly stable or unstable conditions is found, for both subcritical and supercritical flows, through the bilateral inverse Laplace transform. The analysis offers a unified description of the behaviour of different non-newtonian fluids, recovering as particular cases both the Bingham and the power-law models. The influence of the dimensionless governing numbers and of the rheological parameters on the shape and peak of waves is investigated.

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Section: Introductionmentioning

confidence: 99%

Waves dynamics in a linearized mud-flow Shallow model

Cristo¹,

Iervolino²,

Vacca³

2013

ams

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“…The illustrative regions as a broad channel could be in any curved form, which would permit easy analysis of a wide range of different parabolic geometries along with the dimensionless procedure. This can be seen from a previous study which predicted the propagation of the long ocean waves into a channel [25].…”

Section: Introductionmentioning

confidence: 63%

Analysis of the Flow Pattern and Flow Rectification Measures of the Side-Intake Forebay in a Multi-Unit Pumping Station

Nasr

Yang

Zhang

et al. 2021

Water

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To improve the problem of turbulence in the forebay of the lateral inlet pumping station, a typical lateral inlet pumping station project in Xuzhou, Jiangsu Province, China was taken as the research object. The forebay of the pumping station is a building connecting the river channel and the pumping station into the water tank. Based on the Reynolds-averaged Navier-Stokes (RANS) law and the turbulence model, the computational fluid dynamics method (CFD) technology compares and analyzes the numerical simulation with or without rectification measures for the forebay of the lateral intake pumping station when multiple units are operating. The three-dimensional model was created by SolidWorks modeling software and the numerical simulation simulated by CFX-ANSYS. To alter the flow pattern in the forebay of the pumping station, various rectification measures were chosen. Internal rectification flow patterns in the forebay under multiple plans, uniformity of flow velocity distribution in the measuring section, and vortex area reduction rates are investigated and compared. Based on the analysis and comparison of numerical simulation results, when the parabolic wall and some rectification piers are set significantly it improves the flow pattern of the forebay of the lateral inlet pumping station. It also makes the flow pattern of the inlet pool better and increases the uniformity of the flow velocity distribution by 8%. Further, it reduced the vortex area by 70%, effectively improving the operating efficiency of the pump. The research results of this paper provide a technical reference for the improvement of the flow pattern in the forebay of the lateral inlet pumping station.

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“…In the same direction, Xie et al [20] explored the linear long wave reflection by a rectangular obstacle with two scour trenches of power function profile and later Liu et al [21] proposed an exact analytical solution in the form of a Taylor series for linear long wave reflection by a submerged quasi-idealized breakwater or trench. In addition, there are studies applying perturbation techniques to predict the reflection and modulation of long water waves propagating over geometries with variable depth and in channels with constant depth and parabolic width transition; see, for example, [22,23].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Formulas for the Reflection/Transmission of Long Water Waves Propagating in a Tapered and Slender Harbor

Bautista

Méndez

Bautista

2015

Journal of Applied Mathematics

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We obtain asymptotic formulas for the reflection/transmission coefficients of linear long water waves, propagating in a harbor composed of a tapered and slender region connected to uniform inlet and outlet regions. The region with variable character obeys a power-law. The governing equations are presented in dimensionless form. The reflection/transmission coefficients are obtained for the limit of the parameterκ2≪1, which corresponds to a wavelength shorter than the characteristic horizontal length of the harbor. The asymptotic formulas consider those cases when the geometry of the harbor can be variable in width and depth: linear or parabolic among other transitions or a combination of these geometries. For harbors with nonlinear transitions, the parabolic geometry is less reflective than the other cases. The reflection coefficient for linear transitions just presents an oscillatory behavior. We can infer that the deducted formulas provide as first approximation a practical reference to the analysis of wave reflection/transmission in harbors.

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Propagation of shallow water waves in an open parabolic channel using the WKB perturbation technique

Cited by 8 publications

References 22 publications

Waves dynamics in a linearized mud-flow Shallow model

Waves dynamics in a linearized mud-flow Shallow model

Analysis of the Flow Pattern and Flow Rectification Measures of the Side-Intake Forebay in a Multi-Unit Pumping Station

Asymptotic Formulas for the Reflection/Transmission of Long Water Waves Propagating in a Tapered and Slender Harbor

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