scholarly journals A standard test case suite for two-dimensional linear transport on the sphere

2012 ◽  
Vol 5 (1) ◽  
pp. 189-228 ◽  
Author(s):  
P. H. Lauritzen ◽  
W. C. Skamarock ◽  
M. J. Prather ◽  
M. A. Taylor
Keyword(s):  
Initial Conditions ◽  
Model Development ◽  
Standard Test ◽  
Test Case ◽  
Two Dimensional ◽  
Wind Fields ◽  
True Solution ◽  
Functional Relations ◽  
Set Up ◽  
Cubed Sphere

Abstract. It is the purpose of this paper to propose a standard test case suite for two-dimensional transport schemes on the sphere intended to be used for model development and facilitating scheme intercomparison. The test cases are designed to assess important aspects of accuracy in geophysical fluid dynamics such as numerical order of convergence, "minimal" resolution, the ability of the transport scheme to preserve filaments, transport "rough" distributions, and to preserve pre-existing functional relations between species/tracers under challenging flow conditions. The experiments are designed to be easy to set up. They are specified in terms of two analytical wind fields (one non-divergent and one divergent) and four analytical initial conditions (varying from smooth to discontinuous). Both conventional error norms as well as novel mixing and filament preservation diagnostics are used that are easy to implement. The experiments pose different challenges for the range of transport approaches from Lagrangian to Eulerian. The mixing and filament preservation diagnostics do not require an analytical/reference solution which is in contrast to standard error norms where a "true" solution is needed. Results using the CSLAM (Conservative Semi-Lagrangian Multi-tracer) scheme on the cubed-sphere are presented for reference and illustrative purposes.

scholarly journals A standard test case suite for two-dimensional linear transport on the sphere

2012 ◽  
Vol 5 (3) ◽  
pp. 887-901 ◽  
Author(s):  
P. H. Lauritzen ◽  
W. C. Skamarock ◽  
M. J. Prather ◽  
M. A. Taylor
Keyword(s):  
Initial Conditions ◽  
Model Development ◽  
Standard Test ◽  
Test Case ◽  
Two Dimensional ◽  
Wind Fields ◽  
True Solution ◽  
Functional Relations ◽  
Set Up ◽  
Cubed Sphere

Abstract. It is the purpose of this paper to propose a standard test case suite for two-dimensional transport schemes on the sphere intended to be used for model development and facilitating scheme intercomparison. The test cases are designed to assess important aspects of accuracy in geophysical fluid dynamics such as numerical order of convergence, "minimal" resolution, the ability of the transport scheme to preserve filaments, transport "rough" distributions, and to preserve pre-existing functional relations between species/tracers under challenging flow conditions. The experiments are designed to be easy to set up. They are specified in terms of two analytical wind fields (one non-divergent and one divergent) and four analytical initial conditions (varying from smooth to discontinuous). Both conventional error norms as well as novel mixing and filament preservation diagnostics are used that are easy to implement. The experiments pose different challenges for the range of transport approaches from Lagrangian to Eulerian. The mixing and filament preservation diagnostics do not require an analytical/reference solution, which is in contrast to standard error norms where a "true" solution is needed. Results using the CSLAM (Conservative Semi-Lagrangian Multi-tracer) scheme on the cubed-sphere are presented for reference and illustrative purposes.

scholarly journals A standard test case suite for two-dimensional linear transport on the sphere: results from a collection of state-of-the-art schemes

2014 ◽  
Vol 7 (1) ◽  
pp. 105-145 ◽  
Author(s):  
P. H. Lauritzen ◽  
P. A. Ullrich ◽  
C. Jablonowski ◽  
P. A. Bosler ◽  
D. Calhoun ◽  
...  
Keyword(s):  
State Of The Art ◽  
Model Development ◽  
Finite Volume Methods ◽  
Standard Test ◽  
Ocean Modeling ◽  
Test Case ◽  
Linear Transport ◽  
Computing Platform ◽  
Wide Range ◽  
Cubed Sphere

Abstract. Recently, a standard test case suite for 2-D linear transport on the sphere was proposed to assess important aspects of accuracy in geophysical fluid dynamics with a "minimal" set of idealized model configurations/runs/diagnostics. Here we present results from 19 state-of-the-art transport scheme formulations based on finite-difference/finite-volume methods as well as emerging (in the context of atmospheric/oceanographic sciences) Galerkin methods. Discretization grids range from traditional regular latitude–longitude grids to more isotropic domain discretizations such as icosahedral and cubed-sphere tessellations of the sphere. The schemes are evaluated using a wide range of diagnostics in idealized flow environments. Accuracy is assessed in single- and two-tracer configurations using conventional error norms as well as novel diagnostics designed for climate and climate–chemistry applications. In addition, algorithmic considerations that may be important for computational efficiency are reported on. The latter is inevitably computing platform dependent. The ensemble of results from a wide variety of schemes presented here helps shed light on the ability of the test case suite diagnostics and flow settings to discriminate between algorithms and provide insights into accuracy in the context of global atmospheric/ocean modeling. A library of benchmark results is provided to facilitate scheme intercomparison and model development. Simple software and data sets are made available to facilitate the process of model evaluation and scheme intercomparison.

scholarly journals A standard test case suite for two-dimensional linear transport on the sphere: results from a collection of state-of-the-art schemes

2013 ◽  
Vol 6 (3) ◽  
pp. 4983-5076 ◽  
Author(s):  
P. H. Lauritzen ◽  
P. A. Ullrich ◽  
C. Jablonowski ◽  
P. A. Bosler ◽  
D. Calhoun ◽  
...  
Keyword(s):  
State Of The Art ◽  
Model Development ◽  
Finite Volume Methods ◽  
Standard Test ◽  
Ocean Modeling ◽  
Test Case ◽  
Linear Transport ◽  
Computing Platform ◽  
Wide Range ◽  
Cubed Sphere

Abstract. Recently, a standard test case suite for 2-D linear transport on the sphere was proposed to assess important aspects of accuracy in geophysical fluid dynamics with a "minimal" set of idealized model configurations/runs/diagnostics. Here we present results from 19 state-of-the-art transport scheme formulations based on finite-difference/finite-volume methods as well as emerging (in the context of atmospheric/oceanographic sciences) Galerkin methods. Discretization grids range from traditional regular latitude-longitude grids to more isotropic domain discretizations such as icosahedral and cubed-sphere tessellations of the sphere. The schemes are evaluated using a wide range of diagnostics in idealized flow environments. Accuracy is assessed in single- and two-tracer configurations using conventional error norms as well as novel diagnostics designed for climate and climate-chemistry applications. In addition, algorithmic considerations that may be important for computational efficiency are reported on. The latter is inevitably computing platform dependent, The ensemble of results from a wide variety of schemes presented here helps shed light on the ability of the test case suite diagnostics and flow settings to discriminate between algorithms and provide insights into accuracy in the context of global atmospheric/ocean modeling. A library of benchmark results is provided to facilitate scheme intercomparison and model development. Simple software and data-sets are made available to facilitate the process of model evaluation and scheme intercomparison.

The Emergence of Rabbinic Culture from the Perspective of Qumran

2015 ◽  
Vol 6 (2) ◽  
pp. 253-274
Author(s):  
Vered Noam
Keyword(s):  
Early Stage ◽  
Second Temple ◽  
Test Case ◽  
Literary Works ◽  
Jewish Culture ◽  
The Bible ◽  
Set Up

The rabbinic halakhic system, with its many facets and the literary works that comprise it, reflects a new Jewish culture, almost completely distinct in its halakhic content and scope from the biblical and postbiblical culture that preceded it. By examining Jewish legislation in the area of corpse impurity as a test case, the article studies the implications of Qumranic halakhah, as a way-station between the Bible and the Mishnah, for understanding how Tannaitic halakhah developed. The impression obtained from the material reviewed in the article is that the direction of the “Tannaitic revolution” was charted, its methods set up, and its principles established, at a surprisingly early stage, before the destruction of the Second Temple, and thus at the same time that the Qumran literature was created.

POLAR LOW DETECTION USING SOLAB SIOWS ARCTIC PORTAL

2017 ◽  
Author(s):  
Olga Mashtaler ◽  
Olga Mashtaler ◽  
Alexander Myasoedov ◽  
Alexander Myasoedov ◽  
Elizaveta Zabolotskikh ◽  
...  
Keyword(s):  
Model Development ◽  
Sharp Decrease ◽  
Open Water ◽  
The Arctic ◽  
Wind Fields ◽  
Polar Lows ◽  
Statistical Regularities ◽  
Meteorological Observations ◽  
Strong Winds ◽  
Synthetic Aperture Radars

The relevance of the polar lows (PLs) research is justified by their great destructive power and creation of threat to the safety of navigation in the high latitudes and along the Northern Sea Route. The most dangerous effects on maritime activities are strong winds, waves and icing. In addition, the study of the PLs acquires relevance due to the sharp decrease of the sea ice area in the Arctic in recent years and the emergence of areas of open water, suitable for the appearance and development of PLs. However, despite the importance of PLs, they are apparently not sufficiently studied. As there are no meteorological observations in the areas of their appearance, the main source of information about them are satellite observations. By using images on the SOLab SIOWS Arctic Portal from multiple satellites operating in the IR and visible ranges (e.g., MODIS and AVHRR), and using near-water wind fields from high resolution synthetic aperture radars (Sentine-1, ASAR) and low resolution scatterometers (ASCAT), we identify polar lows in various parts of the Arctic, revealing statistical regularities in the appearance of PLs, their distribution and intensity. Collected database of Pls and their characteristics will be used for further PLs forecasting model development.

scholarly journals On Kaufmann's theory of the impact of the pianoforte hammer

1920 ◽  
Vol 97 (682) ◽  
pp. 99-110 ◽  
Keyword(s):  
Initial Conditions ◽  
Practical Importance ◽  
Prima Facie ◽  
Point Of View ◽  
Infinite Length ◽  
Modes Of Vibration ◽  
Rigorous Treatment ◽  
The Subject ◽  
Set Up ◽  
The Impact

The theory of the vibrations of the pianoforte string put forward by Kaufmann in a well-known paper has figured prominently in recent discussions on the acoustics of this instrument. It proceeds on lines radically different from those adopted by Helmholtz in his classical treatment of the subject. While recognising that the elasticity of the pianoforte hammer is not a negligible factor, Kaufmann set out to simplify the mathematical analysis by ignoring its effect altogether, and treating the hammer as a particle possessing only inertia without spring. The motion of the string following the impact of the hammer is found from the initial conditions and from the functional solutions of the equation of wave-propagation on the string. On this basis he gave a rigorous treatment of two cases: (1) a particle impinging on a stretched string of infinite length, and (2) a particle impinging on the centre of a finite string, neither of which cases is of much interest from an acoustical point of view. The case of practical importance treated by him is that in which a particle impinges on the string near one end. For this case, he gave only an approximate theory from which the duration of contact, the motion of the point struck, and the form of the vibration-curves for various points of the string could be found. There can be no doubt of the importance of Kaufmann’s work, and it naturally becomes necessary to extend and revise his theory in various directions. In several respects, the theory awaits fuller development, especially as regards the harmonic analysis of the modes of vibration set up by impact, and the detailed discussion of the influence of the elasticity of the hammer and of varying velocities of impact. Apart from these points, the question arises whether the approximate method used by Kaufmann is sufficiently accurate for practical purposes, and whether it may be regarded as applicable when, as in the pianoforte, the point struck is distant one-eighth or one-ninth of the length of the string from one end. Kaufmann’s treatment is practically based on the assumption that the part of the string between the end and the point struck remains straight as long as the hammer and string remain in contact. Primâ facie , it is clear that this assumption would introduce error when the part of the string under reference is an appreciable fraction of the whole. For the effect of the impact would obviously be to excite the vibrations of this portion of the string, which continue so long as the hammer is in contact, and would also influence the mode of vibration of the string as a whole when the hammer loses contact. A mathematical theory which is not subject to this error, and which is applicable for any position of the striking point, thus seems called for.

Semi-Lagrangian exponential time-integration method for the shallow water equations on the cubed sphere grid

2020 ◽  
Vol 35 (6) ◽  
pp. 355-366
Author(s):  
Vladimir V. Shashkin ◽  
Gordey S. Goyman
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Shallow Water Equations ◽  
Time Integration ◽  
Standard Test ◽  
Integration Scheme ◽  
Test Problems ◽  
Cubed Sphere ◽  
Lagrangian Scheme ◽  
Inertia Gravity Waves

AbstractThis paper proposes the combination of matrix exponential method with the semi-Lagrangian approach for the time integration of shallow water equations on the sphere. The second order accuracy of the developed scheme is shown. Exponential semi-Lagrangian scheme in the combination with spatial approximation on the cubed-sphere grid is verified using the standard test problems for shallow water models. The developed scheme is as good as the conventional semi-implicit semi-Lagrangian scheme in accuracy of slowly varying flow component reproduction and significantly better in the reproduction of the fast inertia-gravity waves. The accuracy of inertia-gravity waves reproduction is close to that of the explicit time-integration scheme. The computational efficiency of the proposed exponential semi-Lagrangian scheme is somewhat lower than the efficiency of semi-implicit semi-Lagrangian scheme, but significantly higher than the efficiency of explicit, semi-implicit, and exponential Eulerian schemes.

scholarly journals Energy budget in internal wave attractor experiments

2019 ◽  
Vol 880 ◽  
pp. 743-763 ◽  
Author(s):  
Géraldine Davis ◽  
Thierry Dauxois ◽  
Timothée Jamin ◽  
Sylvain Joubaud
Keyword(s):  
Velocity Field ◽  
Internal Wave ◽  
Boundary Layers ◽  
Energy Budget ◽  
Dissipation Rate ◽  
Theoretical Expression ◽  
Two Dimensional ◽  
Energy Sink ◽  
Set Up ◽  
Different Sources

The current paper presents an experimental study of the energy budget of a two-dimensional internal wave attractor in a trapezoidal domain filled with uniformly stratified fluid. The injected energy flux and the dissipation rate are simultaneously measured from a two-dimensional, two-component, experimental velocity field. The pressure perturbation field needed to quantify the injected energy is determined from the linear inviscid theory. The dissipation rate in the bulk of the domain is directly computed from the measurements, while the energy sink occurring in the boundary layers is estimated using the theoretical expression for the velocity field in the boundary layers, derived recently by Beckebanze et al. (J. Fluid Mech., vol. 841, 2018, pp. 614–635). In the linear regime, we show that the energy budget is closed, in the steady state and also in the transient regime, by taking into account the bulk dissipation and, more importantly, the dissipation in the boundary layers, without any adjustable parameters. The dependence of the different sources on the thickness of the experimental set-up is also discussed. In the nonlinear regime, the analysis is extended by estimating the dissipation due to the secondary waves generated by triadic resonant instabilities, showing the importance of the energy transfer from large scales to small scales. The method tested here on internal wave attractors can be generalized straightforwardly to any quasi-two-dimensional stratified flow.

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