A new method for avalanche hazard mapping using a combination of statistical and deterministic models

International audienceThe purpose of the present paper is to propose a new method for avalanche hazard mapping using a combination of statistical and deterministic modelling tools. The methodology is based on frequency-weighted impact pressure, and uses an avalanche dynamics model embedded within a statistical framework. The outlined procedure provides a useful way for avalanche experts to produce hazard maps for the typical case of avalanche sites where historical records are either poorly documented or even completely lacking, as well as to derive confidence limits on the proposed zoning. The methodology is implemented using avalanche information from Iceland and the Swiss mapping criteria, and applied to an Icelandic real world avalanche-mapping problem

A Rapid, Empirical Method for Detection and Estimation of Outlier Frames in Particle Imaging Velocimetry Data using Proper Orthogonal Decomposition

This paper develops a method for detection and removal of outlier images from digital Particle Image Velocimetry data using Proper Orthogonal De-composition (POD). The outlier is isolated in the leading POD modes, removed and a replacement value re-estimated. The method is used to estimate and replace whole images within the sequence. This is particularly useful, if a single PIV image is suddenly heavily contaminated with background noise, or to estimate a dropped frame within a sequence. The technique is tested on a synthetic dataset that permits the effective acquisition frequency to be varied systematically, before application to flow field frames obtained from a large-eddy simulation. As expected, outlier re-estimation becomes more difficult when the integral time scale for the flow is long relative to the sampling period. However, the method provides a systematic improvement in predicting frames compared to interpolating from neighbouring(1) frames

Wavelet phase analysis of two velocity components to infer the structure of interscale transfers in a turbulent boundary-layer

Scale-dependent phase analysis of velocity time series measured in a zero pressure gradient boundary layer shows that phase coupling between longitudinal and vertical velocity components is strong at both large and small scales, but minimal in the middle of the inertial regime. The same general pattern is observed at all vertical positions studied, but there is stronger phase coherence as the vertical coordinate, y, increases. The phase difference histograms evolve from a unimodal shape at small scales to the development of significant bimodality at the integral scale and above. The asymmetry in the off-diagonal couplings changes sign at the midpoint of the inertial regime, with the small scale relation consistent with intense ejections followed by a more prolonged sweep motion. These results may be interpreted in a manner that is consistent with the action of low speed streaks and hairpin vortices near the wall, with large scale motions further from the wall, the effect of which penetrates to smaller scales. Hence, a measure of phase coupling, when combined with a scale-by-scale decomposition of perpendicular velocity components, is a useful tool for investigating boundary-layer structure and inferring process from single-point measurements

Conclusions from a recent survey of avalanche computational models

In this paper we summarise a survey report on computational models for snow avalanche motion that was developed within the frame-work of the EU research project SAME (Snow Avalanche Modelling, Mapping and Warning in Europe). An examination of existing models shows that: (l) there is not - and probably never will be - a single model that adequately describes all avalanche types; (2) in order to account for the extraordinary variability of avalanche motion in response to initial and boundary conditions, flow-regime transitions and the snow mass balance should be properly described in future models; (3) calibration and validation of these models will require a comprehensive measurement programme; (4) determination of realistic initial conditions is a serious problem. We suggest that using simple models to scan the relevant parameter space with more advanced models for detailed simulations of selected scenarios could improve this situation. Finally, we discuss the needs for, and benefits of, a co-ordinated programme of avalanche research. The main features of the SAME proposal for an extensive joint experimental programme are described. We suggest that international collaboration could produce high-quality models covering all essential practical needs. Increased interdisciplinary collaboration would be advantageous for model development and facilitate incorporation of other scientific disciplines

(Multi)wavelets increase both accuracy and efficiency of standard Godunov-type hydrodynamic models

This paper presents a scaled reformulation of a robust second-order Discontinuous Galerkin (DG2) solver for the Shallow Water Equations (SWE), with guiding principles on how it can be naturally extended to fit into the multiresolution analysis of multiwavelets (MW). Multiresolution analysis applied to the flow and topography data enables the creation of an adaptive MWDG2 solution on a non-uniform grid. The multiresolution analysis also permits control of the adaptive model error by a single user-prescribed parameter. This results in an adaptive MWDG2 solver that can fully exploit the local (de)compression of piecewise-linear modelled data, and from which a first-order finite volume version (FV1) is directly obtainable based on the Haar wavelet (HFV1) for local (de)compression of piecewise-constant modelled data. The behaviour of the adaptive HFV1 and MWDG2 solvers is systematically studied on a number of well-known hydraulic tests that cover all elementary aspects relevant to accurate, efficient and robust modelling. The adaptive solvers are run starting from a baseline mesh with a single element, and their accuracy and efficiency are measured referring to standard FV1 and DG2 simulations on the uniform grid involving the finest resolution accessible by the adaptive solvers. Our findings reveal that the MWDG2 solver can achieve the same accuracy as the DG2 solver but with a greater efficiency than the FV1 solver due to the smoothness of its piecewise-linear basis, which enables more aggressive coarsening than with the piecewise-constant basis in the HFV1 solver. This suggests a great potential for the MWDG2 solver to efficiently handle the depth and breadth in resolution variability, while also being a multiresolution mesh generator. Accompanying model software and simulation data are openly available online

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

This work explores the properties of the velocity increment distributions for wakes of contrasting local Reynolds number and nature of generation (a cylinder wake and a multiscale-forced case, respectively). It makes use of a technique called gradual wavelet reconstruction (GWR) to generate constrained randomizations of the original data, the nature of which is a function of a parameter, ϑ. This controls the proportion of the energy between the Markov-Einstein length (∼ 0.8 Taylor scales) and integral scale that is fixed in place in the synthetic data. The properties of the increments for these synthetic data are then compared to the original data as a function of ϑ. We write a Fokker-Planck equation for the evolution of the velocity increments as a function of spatial scale, r, and, in line with previous work, expand the drift and diffusion terms in terms up to fourth order in the increments and find no terms are relevant beyond the quadratic terms. Only the linear contribution to the expansion of the drift coefficient is non-zero and it exhibits a consistent scaling with ϑ for different flows above a low threshold. For the diffusion coefficient, we find a local Reynolds number independence in the relation between the constant term and ϑ for the multiscale-forced wakes. This term characterizes small scale structure and can be contrasted with the results for the Kolmogorov capacity of the zero-crossings of the velocity signals, which measures structure over all scales and clearly distinguishes between the types of forcing. Using GWR shows that results for the linear and quadratic terms in the expansion of the diffusion coefficient are significant, providing a new means for identifying intermittency and anomalous scaling in turbulence datasets. All our data showed a similar scaling behavior for these parameters irrespective of forcing type or Reynolds number, indicating a degree of universality to the anomalous scaling of turbulence. Hence, these terms are a useful metric for testing the efficacy of synthetic turbulence generation schemes used in large eddy simulation, and we also discuss the implications of our approach for reduced order modeling of the Navier-Stokes equations

Large eddy simulation of the velocity-intermittency structure for flow over a field of symmetric dunes

Owing to their frequent occurrence in the natural environment, there has been significant interest in refining our understanding of flow over dunes and other bedforms. Recent work in this area has focused, in particular, on their shear-layer characteristics and the manner by which flow structures are generated. However, field-based studies, are reliant on single-, or multi-point measurements, rather than delimiting flow structures from the velocity gradient tensor, as is possible in numerical work. Here, we extract pointwise time series from a well-resolved large eddy simulation as a means to connect these two approaches. The at-a-point analysis technique is termed the velocity-intermittency quadrant method and relates the fluctuating, longitudinal velocity, (Formula presented.), to its fluctuating pointwise Hölder regularity, (Formula presented.). Despite the difference in boundary conditions, our results agree very well with previous experiments that show the importance, in the region above the dunes, of a quadrant 3 ((Formula presented.), (Formula presented.)) flow configuration. Our higher density of sampling beneath the shear layer and close to the bedforms relative to experimental work reveals a negative correlation between (Formula presented.) and (Formula presented.) in this region. This consists of two distinct layers, with quadrant 4 ((Formula presented.), (Formula presented.)) dominant near the wall and quadrant 2 ((Formula presented.), (Formula presented.)) dominant close to the lower part of the separated shear layer. These results are consistent with a near-wall advection of vorticity into a region downstream of a temporarily foreshortened reattachment region, and the entrainment of slow moving and quiescent fluid into a faster, more turbulent shear layer. A comparison of instantaneous vorticity fields to the velocity-intermittency analysis shows how the pointwise results reflect larger-scale organisation of the flow. We illustrate this using results from two instantaneous datasets. In the former, extreme velocity-intermittency events corresponding to a foreshortened recirculation region (and high pressures on the stoss slope of the dune immediately downstream) arise, and the development of intense flow structures occurs as a consequence. In the other case, development of a ‘skimming flow’ with relatively little exchange between the inner and outer regions results in exceedances because of the coherence associated with this high velocity, high turbulence outer region. Thus, our results shed further light on the characteristics of dune flow in the near-wall region and, importantly for field-based research, show that useful information on flow structure can be obtained from single-point single velocity component measurements

The coupling between inner and outer scales in a zero pressure boundary layer evaluated using a Hölder exponent framework

This work considers the connectivity between large and small scales in boundary-layer turbulence by formalizing the modulation effect of the small scales by the large in terms of the pointwise Hölder condition for the small scales. We re-investigate a previously published dataset from this perspective and are able to characterize the coupling effectively using the (cross-)correlative relations between the large scale velocity and the small scale Hölder exponents. The nature of this coupling varies as a function of dimensionless distance from the wall based on inner-scaling, ${y}^{+}$, as well as on the boundary-layer height, δ. In terms of the fundamental change in the sign of the coupling between large and small scales, the critical height appears to be ${y}^{+}\sim 1000$. Below this height, small scale structures are associated with (and occur earlier than) maxima in the large scale velocity. Above this height, while the lag is similar in magnitude, the small scale structures are associated with minima in the large scale velocity. To consider these results further, we introduce a modified quadrant analysis and show that it is the coupling to the large scale low velocity state that is critical for the dynamics