scholarly journals The Stability Principle and global weak solutions of the free surface semi-geostrophic equations in geostrophic coordinates

2019 ◽  
Vol 475 (2229) ◽  
pp. 20180787
Author(s):  
M. J. P. Cullen ◽  
T. Kuna ◽  
B. Pelloni ◽  
M. Wilkinson
Keyword(s):  
Weak Solutions ◽  
Large Scale ◽  
Optimal Transport ◽  
Three Dimensional ◽  
Mathematical Framework ◽  
Atmospheric Flows ◽  
Stability Principle ◽  
The Stability ◽  
Dimensional Domain ◽  
Upper Boundary

The semi-geostrophic equations are used widely in the modelling of large-scale atmospheric flows. In this note, we prove the global existence of weak solutions of the incompressible semi-geostrophic equations, in geostrophic coordinates, in a three-dimensional domain with a free upper boundary. The proof, based on an energy minimization argument originally inspired by the Stability Principle as studied by Cullen, Purser and others, uses optimal transport techniques as well as the analysis of Hamiltonian ODEs in spaces of probability measures as studied by Ambrosio and Gangbo. We also give a general formulation of the Stability Principle in a rigorous mathematical framework.

Potential Flow Field Generated by Downstream Moving Bars and Propagated on a Turbine Blade at Low Reynolds Number

2011 ◽  
Author(s):  
Ve´ronique Penin ◽  
Pascale Kulisa ◽  
Franc¸ois Bario
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Numerical Study ◽  
Three Dimensional ◽  
Potential Effect ◽  
Navier Stokes ◽  
Turbine Cascade ◽  
Wake Interaction ◽  
Rotor Stator Interaction ◽  
The Stability

During the last few decades, the size and weight of turbo-machinery have been continuously reduced. However, by decreasing the distance between rows, rotor-stator interaction is strengthened. Two interactions now have the same magnitude: wake interaction and potential effect. Studying this effect is essential to understand rotor-stator interactions. Indeed, this phenomenon influences the whole flow, including the boundary layer of the upstream and downstream blades, ergo the stability of the flow and the efficiency of the machine. A large scale turbine cascade followed by a specially designed rotating cylinder system is used. Synchronised velocity LDA measurements on the vane profile show the flow and boundary layer behavior due to the moving bars. To help the general understanding and to corroborate our experimental results, numerical investigations are carried out with an unsteady three dimensional Navier-Stokes code. Moreover, the numerical study informs about the potential disturbance to the whole flow of the cascade.

Parallel solution of the obstacle problem in Grid environments

2011 ◽  
Vol 25 (4) ◽  
pp. 488-495 ◽  
Author(s):  
M. Chau ◽  
R. Couturier ◽  
J. Bahi ◽  
P. Spiteri
Keyword(s):  
Iterative Algorithm ◽  
Obstacle Problem ◽  
General Framework ◽  
Large Scale ◽  
Three Dimensional ◽  
Computational Experiments ◽  
Parallel Solution ◽  
Asynchronous Algorithms ◽  
Grid Environments ◽  
Dimensional Domain

The present study deals with the solution of the obstacle problem defined in a three-dimensional domain. In order to solve a large-scale obstacle problem, the use of parallelism is necessary. In this work we present a parallel synchronous iterative algorithm to solve this problem and its asynchronous version. For the considered problem, the convergence of parallel synchronous and asynchronous algorithms is analysed in a general framework. Finally, computational experiments on GRID’5000, the French national grid, are presented and analysed. They allow us to compare both synchronous and asynchronous versions with local and distributed clusters.

Design and Manufacture of a New Large-Scale Three-Dimensional Geomechanics Model Test System

2010 ◽  
Vol 97-101 ◽  
pp. 2770-2773
Author(s):  
Wei Shen Zhu ◽  
Yong Li ◽  
Min Yong ◽  
Q.B. Zhang ◽  
Shu Cai Li
Keyword(s):  
Model Test ◽  
Large Scale ◽  
Three Dimensional ◽  
Great Depth ◽  
Test System ◽  
Great Stability ◽  
Underground Caverns ◽  
Structural Frame ◽  
The Stability ◽  
Design And Manufacture

Geomechanics modeling has played important role in geotechnical engineering. In order to investigate on the stability of underground caverns at great depth, a large-scale geomechanics model test system was designed and manufactured. The system mainly consisted of a steel structural frame and a hydraulic loading control system, which can apply active loading on six sides with a true three-dimensional stress state. Newly developed combinational ball sliding walls were installed on each of the major loading surfaces, which were significantly reduced the friction due to model deformation. The system has apparent technical advantages such as high stiffness, great stability, and flexibility of assembly, and easy adjustment of its dimensions.

scholarly journals A Large Goaf Group Treatment by means of Mine Backfill Technology

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Hanwen Jia ◽  
Baoxu Yan ◽  
Erol Yilmaz
Keyword(s):  
Group Treatment ◽  
Laser Scanning ◽  
Large Scale ◽  
Mechanical Characteristics ◽  
Three Dimensional ◽  
Stability Diagram ◽  
Surrounding Rock ◽  
Mine Backfill ◽  
Treatment Scheme ◽  
The Stability

There are few studies on the management methods of large-scale goaf groups per the specific surrounding rock mass conditions of each goaf. This paper evaluates comprehensively the stability of the multistage large-scale goaf group in a Pb-Zn mine in Inner Mongolia, China, via the modified Mathews stability diagram technique. The volume of each goaf to be backfilled was quantitatively analyzed in the combination of theoretical analysis and three-dimensional laser scanning technology. The corresponding mechanical characteristics of the filling were determined by laboratory testing while formulating the treatment scheme of the large goaf group using the backfill method. The applicability of the treatment scheme using the backfill was verified by the combination of the numerical results of the distribution of the surrounding rock failure zone and the monitored data of the surface subsidence. The research results and treatment scheme using the backfill can provide a reference for similar conditions of mines worldwide.

Large-scale geomechanical model testing of an underground cavern group in a true three-dimensional (3-D) stress state

2010 ◽  
Vol 47 (9) ◽  
pp. 935-946 ◽  
Author(s):  
W. S. Zhu ◽  
Q. B. Zhang ◽  
H. H. Zhu ◽  
Y. Li ◽  
J.-H. Yin ◽  
...  
Keyword(s):  
Stress State ◽  
Large Scale ◽  
Three Dimensional ◽  
Great Depth ◽  
Model Tests ◽  
Geomechanical Model ◽  
Testing Procedures ◽  
Test Initiation ◽  
The Stability ◽  
Made In

The stability of a large cavern group at great depth is discussed on the basis of large-scale three-dimensional (3-D) geomechanical model tests and numerical simulations. The model tests are described in detail. Improvements in the tests were made in terms of experimental techniques and advanced measurement methods. The model tests utilized active loading on six sides of a rock mass in a true 3-D stress state. During the model construction, precast blocks were fabricated and monitoring holes were defined prior to test initiation. Newly developed combination ball-sliding walls were installed on each of the major loading surfaces to reduce the friction induced by model deformation. A unique grouting and installation technique employing prestressed cables was adopted in the tests. A digital photogrammetric technique, displacement sensing bars using fiber Bragg grating (FBG) technology, and mini multipoint extensometers were developed for measuring deformation. Overloading tests were then conducted for different overburden depths, and 3-D numerical analyses were performed to simulate the testing procedures. Conclusions regarding the stability of the cavern group were developed based on a comparison between the experimental and numerical results.

The Nontraditional Coriolis Terms and Tropical Convective Clouds

2020 ◽  
Vol 77 (12) ◽  
pp. 3985-3998
Author(s):  
Matthew R. Igel ◽  
Joseph A. Biello
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Zonal Flow ◽  
Mathematical Framework ◽  
Freezing Level ◽  
Almost Everywhere ◽  
Mesoscale Convective ◽  
Simple Scaling ◽  
Upper Level ◽  
Scale Limit

AbstractThe full, three-dimensional Coriolis force includes the familiar sine-of-latitude terms as well as frequently dropped cosine-of-latitude terms [nontraditional Coriolis terms (NCT)]. The latter are often ignored because they couple the zonal and vertical momentum equations that in the large-scale limit of weak vertical velocity are considered insignificant almost everywhere. Here, we ask whether equatorial mesoscale clouds that fall outside the large-scale limit are affected by the NCT. A simple scaling indicates that a Lagrangian parcel convecting at 10 m s−1 through the depth of the troposphere should be deflected over 2 km to the west. To understand the real impact of NCT, we develop a mathematical framework that describes an azimuthally symmetric convective circulation with an analytical expression for an incompressible poloidal flow. Because the model incorporates the full three-dimensional flow associated with convection, it uniquely predicts not only the westward tilt of clouds but also a meridional diffluence of western cloud outflow. To test these predictions, we perform a set of cloud-resolving simulations whose results show preferential lifting of surface parcels with positive zonal momentum and zonal asymmetry in convective strength. RCE simulations show changes to the organization of coherent precipitation regions and a decrease in mean convective intensity of approximately 2 m s−1 above the freezing level. An additional pair of dry cloud-resolving simulations designed to mimic the steady-state flow of the model show maximum perturbations to the upper-level zonal flow of 8 m s−1. Together, the numerical and analytic results suggest the NCT consequentially alter equatorial mesoscale convective circulations and should be considered in conceptual models.

scholarly journals Study on the Influence of Sponge Road Bioretention Facility on the Stability of Subgrade Slope

Water ◽  
2021 ◽  
Vol 13 (23) ◽  
pp. 3466
Author(s):  
Wensheng Tang ◽  
Haiyuan Ma ◽  
Xinyue Wang ◽  
Zhiyu Shao ◽  
Qiang He ◽  
...  
Keyword(s):  
Large Scale ◽  
Water Pressure ◽  
Three Dimensional ◽  
Road Construction ◽  
Element Model ◽  
Factors Affecting ◽  
Runoff Pollution Control ◽  
The Stability ◽  
Three Dimensional Finite Element ◽  
Geotechnical Tests

With the large-scale application of sponge city facilities, the bioretention facility in urban roads will be one of the key factors affecting the safety of construction facilities in areas with abundant rainfall. In this study, by establishing a three-dimensional finite element model for numerical analysis and combining it with geotechnical tests, the effects of bioretention facility on water pressure distribution, seepage path, and slope stability under rainwater seepage conditions are proposed. In addition, this study puts forward the relationship between the parameters of the bioretention facility and the stability of the slope in combination with the effect of runoff pollution control, which provides direction and basis for the planning, design, and construction of sponge cities in road construction.

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