Discrete element model for crack propagation in brittle materials

We propose a discrete element model for brittle rupture. The material consists of a bidimensional set of closed‐packed particles in contact. We explore the isotropic elastic behavior of this regular structure to derive a rupture criterion compatible to continuum mechanics. We introduce a classical criterion of mixed mode crack propagation based on the value of the stress intensity factors, obtained by the analysis of two adjacent contacts near a crack tip. Hence, the toughness becomes a direct parameter of the model, without any calibration procedure. We verify the consistency of the formulation as well as its convergence by comparison with theoretical solutions of tensile cracks, a pre‐cracked beam, and an inclined crack under biaxial stress. Copyright © 2015 John Wiley & Sons, Ltd.     

Study of the moist Convective Boundary Layer structure by backscattering lidar

Measurements of the structure of the Convective Boundary Layer (CBL) were made from the ground and from the ARAT aircraft with a backscattering lidar during the preliminary phase of the French project LEANDRE. A numerical model of Mie theory diffusion was used to determine a theoretical profile of the extinction coefficient, as a function of relative humidity. Comparisons between theoretical and measured profiles were made. Good agreement was found, which confirms that the variation of the extinction coefficient in the CBL is primarily controlled by the relative humidity. This paper also presents a detailed analysis of the small-scale structure of the CBL. The normalized length and number of thermals are estimated. Results are in agreement with previousin-situ measurements. An analysis of the bidimensional cross-section of the extinction coefficient shows that this coefficient permits one to retrieve more quantitative information than the range-corrected signal, as the fractions of entrained air and surface-layer air at a given altitude.     

Study of the air-sea interactions at the mesoscale: the SEMAPHORE experiment

The SEMAPHORE (Structure des Echanges Mer-Atmosphère, Propriétés des Hétérogénéités Océaniques: Recherche Expérimentale) experiment has been conducted from June to November 1993 in the Northeast Atlantic between the Azores and Madeira. It was centered on the study of the mesoscale ocean circulation and air-sea interactions. The experimental investigation was achieved at the mesoscale using moorings, floats, and ship hydrological survey, and at a smaller scale by one dedicated ship, two instrumented aircraft, and surface drifting buoys, for one and a half month in October-November (IOP: intense observing period). Observations from meteorological operational satellites as well as spaceborne microwave sensors were used in complement. The main studies undertaken concern the mesoscale ocean, the upper ocean, the atmospheric boundary layer, and the sea surface, and first results are presented for the various topics. From data analysis and model simulations, the main characteristics of the ocean circulation were deduced, showing the close relationship between the Azores front meander and the occurrence of Mediterranean water lenses (meddies), and the shift between the Azores current frontal signature at the surface and within the thermocline. Using drifting buoys and ship data in the upper ocean, the gap between the scales of the atmospheric forcing and the oceanic variability was made evident. A 2 °C decrease and a 40-m deepening of the mixed layer were measured within the IOP, associated with a heating loss of about 100 W m⁻². This evolution was shown to be strongly connected to the occurrence of storms at the beginning and the end of October. Above the surface, turbulent measurements from ship and aircraft were analyzed across the surface thermal front, showing a 30% difference in heat fluxes between both sides during a 4-day period, and the respective contributions of the wind and the surface temperature were evaluated. The classical momentum flux bulk parameterization was found to fail in low wind and unstable conditions. Finally, the sea surface was investigated using airborne and satellite radars and wave buoys. A wave model, operationally used, was found to get better results compared with radar and wave-buoy measurements, when initialized using an improved wind field, obtained by assimilating satellite and buoy wind data in a meteorological model. A detailed analysis of a 2-day period showed that the swell component, propagating from a far source area, is underestimated in the wave model. A data base has been created, containing all experimental measurements. It will allow us to pursue the interpretation of observations and to test model simulations in the ocean, at the surface and in the atmospheric boundary layer, and to investigate the ocean-atmosphere coupling at the local and mesoscales.     

On the Correlation between Convective Plume Updrafts and Downdrafts,Lidar Reflectivity and Depolarization Ratio

We question the correlation between vertical velocity (w) on the one hand and the occurrence of convective plumes in lidar reflectivity (i.e. range corrected backscatter signal Pz ²) and depolarization ratio (Δ) on the other hand in the convective boundary layer (CBL). Thermal vertical motion is directly investigated using vertical velocities measured by a ground-based Doppler lidar operating at 2 μm. This lidar provides also simultaneous measurements of lidar reflectivity. In addition, a second lidar 200 m away provides reflectivities at 0.53 and 1 μm and depolarization ratio at 0.53 μm. The time series from the two lidars are analyzed in terms of linear correlation coefficient (ρ). The main result is that the plume-like structures provided by lidar reflectivity within the CBL as well as the CBL height are not a clear signature of updrafts. It is shown that the lidar reflectivity within the CBL is frequently anti-correlated (ρ (w, Pz ² )) with the vertical velocity. On the contrary, the correlation coefficient between the depolarization ratio and the vertical velocity ρ (w, Δ ) is always positive, showing that the depolarization ratio is a fair tracer of updrafts. The importance of relative humidity on the correlation coefficient is discussed. An erratum to this article can be found at     

An elastoplastic model based on the shakedown concept for flexible pavements unbound granular materials

Nowadays, the problem of rutting of flexible pavements linked to permanent deformations occurring in the unbound layers is taken into account only by mechanistic empirical formulas. Finite element modelling of realistic boundary value problems with incremental rheological models will lead to unrealistic calculation time for large cycle numbers. The objective of the authors is to present a simplified model which can be used to model the flexible pavements rutting with the finite elements framework. This method is based on the shakedown theory developed by Zarka which is usually associated to materials like steels. It has been adapted for granular materials by introducing a yield surface taking into account the mean stress influence on the mechanical behaviour and a dependency of the hardening modulus with the stress state. The Drucker–Prager yield surface has been used with a non‐associated flow rule. Comparisons with repeated load triaxial tests carried out on a subgrade soil have been done. These comparisons underline the capabilities of the model to take into account the cyclic behaviour of unbound materials for roads. Finally, a discussion, dealing with the use of the simplified method within a finite element modelling of a full‐scale experiment, is presented. Copyright © 2005 John Wiley & Sons, Ltd.     

Gap flow measurements during the Mesoscale Alpine Programme

Summary The lowest pass through the Alpine crest, the Brenner Pass, was heavily instrumented with ground-based and air-borne in-situ and remote sensors during the Special Observation Period (SOP) of the Mesoscale Alpine Programme (MAP) in the fall of 1999 to study gap flow. The main objectives were to study the combined effects of changes of terrain height and changes of width in altering the flow characteristics, to investigate the coupling of the gap flow to the flow aloft, and to provide high-density measurements in the along- and cross-gap directions.Gap flows occurred during one third of the 70-day SOP, a frequency above the long term average. Gap flows took place with and without accompanying cross-barrier flow and with and without a capping inversion. A case study demonstrates the hydraulic jump-like features that occurred in gap flow on 30 October 1999 and illustrates the types of data available for further analyses.     

Flow splitting at the bifurcation between two valleys: idealized simulations in comparison with Mesoscale Alpine Programme observations

Summary This paper investigates the characteristics of channelled airflow in the vicinity of a junction of three idealized valleys (one valley carrying the incoming flow and two tributaries carrying the outflow), using a two-dimensional single-layer shallow water model. Particular attention is given to the flow splitting occurring at the junction. Nondimensionalized, the model depends on the valley geometry, the Reynolds number, which is related to the eddy viscosity, and on the difference of the hydrostatic pressure imposed at the exit of the tributaries. At the spatial scale considered in this study, the Rossby number relating the inertial and Coriolis forces is always larger than 1, implying that the effect of earth rotation can be neglected to a first approximation. The analysis of the flow structure within the three valleys as well as the calculation of the split ratio (fraction of the air flow diverted into one of the two downstream valleys with respect to the total mass flux in the upstream valley) show that (i) the flow pattern depends strongly on the Reynolds number while the split ratio is comparatively insensitive; (ii) the valley geometry and the difference between the upstream and downstream hydrostatic pressures affect the flow pattern, the location of the split point and the split ratio; (iii) the relative contribution of flow deflection by the sidewalls and the blocking/splitting mechanism differs between the settings of a “Y-shape” valley and a “T-shape” valley. Quantitative comparison of the present results with numerical simulations of realistic cases and with observations collected in the region of the Rhine and Seez valleys (Switzerland) (“Y-shape” valley) and in the region of the Inn and Wipp valleys (Austria) (“T-shape” valley) during the Mesoscale Alpine Programme (MAP) field experiment shows good agreement provided that the normalized valley depth NΔH/U_u significantly exceeds 1, i.e., when “flow around” is expected. A structural disagreement between the idealized simulations and the observed wind field is found only when NΔH/U_u ≃ 1, that is, in the “flow over” regime. This shows that the dimensionless valley depth is indeed a good indicator for flow splitting, implying that the stratification is a key player in reality.     

Evidence of a Mixed-Layer Dynamics Contribution to the Entrainment Process

The internal thermal boundary layer developing over the Mediterranean during a cold-air outbreak associated with a Tramontane event has been studied by means of airborne lidar, in situ sensors, and a modelling approach that consisted of nesting the University of Washington (UW) planetary boundary-layer (PBL) model in an advective zero-order jump model. This approach bypasses some of the deficiencies associated with each model: the absence of the dynamics in the mixed layer for the zero-order jump model and the lack of an inversion at the PBL top for the UW PBL model. Particular attention is given to the parameterization of the entrainment flux at the PBL top. Values of the entrainment closure parameter derived with the model when matching PBL structure observations are much lower than those derived with standard zero-order jump models. They also are in good agreement with values measured in different meteorological situations by other studies. This improvement is a result of the introduction of turbulent kinetic energy production in the mixed layer.     

Combined L1/L2 Kalman filter-based tracking scheme for weak signal environments

A Kalman filter-based method combining the energy of both L1 C/A and L2C GPS signals in a combined tracking loop method to enhance performance under adverse conditions is developed. Standard tracking methods and the ionospheric effect on GPS signals are reviewed and compared to a new Kalman filter that simultaneously estimates delay, phase and total electron content by combining L1 C/A and L2C code and phase discriminator outputs. The new filter is tested and compared to standard methods for tracking L1 C/A and L2C using both simulated and real data. The new method is found to have improved sensitivity of 3 dB compared to standard L1 tracking and 4.5 dB compared to standard L2C tracking while at the same time providing an accurate estimate of the total electron content along the signal path.