Experimental study of granular surface flows via a fast camera: a continuous description

Depth averaged conservation equations are written for granular surface flows. Their application to the study of steady surface flows in a rotating drum allows to find experimentally the constitutive relations needed to close these equations from measurements of the velocity profile in the flowing layer at the center of the drum and from the flowing layer thickness and the static/flowing boundary profiles. The velocity varies linearly with depth, with a gradient independent of both the flowing layer thickness and the static/flowing boundary local slope. The first two closure relations relating the flow rate and the momentum flux to the flowing layer thickness and the slope are then deduced. Measurements of the profile of the flowing layer thickness and the static/flowing boundary in the whole drum explicitly give the last relation concerning the force acting on the flowing layer. Finally, these closure relations are compared to existing continuous models of surface flows.Comment: 20 pages, 11 figures, submitted to Phys. FLuid

Entropy-satisfying scheme for a hierarchy of dispersive reduced models of free surface flow

International audienceThis work is devoted to the numerical resolution in multidimensional framework of a hierarchy of reduced models of the free surface Euler equations, also called water waves equations.The current paper, the first in a series of two, focuses on a hierarchy of monolayer dispersive models, such is the Serre-Green-Naghdi model.A particular attention is given to the dissipation of the mechanical energy at the discrete level, i.e. to design an entropy-satisfying scheme.To illustrate the accuracy and the robustness of the strategy, several numerical experiments are performed.In particular, the strategy is able to deal with dry areas without particular treatment

Shallow water equations for large bathymetry variations

In this study, we propose an improved version of the nonlinear shallow water (or Saint-Venant) equations. This new model is designed to take into account the effects resulting from the large spacial and/or temporal variations of the seabed. The model is derived from a variational principle by choosing the appropriate shallow water ansatz and imposing suitable constraints. Thus, the derivation procedure does not explicitly involve any small parameter.Comment: 7 pages. Other author's papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh

Unsteady turbulence in tidal bores: Effects of bed roughness

A tidal bore is a wave propagating upstream as the tidal flow turns to rising. It forms during spring tide conditions when the flood tide is confined to a narrow funneled channel. To date, theoretical and numerical studies rely upon physical experiments to validate the developments, but the experimental data are limited mostly to visual observations and sometimes free-surface measurements. Herein turbulent velocity measurements were obtained in a large-size laboratory facility with a fine spatial and temporal resolution. The instantaneous velocity measurements showed rapid flow deceleration at all vertical elevations, and large fluctuations of all velocity components were recorded beneath the bore and secondary waves. A comparison between undular (nonbreaking) and breaking bores suggested some basic differences. In an undular bore, large velocity fluctuations were recorded beneath the first wave crest and the secondary waves showing a long-lasting effect after the bore passage. In a breaking bore, some large turbulent stresses were observed next to the shear zone in a region of high velocity gradients, while some transient flow recirculation was recorded next to the bed. The effects of bed roughness were tested further. The boundary friction contributed to some wave attenuation and dispersion, and the free-surface data showed some agreement with the wave dispersion theory for intermediate gravity waves. The instantaneous velocity data showed however a significant effect of the boundary roughness on the velocity field next to the boundary (z/d(o)< 0.2) for both undular and breaking bores. Overall the findings were consistent with field observations of tidal bores and highlighted the significant impact of undular (nonbreaking) bores on natural systems

Asymptotic models for the generation of internal waves by a moving ship, and the dead-water phenomenon

This paper deals with the dead-water phenomenon, which occurs when a ship sails in a stratified fluid, and experiences an important drag due to waves below the surface. More generally, we study the generation of internal waves by a disturbance moving at constant speed on top of two layers of fluids of different densities. Starting from the full Euler equations, we present several nonlinear asymptotic models, in the long wave regime. These models are rigorously justified by consistency or convergence results. A careful theoretical and numerical analysis is then provided, in order to predict the behavior of the flow and in which situations the dead-water effect appears.Comment: To appear in Nonlinearit

Performance of CUF approach to analyze the structural behavior of slender bodies

This paper deals with the accurate evaluation of complete three-dimensional (3D) stress fields in beam structures with compact and bridge-like sections. A refined beam finite-element (FE) formulation is employed, which permits any-order expansions for the three displacement components over the section domain by means of the Carrera Unified Formulation (CUF). Classical (Euler-Bernoulli and Timoshenko) beam theories are considered as particular cases. Comparisons with 3D solid FE analyses are provided. End effects caused by the boundary conditions are investigated. Bending and torsional loadings are considered. The proposed formulation has shown its capability of leading to quasi-3D stress fields over the beam domain. Higher-order beam theories are necessary for the case of bridge-like sections. Various theories are also compared in terms of shear correction factors on the basis of definitions found in the open literature. It has been confirmed that different theories could lead to very different values of shear correction factors, the accuracy of which is subordinate to a great extent to the section geometries and loading conditions. However, an accurate evaluation of shear correction factors is obtained by means of the present higher-order theories

Turbulence measurements in positive surges and bores

A positive surge results from a sudden change in flow that increases the flow depth. New experiments were conducted in a large channel. Most positive surge tests were conducted with a horizontal bed slope, a constant flow rate and uncontrolled flow conditions. The only dependant variable was the downstream gate opening after closure. Detailed turbulence measurements were performed with high-temporal resolution using side-looking acoustic Doppler velocimetry. Two types of positive surge were observed: undular surge for Froude numbers less than 1.7, and weak (breaking) surges above. Instantaneous velocity measurements beneath advancing surges showed a marked effect of the surge passage on the velocity field. Streamwise velocities showed rapid flow deceleration at all vertical elevations. Large fluctuations of longitudinal and transverse velocities were recorded beneath the surges, including some unsteady flow recirculation beneath a weak surge front. Turbulent stresses were deduced from high-pass filtered data. The results showed large normal and tangential Reynolds stresses beneath the surges. A comparison between undular and weak surges suggested some major difference. In weak surge flows, the data showed rapid flow separation beneath the surge front. In undular surges, maximum Reynolds stresses were observed beneath and just before each wave crest behind the leading wave

A computational study of the influence of surface roughness on material strength

In machine component stress analysis, it usually assumed that the geometry specified in CAD provides a fair representation of the geometry of the real component. While in particular circumstances, tolerance information, such as minimum thickness of a highly stressed region, might be taken into consideration, there is no standard practice for the representation of surface quality. It is known that surface roughness significantly influences fatigue life, but for this to be useful in the context of life prediction, there is a need to examine the nature of surface roughness and determine how best to characterise it. Non-smooth geometry can be represented in mathematics by fractals or other methods, but for a representation to have a practical value for a manufactured component, it is necessary to accept that there is a lower limit to surface profile measurement resolution. Resolution and mesh refinement also play a part in any computational analysis undertaken to assess surface profile effects: in the analyses presented, a nominal axi-symmetric geometry has been taken, with a finite non-smooth region on the boundary. Various surface roughness representations are modelled, and the significance of the characterized surface roughness type is investigated. It is shown that the applied load gives rise to a nominally uni-axial stress state of 90% of the yield, although surface roughness features have the effect of modifying the load path, and give rise to localized regions of plasticity near to the surface. The material of the test model is assumed to be elasto-plastic, and the development and evolution of plastic zones formed within the geometry are shown for multiple load cycles