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Lars Erik Holmedal - One of the best experts on this subject based on the ideXlab platform.
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LAMINAR BOTTOM Friction BENEATH NONLINEAR RANDOM WAVES
Coastal Engineering Journal, 2003Co-Authors: Dag Myrhaug, Lars Erik HolmedalAbstract:An approach by which the stochastic properties of the Bed shear stresses can be derived from the irregular nonlinear wave motion outside the laminar bottom boundary layer is presented. It is demonstrated how Bed Friction formulas valid for regular second order Stokes waves can be used to find the cumulative distribution function of individual shear stress maxima for nonlinear irregular waves. The Friction factor for nonlinear random waves is also determined. An example is given, and an extension to nonlinear random waves plus current flow is also suggested.
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Bed Friction in Combined Wave-Current Flows
Coastal Engineering 2000, 2001Co-Authors: Richard R. Simons, Dag Myrhaug, Laurent Thais, Georges Chapalain, Lars Erik Holmedal, Ruairi D. MaciverAbstract:Experiments have been performed over a wide range of wave-current combinations in a laboratory flume and a large oscillating water tunnel. Direct measurements of the Bed shear stress with a shear cell show that the oscillatory Friction factor scales with a/k in the same way irrespective of whether or not a mean current is superimposed. Thus, for a combined wave-current flow over a rough boundary, if the near-Bed oscillatory velocity component is known or can be predicted accurately, then the oscillatory component of bottom shear stress can be determined, irrespective of relative current strength, using Friction factor formulae developed for wave-alone conditions. Many numerical models tend to overpredict the wave-induced shear stress in combined waves and currents.
Kolumban Hutter - One of the best experts on this subject based on the ideXlab platform.
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the savage hutter theory a system of partial differential equations for avalanche flows of snow debris and mud
Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik, 2004Co-Authors: Yongqi Wang, Kolumban Hutter, Shiva P PudasainiAbstract:The Savage-Hutter (SH) equations of granular avalanche flows are a hyperbolic system of equations determining the distribution of depth and depth-averaged velocity components tangential to the sliding Bed. We review the equations and point out the geometrical complexities to which these equations have been generalized. Because of the hyperbolicity of the equations, successful numerical modelling is challenging, particularly when large gradients of the physical variables occur, e.g. for a moving front or possibly formed shock waves in avalanche flows if velocities change from supercritical to subcritical e.g. during the deposition. Numerical schemes solving these free surface flows must be able to cope with smooth as well as non-smooth solutions. In this paper several numerical methods are applied to solve the SH equations and compared, including traditional difference schemes, e.g. central and upstream difference schemes, as well as high-resolution NOC (Non-Oscillatory Central Differencing) schemes, in which several second-order TVD (Total Variation Diminishing) limiters and a third-order ENO (Essentially Non-Oscillatory) cell reconstruction scheme are used. Results show that the high-resolution schemes, particularly the NOC scheme with the Minmod TVD limiter or the van Leer limiter, provide excellent performances. In the SH theory the material response is expressed by only two phenomenological parameters - the internal and the Bed Friction angles. Parameter investigations show that avalanche flows are much more sensitive against variations of the Bed Friction angle than that of the internal angle of Friction. Effects due to a pressure dependence of the Bed Friction angle and lateral variations of the basal topography are therefore also numerically examined.
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The Savage‐Hutter theory: A system of partial differential equations for avalanche flows of snow, debris, and mud
ZAMM, 2004Co-Authors: Yongqi Wang, Kolumban Hutter, Shiva P PudasainiAbstract:The Savage-Hutter (SH) equations of granular avalanche flows are a hyperbolic system of equations determining the distribution of depth and depth-averaged velocity components tangential to the sliding Bed. We review the equations and point out the geometrical complexities to which these equations have been generalized. Because of the hyperbolicity of the equations, successful numerical modelling is challenging, particularly when large gradients of the physical variables occur, e.g. for a moving front or possibly formed shock waves in avalanche flows if velocities change from supercritical to subcritical e.g. during the deposition. Numerical schemes solving these free surface flows must be able to cope with smooth as well as non-smooth solutions. In this paper several numerical methods are applied to solve the SH equations and compared, including traditional difference schemes, e.g. central and upstream difference schemes, as well as high-resolution NOC (Non-Oscillatory Central Differencing) schemes, in which several second-order TVD (Total Variation Diminishing) limiters and a third-order ENO (Essentially Non-Oscillatory) cell reconstruction scheme are used. Results show that the high-resolution schemes, particularly the NOC scheme with the Minmod TVD limiter or the van Leer limiter, provide excellent performances. In the SH theory the material response is expressed by only two phenomenological parameters - the internal and the Bed Friction angles. Parameter investigations show that avalanche flows are much more sensitive against variations of the Bed Friction angle than that of the internal angle of Friction. Effects due to a pressure dependence of the Bed Friction angle and lateral variations of the basal topography are therefore also numerically examined.
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the dynamics of avalanches of granular materials from initiation to runout part ii experiments
Acta Mechanica, 1995Co-Authors: Kolumban Hutter, Thilo Koch, C Pluuss, S. B. SavageAbstract:This paper describes a model to predict the flow of an initially stationary mass of cohesionsless granular material down a rough curved Bed and checks it against laboratory experiments that were conducted with two different kinds of granular materials that are released from rest and travel in a chute consisting of a straight inclined section, a curved segment that is followed by a straight horizontal segment. This work is of interest in connection with the motion of landslides, rockfalls and ice and dense flow snow avalanches. Experiments were performed with two different granular materials, nearly spherical glass beads of 3 mm nominal diameter, Vestolen particles (a light plastic material) of lense type shape and 4 mm nominal diameter and 2,5 mm height. Piles of finite masses of these granular materials with various initial shapes and weight were released from rest in a 100 mm wide chute with the mentioned bent profile. The basal surface consisted of smooth PVC, but was in other experiments also coated with drawing paper and with sandpaper. The granular masses under motion were photographed and partly video filmed and thus the geometry of the avalanche was recorded as a function of position and time. For the two granular materials and for the three Bed linings the angle of repose and the Bed Friction angle were determined. The experimental technique with which the laboratory avalanches were run are descriBed in detail as is the reliability of the generated data. We present and use the depth-averaged field equations of balance of mass and linear momentum as presented by Savage and Hutter [28]. These are partial differential equations for the depth averaged streamwise velocity and the distribution of the avalanche depth and involve two phenomenological parameters, the internal angle of Friction, o, and a Bed Friction angle, δ, both as constitutive properties of Coulomb-type behaviour. We present the model but do not derive its equations. The numerical integration scheme for these equations is a Lagrangian finite difference scheme used earlier by Savage and Hutter [27],[28]. We present this scheme for completeness but do not discuss its peculiarities. Comparison of the theoretical results with experiments is commenced by discussing the implementation of the initial conditions. Observations indicate that with the onset of the motion a dilatation is involved that should be accomodated for in the definition of the initial conditions. Early studies of the temporal evolution of the trailing and leading edges of the granular avalanche indicate that their computed counterparts react sensitively to variations in the Bed Friction angle but not to those of the internal angle of Friction. Furthermore, a weak velocity dependence of the Bed Friction angle, δ, is also scen to have a small, but negligible influence on these variables. We finally compare the experimental results with computational findings for many combinations of the masses of the granular materials and Bed linings. It is found that the experimental results and the theoretical predictions agree satisfactorily. They thus validate the simple model equations that were proposed in Savage and Hutter [28].
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Two-dimensional similarity solutions for finite-mass granular avalanches with coulomb- and viscous-type Frictional resistance
Journal of Glaciology, 1993Co-Authors: Kolumban Hutter, Ralf GreveAbstract:AbstractThis paper is concerned with the motion of an unconfined finite mass of granular material down an inclined plane when released from a rest position in the shape of a circular or elliptical paraboloid. The granular mass is treated as a Frictional Coulomb-like continuum with a constant angle of internal Friction. The basal Friction force is assumed to be composed of a Coulomb-type component with a Bed-Friction angle that is position-dependent and a viscous Voellmy-type resistive stress that is proportional to the velocity squared. The model equations are those of Hutter and others (in press b) and form a spatially two-dimensional set for the evolution of the avalanche height and the depth averaged in-plane velocity components; they hold for a motion of a granular mass along a plane surface.Similarity solutions, i.e. solutions which preserve the shape and the structure of the velocity field, are constructed by decomposing the motion into that of the centre of mass and the deformation relative to it. This decomposition is possible provided the effect of the Voellmy drag on the deformation is ignored. With it, the depth and velocities relative to those of the centre of mass of the moving pile can be determined analytically. It is shown that the pile has a parabolic cap shape and contour lines are elliptical. The semi-axes and the position and velocity of the centre of mass are calculated numerically. We explicitly show that (i)For two-dimensional spreading, a rigid-body motion does not exist, no matter what be the values of the Bed-Friction angle and the coefficient of viscous drag.(ii)A steady final velocity of the centre of the mass cannot be assumed, but the motion of the centre of mass depends strongly on the value of the Voellmy coefficient.(iii)The geometry of the moving pile depends on the variation of the Bed-Friction angle with position, as well as on the value of the coefficient of viscous drag.
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Motion of a granular avalanche in a convex and concave curved chute: experiments and theoretical predictions
Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences, 1993Co-Authors: Ralf Greve, Kolumban HutterAbstract:This paper deals with the theoretical-numerical and experimental treatment of two-dimensional avalanches of cohesionless granular materials moving down a confined curved chute. Depth-averaged field equations of balance of mass and linear momentum as prescriBed by Savage & Hutter (1991) are used. They describe the temporal evolution of the depth averaged streamwise velocity and the distribution of the avalanche depth and involve two phenomenological parameters, the internal angle of Friction, $\phi $, and the Bed Friction angle, $\delta $, both as constitutive properties of Coulomb-type behaviour. The equations incorporate weak to moderate curvature effects of the Bed. Experiments were carried out with different granular materials in a chute with partly convex and partly concave curved geometry. In these experiments the motion of the granular avalanche is followed from the moment of release to its standstill by using high speed photography, whence recording the geometry of the avalanche as a function of position and time. Two different Bed linings, drawing paper and no. 120 SIA sandpaper, were used to vary the Bed Friction angle, $\delta $. Both, the internal angle of Friction, $\phi $, and the Bed Friction angle, $\delta $, were measured, and their values used in the theoretical model. Because of the bump and depending upon the granulate-Bed combination an initial single pile of granular avalanche could evolve as a single pile throughout its motion and be deposited above or below the bump in the Bed; or it could separate in the course of the motion into two piles which are separately deposited above and below the bump. Comparison of the experimental findings with the computational results proved to lead to good to excellent correspondence between experiment and theory. Even the development of the detailed geometry of the granular avalanche is excellently reproduced by the model equations, if $\delta $ < $\phi $. Occasional deviations may occur; however, they can in all cases be explained by onsetting instabilities of the numerical scheme or by experimental artefacts that only arise when single particles have shapes prone to rolling.
Dag Myrhaug - One of the best experts on this subject based on the ideXlab platform.
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LAMINAR BOTTOM Friction BENEATH NONLINEAR RANDOM WAVES
Coastal Engineering Journal, 2003Co-Authors: Dag Myrhaug, Lars Erik HolmedalAbstract:An approach by which the stochastic properties of the Bed shear stresses can be derived from the irregular nonlinear wave motion outside the laminar bottom boundary layer is presented. It is demonstrated how Bed Friction formulas valid for regular second order Stokes waves can be used to find the cumulative distribution function of individual shear stress maxima for nonlinear irregular waves. The Friction factor for nonlinear random waves is also determined. An example is given, and an extension to nonlinear random waves plus current flow is also suggested.
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Bed Friction in Combined Wave-Current Flows
Coastal Engineering 2000, 2001Co-Authors: Richard R. Simons, Dag Myrhaug, Laurent Thais, Georges Chapalain, Lars Erik Holmedal, Ruairi D. MaciverAbstract:Experiments have been performed over a wide range of wave-current combinations in a laboratory flume and a large oscillating water tunnel. Direct measurements of the Bed shear stress with a shear cell show that the oscillatory Friction factor scales with a/k in the same way irrespective of whether or not a mean current is superimposed. Thus, for a combined wave-current flow over a rough boundary, if the near-Bed oscillatory velocity component is known or can be predicted accurately, then the oscillatory component of bottom shear stress can be determined, irrespective of relative current strength, using Friction factor formulae developed for wave-alone conditions. Many numerical models tend to overpredict the wave-induced shear stress in combined waves and currents.
Ruairi D. Maciver - One of the best experts on this subject based on the ideXlab platform.
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Bed Friction in Combined Wave-Current Flows
Coastal Engineering 2000, 2001Co-Authors: Richard R. Simons, Dag Myrhaug, Laurent Thais, Georges Chapalain, Lars Erik Holmedal, Ruairi D. MaciverAbstract:Experiments have been performed over a wide range of wave-current combinations in a laboratory flume and a large oscillating water tunnel. Direct measurements of the Bed shear stress with a shear cell show that the oscillatory Friction factor scales with a/k in the same way irrespective of whether or not a mean current is superimposed. Thus, for a combined wave-current flow over a rough boundary, if the near-Bed oscillatory velocity component is known or can be predicted accurately, then the oscillatory component of bottom shear stress can be determined, irrespective of relative current strength, using Friction factor formulae developed for wave-alone conditions. Many numerical models tend to overpredict the wave-induced shear stress in combined waves and currents.
Luis Cea - One of the best experts on this subject based on the ideXlab platform.
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Experimental study of the water depth and rainfall intensity effects on the Bed roughness coefficient used in distributed urban drainage models
Journal of Hydrology, 2013Co-Authors: Ignacio Fraga, Luis Cea, Jerónimo PuertasAbstract:Summary The work presented in this paper analyses the effect of water depth and rainfall intensity on the surface roughness coefficients used in overland flow models based on the shallow water equations. The relation between the Manning coefficient and the water depth and rainfall intensity has been quantified using different methodologies based on the analysis of two sets of experimental data. In the first set uniform overland flow conditions were generated, and the Bed roughness coefficient was computed from direct measurements of the water depth and discharge. In the second set of experiments, unsteady rainfall–runoff transformations with different rainfall intensities were generated in a flume and computed with a shallow water model in which different Bed Friction formulations were implemented and calibrated. Results show that for very low water depth values there is a significant increase in the surface resistance, which is not captured by any standard Bed Friction formulation. Rainfall intensity also increases surface resistance especially as the water depth diminishes below a critical threshold. Using a Reynolds dependent formulation for the Manning coefficient improves model predictions.
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unstructured finite volume discretisation of Bed Friction and convective flux in solute transport models linked to the shallow water equations
Journal of Computational Physics, 2012Co-Authors: Luis Cea, M E VazquezcendonAbstract:The finite volume discretisation of the shallow water equations has been the subject of many previous studies, most of which deal with a well-balanced conservative discretisation of the convective flux and bathymetry. However, the Bed Friction discretisation has not been so profusely analysed in previous works, while it may play a leading role in certain applications of shallow water models. In this paper we analyse the numerical discretisation of the Bed Friction term in the two-dimensional shallow water equations, and we propose a new unstructured upwind finite volume discretisation for this term. The new discretisation proposed improves the accuracy of the model in problems in which the Bed Friction is a relevant force in the momentum equation, and it guarantees a perfect balance between gravity and Bed Friction under uniform flow conditions. The relation between the numerical scheme used to solve the hydrodynamic equations and the scheme used to solve a scalar transport model linked to the shallow water equations, is also analysed in the paper. It is shown that the scheme used in the scalar transport model must take into consideration the scheme used to solve the hydrodynamic equations. The most important implication is that a well-balanced and conservative scheme for the scalar transport equation cannot be formulated just from the water depth and velocity fields, but has to consider also the way in which the hydrodynamic equations have been solved.
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Bathymetric error estimation for the calibration and validation of estuarine hydrodynamic models
Estuarine Coastal and Shelf Science, 2012Co-Authors: Luis Cea, Jon FrenchAbstract:Abstract This paper investigates the impact of uncertainty in the definition of bathymetry on the performance of estuarine shallow water models. A depth-averaged hydrodynamic model is used to simulate tidal flows in a meso-tidal estuary. Simulations are performed for a range of bathymetric and Bed roughness scenarios, which encompass the uncertainties typically encountered in the specification of estuarine and shallow coastal models. The relative sensitivity of model output to uncertainty in bathymetry and Bed Friction is analysed using Monte Carlo methods, and a new generalised error model is presented that allows various sources of error in bathymetry to be treated as a calibration parameter. Numerical results are compared with observed current speed and water level time series at multiple locations. It is shown that calibration that incorporates bathymetric uncertainty can be significantly more efficient than a classic calibration based only on adjustment of a Bed Friction coefficient. These findings have wide-ranging implications for the calibration and validation of estuarine and shallow coastal hydrodynamic models. Importantly, our proposed bathymetry calibration framework offers the prospect of significantly improved performance from the current generation of numerical models.