Gravity Waves Generated by Sheared Three-Dimensional Potential Vorticity Anomalies

International audienceThe gravity waves (GWs) produced by three-dimensional potential vorticity (PV) anomalies are examined under the assumption of constant vertical shear, constant stratication, and unbounded domain. As in the two-dimensional case analyzed in an earlier paper, the disturbance near the PV anomaly is well modeled by quasi-geostrophic theory. At larger distances the nature of the disturbance changes across the two inertial layers that are located above and below the anomaly, and it takes the form of a vertically propagating GW beyond these. For a horizontally monochromatic PV anomaly of innitesimal depth, the disturbance is described ana-lytically using both an exact solution and a WKB approximation; the latter includes an exponentially small term that captures the change of the solution near the PV anomaly induced by the radiation boundary condition in the far eld. The analytical results reveal a strong sensitivity of the emission to the Richardson number and to the orientation of the horizontal wavenumber: the absorptive properties of the inertial layers are such that the emission is maximized in the Northern Hemisphere for wavenumbers at negative angles to the shear. For localized PV anomalies, numerical computations give the temporal evolution of the GW eld. Ana-lytical and numerical results are also used to establish an explicit formfor the Eliassen-Palmux that could be used to parameterize GW sources in GCMs. The properties of the Eliassen-Palm ux vector imply that in a westerly shear, the GWs exert a drag in a southwest direction in the upper inertial layer, and in a northwest direction at the altitudes where the GWs dissipate aloft. © 2012 American Meteorological Society

Gravity waves generated by sheared potential vorticity anomalies

International audienceThe gravity waves (GWs) generated by potential vorticity (PV) anomalies in a rotating stratified shear flow are examined under the assumptions of constant vertical shear, two-dimensionality, and unbounded domain. Near a PV anomaly, the associated perturbation is well modeled by quasigeostrophic theory. This is not the case at large vertical distances, however, and in particular beyond the two inertial layers that appear above and below the anomaly; there, the perturbation consists of vertically propagating gravity waves. This structure is described analytically, using an expansion in the continuous spectrum of the singular modes that results from the presence of critical levels. Several explicit results are obtained. These include the form of the Eliassen-Palm (EP) flux as a function of the Richardson number N2/?2, where N is the Brunt-Väisälä frequency and L the vertical shear. Its nondimensional value is shown to be approximately exp(-N/L)/8 in the far-fieldGWregion, approximately twice that between the two inertial layers. These results,which imply substantialwave-flowinteractions in the inertial layers, are valid for Richardson numbers larger than 1 and for a large range of PV distributions. In dimensional form they provide simple relationships between the EP fluxes and the large-scale flow characteristics. As an illustration, the authors consider a PV disturbance with an amplitude of 1 PVU and a depth of 1 km, and estimate that the associated EP flux ranges between 0.1 and 100 mPa for a Richardson number between 1 and 10. These values of the flux are comparable with those observed in the lower stratosphere, which suggests that the mechanism identified in this paper provides a substantial gravity wave source, one that could be parameterized in GCMs. © 2010 American Meteorological Society

Lagrangian temperature and vertical velocity fluctuations due to gravity waves in the lower stratosphere

International audienceWave-induced Lagrangian fluctuations of temperature and vertical velocity in the lower stratosphere are quantified using measurements from superpressure balloons (SPBs). Observations recorded every minute along SPB flights allow the whole gravity wave spectrum to be described and provide unprecedented information on both the intrinsic frequency spectrum and the probability distribution function of wave fluctuations. The data set has been collected during two campaigns coordinated by the French Space Agency in 2010, involving 19 balloons over Antarctica and 3 in the deep tropics. In both regions, the vertical velocity distributions depart significantly from a Gaussian behavior. Knowledge on such wave fluctuations is essential for modeling microphysical processes along Lagrangian trajectories. We propose a new simple parameterization that reproduces both the non-Gaussian distribution of vertical velocities (or heating/cooling rates) and their observed intrinsic frequency spectrum

Jets, vortex et ondes d'inertie-gravité: séparation dynamique et émission

Nonlinear geostrophic adjustment of rectilinear jets is examined analytically. It is shown that the Lagrangian formalism is best suited to describe unambiguously the splitting between a balanced part and a fast, gravity wave part of the flow. Modifications to the standard scenario of geostrophic adjustment are highlighted. Data analysis of FASTEX radiosoundings is carried out to show that atmospheric jets and fronts are a significant source of inertia-gravity waves. A mechanism for the radiation of gravity waves from non-stationary vortical motions is illustrated theoretically by considering the waves excited by an ellipsoidal vortex in a stratified fluid.L'ajustemnt géostrophique nonlinéaire de fronts et de jets est analysé. Il est démontré que le formalisme lagrangien est le mieux adapté pour décrire sans ambiguité ce problème. Des modifications du scenario classique d'ajustement de Rossby sont mises en évidence. L'analyse de radiosondages de la campagne FASTEX montre que les jets et les fronts atmosphériques aux moyennes latitudes sont des sources importantes d'ondes de gravité. Un mécanisme d'excitation d'ondes de gravité à partir de mouvements vorticaux est analysé théoriquement dans le cadre d'un fluide stratifié, pour les ondes excitées par un tourbillon ellispoïdal

A barycenter-based approach for the multi-model ensembling of subseasonal forecasts

Ensemble forecasts and their combination are explored from the perspective of a probability space. Manipulating ensemble forecasts as discrete probability distributions, multi-model ensembles (MMEs) are reformulated as barycenters of these distributions. Barycenters are defined with respect to a given distance. The barycenter with respect to the L2-distance is shown to be equivalent to the pooling method. Then, the barycenter-based approach is extended to a different distance with interesting properties in the distribution space: the Wasserstein distance. Another interesting feature of the barycenter approach is the possibility to give different weights to the ensembles and so to naturally build weighted MME. As a proof of concept, the L2- and the Wasserstein-barycenters are applied to combine two models from the S2S database, namely the European Centre Medium-Range Weather Forecasts (ECMWF) and the National Centers for Environmental Prediction (NCEP) models. The performance of the two (weighted-) MMEs are evaluated for the prediction of weekly 2m-temperature over Europe for seven winters. The weights given to the models in the barycenters are optimized with respect to two metrics, the CRPS and the proportion of skilful forecasts. These weights have an important impact on the skill of the two barycenter-based MMEs. Although the ECMWF model has an overall better performance than NCEP, the barycenter-ensembles are generally able to outperform both. However, the best MME method, but also the weights, are dependent on the metric. These results constitute a promising first implementation of this methodology before moving to combination of more models.Comment: 24 pages, 9 figure

Applying a deformable surface model to identify foam beads in a sample of polypropylene foam and follow their evolution in a dynamic crash loading experiment

The objective of this work is to study the deformation of polypropylene foam during a dynamic crash loading. The first difficulty consisted in conceiving an experimental setup that would allow to visualise intermediate steps in the deformation of the foam, which requires a non-destructive imaging technique. Fast external surface imaging is not sufficient for an accurate study of the deformation, therefore our attention focused on X-ray tomography. Because crash loading time is much smaller than tomogaphic acquisition time (a few milliseconds vs. almost an hour), several interrupted crashes are applied (a dynamic loading with a constraint on the strain), in between which a micro-tomogram is acquired. If we assume that the foam behaviour is not modified by the interruptedness of the dynamic loading (as in quasi-static loading), then we obtain a series of tomograms showing the evolution of the foam sample during dynamic compression. The second difficulty, that is presented here, is to use this information to quantify the foam deformation (and subsequently use this experimental data for predictive modelling) at the mesoscopic scale, i.e. that of the beads. Polypropylene foam is a multi-cellular material, each bead (around 2mm in diameter) is composed of micrometric cells, making the separation of the beads a difficult image analysis problem, as compared to separation of foam bubbles in a metallic foam, for instance. The solution we propose extracts a representative volume inside each bead, in order to calculate, at each stage of the compression, values such as grain density. For this purpose, a first processing, consisting of a sequence of simple signal processing and discrete morphological operators, determines approximate bead centres. With a simple nearest neighbours approach, the position for a given bead is identified for each stage of the experiment. From each centre a deformable surface algorithm is applied: a spherical mesh is placed inside the bead and expands until reaching the bead walls. This allows us to visualise the deformation and measure the average density of each bead during the compression. Unfortunately, due to the difficulty in precisely identifying bead walls (even manually), complete bead volumes and wall thickness is not yet determined: the deformable surfaces contain only the majority of the inside of the beads, and there still remains significant intersticial volume which has no physical significance (it represents a volume in which the bead wall is located, volume that is a function of the image processing). Future work to obtain more accurate data would focus on methods such as skeletonisation of the intersticial volume

Geostrophic instabilities of a front in a stratified rotating fluid

Les instabilités d'une région de front dans un fluide stratifié en rotation sont étudiées. On s'intéresse plus particulièrement à l'instabilité dite de Rossby-Kelvin, qui existe grâce au couplage d'une onde de Rossby et d'une onde Kelvin. La stabilité linéaire d'un front dans un fluide à deux couches est étudiée numériquement par la méthode de collocation. Les résultats de Sakai (1989) pour le cas de deux couches d'égale hauteur sont confirmés et ceci valide notre approche. Celle-ci permet d'étendre ces résultats aux cas non-symétriques et au cas où le front intersecte le fond ou la surface. Ensuite, la stabilité d'un front dans un fluide continuement stratifié est analysée par des simulations numériques à l'aide du modèle méso-échelle WRF (Weather Research and Forecast). L'existence de l'instabilité de Rossby-Kelvin dans un fluide stratifié est ainsi confirmée, avec des taux de croissance comparables au cas du fluide à deux couches