An overview of the parametrization of gravity ‐wave drag in numerical ‐weather prediction and climate simulation models is presented. The focus is primarily on understanding the current status of gravity wave drag parametrization as a step towards the new parametrizations that will be needed for the next generation of atmospheric models. Both the early history and latest developments in the field are discussed. Parametrizations developed specifically for orographic and convective sources of gravity waves are described separately, as are newer parametrizations that collectively treat a spectrum of gravity wave motions. The differences in issues in and approaches for the parametrization of the lower and upper atmospheres are highlighted. Various emerging issues are also discussed, such as explicitly resolved gravity waves and gravity wave drag in models, and a range of unparametrized gravity wave processes that may need attention for the next generation of gravity wave drag parametrizations in models.

An overview of the past, present and future of gravity-wave drag parametrization for numerical climate and weather prediction models

Stress Intensity Fctor for Intermal and Extemal Surface Cracks in Cylindrical Vessels

The thickness of the entrainment zone at the top of the marine atmosphericboundary layer (MABL) has been documented by an airborne lidar on twoconsecutive days during a cold-air outbreak episode over the Mediterranean.In addition to the lidar observations, in situ turbulent flux measurementsat three levels in the MABL were made by a second aircraft. The flights' tracksare broken down in segments 25–30 km long and the data are filtered for theparametrization of turbulent entrainment in the MABL at scales smaller thana few kilometres. The structural parameters of the entrainment zone aredetermined by lidar from the distributions of the instantaneous MABL topheight. The average values Ph0 and Ph2 of the cumulativeprobability distributions are used to define the bottom and top heights of the entrainment zone h0 and h2, respectively. The parameters h0 andh2 are calculated by reference to a linear vertical buoyancy flux profilein the framework of a first-order jump model. The model is constrained by bothlidar and in situ data to determine Ph0 and Ph2 and so h0and h2. In unstable conditions theaverage fraction Ph0 is estimated to be 6.0 ± 1%. It is shown to beslightly sensitive to the presence of cloud at small cloud fractions.The mean value of the ratio of the inversion level buoyancy flux to the surfacebuoyancy flux ARv is found to range from 0.15 to 0.30 depending on the shearin the MABL. The average value is 0.22 ± 0.05. Our resultsare in good agreement with previous analysis at comparable spatial scales.In purely convective conditions, the value of ARv given by theparametrizations fitted to our results is about 0.10–0.12, a value smallerthan the commonly accepted value of 0.2. When compared to previousparametrization results, our proportionality constant for the mechanicalproduction of turbulent kinetic energy is also found to be scaled down, ingood agreement with large-eddy simulation results. It is suggestedthat mesoscale organized motions in the MABL is the source of thisdifference.

Lidar determination of the entrainment zone thickness at the top of the unstable marine atmospheric boundary layer

This paper utilizes the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) mesoscale model (MM5) in a two-dimensional (2D) configuration at 4-km horizontal grid spacing in order to better understand the relationship between orographic precipitation and the height and width of a barrier, as well as the ambient flow, uniform moist static stability, and freezing level. The focus is on how these parameters affect the orographic precipitation by changing the circulation and microphysical structures over the barrier. As the low-level flow becomes blocked for moist nondimensional mountain heights greater than 3.0, there is a rapid upstream shift in the precipitation maximum and a reduction in precipitation over the upper windward slope. For the terrain geometries used in this study (500 to 3500 m high and 25- to 50-km half-width), the maximum precipitation is a strong function of barrier slope for relatively weak upstream flow (U = 10 m s−1). For moderate ...

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Sensitivity of Orographic Precipitation to Changing Ambient Conditions and Terrain Geometries: An Idealized Modeling Perspective

Thank you very much for downloading theoretical numerical analysis a functional analysis framework. Maybe you have knowledge that, people have look numerous times for their chosen readings like this theoretical numerical analysis a functional analysis framework, but end up in malicious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they juggled with some harmful bugs inside their laptop.

Theoretical Numerical Analysis A Functional Analysis Framework

The PYREX program is a major field study of the dynamical influence of the Pyrenees mountains (on the border between France and Spain) on the atmospheric circulation. In October and November 1990 a large number of experimental means had been deployed in the area, including additional sounding systems, automated stations at high elevation sites, wind profilers, sodars, constant level balloons, and four research airplanes. The main focus was on the quantification of the retardation of the cross-mountain flow by the range, but a number of related mesoscale phenomena had been captured, e.g. the formation of lee waves, lee eddies, sheltering areas, and local surface winds. The data interpretation was supported by an extensive effort in meso-scale numerical modelling, and it is argued that only numerical models, conveniently qualified by observations, can document the momentum budget in a consistent way. Improvements in the field of mountain waves and mountain roughness representation in the large-scale atmospheric models are expected from the PYREX results, as well as improvements in the performance of mesoscale models for the operational forecasts. The present paper presents a broad introduction to the experiment. It reviews the experimental set-up and the available data sets. Finally, two more specific topics are discussed in depth, as examples of the available data and modelling strategy: the lee wave event of 15 October 1990 is presented with both experimental and model results. Some of the findings concerning the Tramontana wind are also discussed

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The Atmospheric Momentum Budget over a Major Mountain Range: First Results of the PYREX Field Program

Evaluation of structural integrity of a cracked structure has become an important matter in the industrial field since couples of decades. However, damage process occurred in a structural component is not yet fixed. The objective of this research was to compute the stress intensity factor KI, in mode I, using in the linear elastic domain, by the finite element method and the extended finite element method. The defect studied in this survey has a form of a longitudinal semi-elliptic crack, located on the outer surface of the tube. A summary of the paper contains a numerical convergence for each method in terms of accuracy and limitations. The proposed methodology and outcomes released from this study act as novel design tool for the industrial engineers when is required to generate a robust solution for product development working in critical conditions.

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Computation of the stress intensity factor KI for external longitudinal semi-elliptic cracks in the pipelines by FEM and XFEM methods

Numerical simulations of a mountain wave observed during the Pyrenees Experiment': hydrostatic/non hydrostatic comparison and time evolution

For a long time, cracked structures have triggered various researchers to develop a structural integrity approach and design models to address the fracture problems. In the present study, a pipeline with an axial semi-elliptical surface defect was examined in detail. Recent works have highlighted the use of the classical finite element method (CFEM) as numerical tools to solve the fracture mechanics; however, this approach comes with a few difficulties in the modelling aspects. To overcome this issue, we proposed the use of the extended finite element method (XFEM), which was implemented in the commercial version of Abaqus software. Moreover, we have used the results based on this technique in the volumetric method to estimate the stress intensity factors (SIFs). Then, this parameter was employed to build the failure assessment diagram (FAD). The FAD curve was used in the current investigation because it is one of the conventional methods for the evaluation of flaws in steel pipes. The XFEM simulations enable us to draw an FAD curve that can be used as a practical reference for defect evaluation in pipeline systems in the industrial world.

Analysis of Crack Behaviour in Pipeline System Using FAD Diagram Based on Numerical Simulation under XFEM

In this work, a numerical solution of the incompressible Navi- er-Stokes equations is proposed. The method suggested is based on an algorithm of discretization by mixednite elements with a posteriori er- ror estimation of the computed solutions. In order to evaluate the per- formance of the method, the numerical results are compared with some previously published works or with others coming from commercial code like Adina system.

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Ahmed Elkhalfi

Papers

The Atmospheric Momentum Budget over a Major Mountain Range: First Results of the PYREX Field Program

Computation of the stress intensity factor KI for external longitudinal semi-elliptic cracks in the pipelines by FEM and XFEM methods

Numerical simulations of a mountain wave observed during the Pyrenees Experiment': hydrostatic/non hydrostatic comparison and time evolution

Analysis of Crack Behaviour in Pipeline System Using FAD Diagram Based on Numerical Simulation under XFEM

An a posteriori error estimate for mixed finite element approximations of the navier-stokes equations