Steady shallow flow over curved beds

Sivakumaran, N. S.; Tingsanchali, Tawatchai; Hosking, Roger J.

doi:10.1017/s0022112083000567

Cited by 74 publications

(76 citation statements)

References 3 publications

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“…A minor difference between the measured and predicted results can be seen from these figures farther downstream of the crest of the humps. As described by Sivakumaran (1981), the observed bed pressure in this flow region might have some systematic errors due to small local turbulence and curvature error introduced by the flat end piezometer tappings. It is clear from Figures 4 and 5 that the pressure distribution is definitely non-hydrostatic in the flow regions around the crest and toe of the humps due to the substantial vertical curvatures of the free-surface and bed.…”

Section: Sivakumaran's (1981) Experimentsmentioning

confidence: 81%

“…Measurements for free-surface and bed pressure profiles for model validations are obtained from the experiments performed by Sivakumaran (1981). The experiments were conducted in a rectangular, horizontal flume, 9.15 m long, 650 mm high and 300 mm wide.…”

Section: Effect Of Step Size Refinementmentioning

confidence: 99%

“…Similarly, the bed pressure was observed at different tapping points along the centreline of the curved beds using vertical piezometers of accuracy 1 mm. Full details of the description of the experimental system can be found in Sivakumaran (1981). For this test problem, a smooth boundary resistance method was applied to compute the friction factors.…”

Section: Effect Of Step Size Refinementmentioning

confidence: 99%

“…The performance of the model is further assessed by simulating strongly-curved flows over symmetrical and asymmetrical humps and the results are compared with Sivakumaran's (1981) experimental data in Figures 4 and 5. For both cases, the model results for the upstream free-surface profile show close agreement with experimental data, revealing that the discharge capacity of such an overflow structure can be estimated accurately by this model (see Figures 4a and 5a).…”

Section: Sivakumaran's (1981) Experimentsmentioning

confidence: 99%

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A Numerical Study of Non-hydrostatic Shallow Flows in Open Channels

Zerihun¹

2017

Archives of Hydro-Engineering and Environmental Mechanics

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The flow field of many practical open channel flow problems, e.g. flow over natural bed forms or hydraulic structures, is characterised by curved streamlines that result in a non-hydrostatic pressure distribution. The essential vertical details of such a flow field need to be accounted for, so as to be able to treat the complex transition between hydrostatic and non-hydrostatic flow regimes. Apparently, the shallow-water equations, which assume a mild longitudinal slope and negligible vertical acceleration, are inappropriate to analyse these types of problems. Besides, most of the current Boussinesq-type models do not consider the effects of turbulence. A novel approach, stemming from the vertical integration of the Reynolds-averaged Navier-Stokes equations, is applied herein to develop a non-hydrostatic model which includes terms accounting for the effective stresses arising from the turbulent characteristics of the flow. The feasibility of the proposed model is examined by simulating flow situations that involve non-hydrostatic pressure and/or nonuniform velocity distributions. The computational results for free-surface and bed pressure profiles exhibit good correlations with experimental data, demonstrating that the present model is capable of simulating the salient features of free-surface flows over sharply-curved overflow structures and rigid-bed dunes.

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Section: Sivakumaran's (1981) Experimentsmentioning

confidence: 81%

Section: Effect Of Step Size Refinementmentioning

confidence: 99%

Section: Effect Of Step Size Refinementmentioning

confidence: 99%

Section: Sivakumaran's (1981) Experimentsmentioning

confidence: 99%

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A Numerical Study of Non-hydrostatic Shallow Flows in Open Channels

Zerihun¹

2017

Archives of Hydro-Engineering and Environmental Mechanics

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“…Moreover, noting that the trend in avalanche modeling is to account for curvature effects (see, e.g., Sivakumaran et al [14], Dewals et al [15], Iverson [16], Pudasaini et al [17,18], Bouchut and Westdickenberg [19], De Toni and Scotton [20], Bouchut et al [21], Tai and Kuo [22], Tai and Lin [23], Pelanti et al [24], Luca et al [25][26][27]5]), emphasis is on the description of the flow on arbitrary terrain, using the approach initiated by Bouchut and Westickenberg [19], and not on the formulation of constitutive laws, even if we indicate such laws as possible choices. In particular, the shallow saturated mixture in the lower layer is treated in Truesdell's sense, in the same manner as it has been done by Luca et al [27].…”

Section: Introductionmentioning

confidence: 99%

Modeling Shallow Over-Saturated Mixtures on Arbitrary Rigid Topography

Luca

Kuo

Hutter³

et al. 2012

J. mech.

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In this paper a system of depth-integrated equations for over-saturated debris flows on threedimensional topography is derived. The lower layer is a saturated mixture of density preserving solid and fluid constituents, where the pore fluid is in excess, so that an upper fluid layer develops above the mixture layer. At the layer interface fluid mass exchange may exist and for this a parameterization is needed. The emphasis is on the description of the influence on the flow by the curvature of the basal surface, and not on proposing rheological models of the avalanching mass. To this end, a coordinate system fitted to the topography has been used to properly account for the geometry of the basal surface. Thus, the modeling equations have been written in terms of these coordinates, and then simplified by using (1) the depth-averaging technique and (2) ordering approximations in terms of an aspect ratio ε which accounts for the scale of the flowing mass. The ensuing equations have been complemented by closure relations, but any other such relations can be postulated. For a shallow two-layer debris with clean water in the upper layer, flowing on a slightly curved surface, the equilibrium free surface is shown to be horizontal.

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Free-surface flow over curved surfaces: Part I: Perturbation analysis

Berger¹,

Carey

1998

Int. J. Numer. Meth. Fluids

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The standard two‐dimensional shallow water equation formulation assumes a mild bed slope and no curvature effect. These assumptions limit the applicability of these equations for some important classes of problems. In particular, flow over a spillway is affected by the bed curvature via a decidedly non‐hydrostatic pressure distribution. A detailed derivation of a more general equation set is given here in Part I. The method relies upon a perturbation expansion to simplify a bed‐fitted co‐ordinate configuration of the three‐dimensional Euler equations. The resulting equations are essentially the equivalent of the two‐dimensional shallow water equations but with curvature included and without the mild slope assumption. A finite element analysis and flume result are given in Part II. © 1998 John Wiley & Sons, Ltd.

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Steady shallow flow over curved beds

Cited by 74 publications

References 3 publications

A Numerical Study of Non-hydrostatic Shallow Flows in Open Channels

A Numerical Study of Non-hydrostatic Shallow Flows in Open Channels

Modeling Shallow Over-Saturated Mixtures on Arbitrary Rigid Topography

Free-surface flow over curved surfaces: Part I: Perturbation analysis

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