scholarly journals Overshooting in simulations of compressible convection

2019 ◽  
Vol 631 ◽  
pp. A122 ◽  
Author(s):  
P. J. Käpylä
Keyword(s):  
Heat Conduction ◽  
Energy Flux ◽  
Heat Conductivity ◽  
Convection Zone ◽  
Strong Dependence ◽  
Three Dimensional ◽  
Power Laws ◽  
Solar Convection ◽  
Thermal Saturation ◽  
Set Up

Context. Convective motions that overshoot into regions that are formally convectively stable cause extended mixing. Aims. We aim to determine the scaling of the overshooting depth (dos) at the base of the convection zone as a function of imposed energy flux (ℱn) and to estimate the extent of overshooting at the base of the solar convection zone. Methods. Three-dimensional Cartesian simulations of hydrodynamic compressible non-rotating convection with unstable and stable layers were used. The simulations used either a fixed heat conduction profile or a temperature- and density-dependent formulation based on Kramers opacity law. The simulations covered a range of almost four orders of magnitude in the imposed flux, and the sub-grid scale diffusivities were varied so as to maintain approximately constant supercriticality at each flux. Results. A smooth heat conduction profile (either fixed or through Kramers opacity law) leads to a relatively shallow power law with dos ∝ ℱn0.08 for low ℱn. A fixed step-profile of the heat conductivity at the bottom of the convection zone leads to a somewhat steeper dependency on dos ∝ ℱn0.12 in the same regime. Experiments with and without subgrid-scale entropy diffusion revealed a strong dependence on the effective Prandtl number, which is likely to explain the steep power laws as a function of ℱn reported in the literature. Furthermore, changing the heat conductivity artificially in the radiative and overshoot layers to speed up thermal saturation is shown to lead to a substantial underestimation of the overshooting depth. Conclusions. Extrapolating from the results obtained with smooth heat conductivity profiles, which are the most realistic set-up we considered, suggest that the overshooting depth for the solar energy flux is about 20% of the pressure scale height at the base of the convection zone. This is two to four times higher than the estimates from helioseismology. However, the current simulations do not include rotation or magnetic fields, which are known to reduce convective overshooting.

scholarly journals Rotational Effects on Reynolds Stresses in the Solar Convection Zone

1991 ◽  
Vol 130 ◽  
pp. 98-100
Author(s):  
P. Pulkkinen ◽  
I. Tuominen ◽  
A. Brandenburg ◽  
Å. Nordlund ◽  
R.F. Stein
Keyword(s):  
Reynolds Stress ◽  
Convection Zone ◽  
Rotation Axis ◽  
Three Dimensional ◽  
External Parameter ◽  
Reynolds Stresses ◽  
Solar Convection Zone ◽  
Hydrodynamic Simulations ◽  
Solar Convection ◽  
Good Agreement

AbstractThree-dimensional hydrodynamic simulations are carried out in a rectangular box. The angle between gravity and rotation axis is kept as an external parameter in order to study the latitude-dependence of convection. Special attention is given to the horizontal Reynolds stress and the ∧-effect (Rüdiger, 1989). The results of the simulations are compared with observations and theory and a good agreement is found.

Challenges of magnetism in the turbulent Sun

2006 ◽  
Vol 2 (S239) ◽  
pp. 488-493
Author(s):  
Allan Sacha Brun ◽  
Mark S. Miesch ◽  
Juri Toomre
Keyword(s):  
Magnetic Fields ◽  
Differential Rotation ◽  
Convection Zone ◽  
Three Dimensional ◽  
Reynolds Stresses ◽  
Turbulent Layer ◽  
Solar Convection ◽  
Mean Fields ◽  
Global Modelling ◽  
Parallel Supercomputers

AbstractThree-dimensional global modelling of turbulent convection coupled to rotation and magnetism within the Sun are revealing processes relevant to many stars. We study spherical shells of compressible convection spanning many density scale heights using the MHD version of the anelastic spherical harmonic (ASH) code on massively parallel supercomputers. The simulations reveal that strong magnetic fields can be realized in the bulk of the solar convection zone while still attaining differential rotation profiles that make good contact with helioseismic findings. We find that the Maxwell and Reynolds stresses present in such a turbulent layer play an important role in redistributing angular momentum, with the latter maintaining the differential rotation, aided by baroclinic forcing at the base of the convection zone which is consistent with a tachocline there. The dynamo processes generate strong non-axisymmetric and intermittent fields and weak mean (axisymmetric) fields, but do not possess a regular cyclic magnetism. The explicit inclusion of penetrative convection into the tachocline below is modifying such behavior, serving to build strong toroidal magnetic fields there that may yield more prominent mean fields that have the potential of erupting upward.

scholarly journals Numerical simulations of sunspots

2006 ◽  
Vol 2 (S239) ◽  
pp. 507-509
Author(s):  
G. J. J. Botha ◽  
A. M. Rucklidge ◽  
N. E. Hurlburt
Keyword(s):  
Convection Zone ◽  
Three Dimensional ◽  
Mhd Equations ◽  
Numerical Code ◽  
Axisymmetric Solution ◽  
Solar Convection Zone ◽  
Solar Convection ◽  
Linear Evolution ◽  
Compressible Mhd Equations ◽  
Parameter Values

AbstractThe origin, structure and evolution of sunspots are investigated using a numerical model. The compressible MHD equations are solved with physical parameter values that approximate the top layer of the solar convection zone. A three dimensional (3D) numerical code is used to solve the set of equations in cylindrical geometry, with the numerical domain in the form of a wedge. The linear evolution of the 3D solution is studied by perturbing an axisymmetric solution in the azimuthal direction. Steady and oscillating linear modes are obtained.

scholarly journals Large-scale flows and convection at the base of solar convection zone

2006 ◽  
Vol 2 (S239) ◽  
pp. 425-430
Author(s):  
Evgeniy Tikhomolov
Keyword(s):  
Magnetic Fields ◽  
Large Scale ◽  
Convection Zone ◽  
Three Dimensional ◽  
Solar Radius ◽  
Solar Convection Zone ◽  
Solar Convection ◽  
Rotation Periods ◽  
Scale Temperature ◽  
Local Sound

AbstractDevelopment of convection in sun's outer shell is caused by reduction of effectiveness of energy transfer by radiation. Traditionally, models of solar convection are considered to be axisymmetric on the scale of solar radius. Such models provide basic understanding of convection under solar conditions. However, interpretation of a number of observable large-scale long-lived solar phenomena requires developing a non-axisymmetric approach. We present such a model in which large-scale non-axisymmetry is caused by large-scale flows such as Rossby waves and vortices. We model flows near the base of the solar convection zone. Anelastic approximation is used, which is valid for flow velocities much smaller than local sound speed. Our three-dimensional numerical simulations show that interaction of convection with large-scale flows leads to the establishment of non-axisymmetric large-scale temperature distribution. The interaction also gives rise to large-scale variations of penetration depth of convective plumes. Generation of the magnetic field by large-scale non-axisymmetric flows can explain such solar phenomena as complexes of activity, active longitudes, drifts of large-scale magnetic fields from equator to the poles, and appearance of distinct rotation periods of magnetic fields at some latitudes. We discuss a possibility of detection of large-scale non-axisymmetric flows and temperature distributions associated with them by the methods of helioseismology.

scholarly journals Magnetic Pumping at the Base of the Solar Convection Zone

2001 ◽  
Vol 203 ◽  
pp. 156-158
Author(s):  
S. M. Tobias ◽  
N. H. Brummell ◽  
J. Toomre
Keyword(s):  
Magnetic Flux ◽  
Numerical Experiments ◽  
Convection Zone ◽  
Three Dimensional ◽  
Solar Dynamo ◽  
Penetrative Convection ◽  
Solar Convection Zone ◽  
Solar Convection

The transport of magnetic flux from the convection zone into the stably-stratified tachocline is a key component of the proposed interface scenario for the solar dynamo. In this paper we give a summary of the results from three-dimensional numerical experiments (detailed in Tobias et al. 2000) of pumping of magnetic flux by turbulent, penetrative convection. We also list how the efficiency of pumping depends on the parameters of the convection.

scholarly journals Vibration characteristics of triple-gear-rotor system in compressed air energy storage under variable torque load

2021 ◽  
Vol 104 (1) ◽  
pp. 003685042098705
Author(s):  
Xinran Wang ◽  
Yangli Zhu ◽  
Wen Li ◽  
Dongxu Hu ◽  
Xuehui Zhang ◽  
...  
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Element Model ◽  
Rotor System ◽  
Dynamic Responses ◽  
System Response ◽  
Rotating Speed ◽  
Torque Load ◽  
Set Up ◽  
Two Stages

This paper focuses on the effects of the off-design operation of CAES on the dynamic characteristics of the triple-gear-rotor system. A finite element model of the system is set up with unbalanced excitations, torque load excitations, and backlash which lead to variations of tooth contact status. An experiment is carried out to verify the accuracy of the mathematical model. The results show that when the system is subjected to large-scale torque load lifting at a high rotating speed, it has two stages of relatively strong periodicity when the torque load is light, and of chaotic when the torque load is heavy, with the transition between the two states being relatively quick and violent. The analysis of the three-dimensional acceleration spectrum and the meshing force shows that the variation in the meshing state and the fluctuation of the meshing force is the basic reasons for the variation in the system response with the torque load. In addition, the three rotors in the triple-gear-rotor system studied show a strong similarity in the meshing states and meshing force fluctuations, which result in the similarity in the dynamic responses of the three rotors.

Optimum Design for the Frame of Open Type Abrasive Flow Polish Machine

2012 ◽  
Vol 497 ◽  
pp. 89-93
Author(s):  
Liang Liang Yuan ◽  
Ke Hua Zhang ◽  
Li Min
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Finite Element Methods ◽  
Optimization Design ◽  
Low Cost ◽  
Three Dimensional ◽  
Force Model ◽  
Optimization Analysis ◽  
Open Type ◽  
Set Up

In order to process heterotype hole of workpiece precisely, an open abrasive flow polish machine is designed, and the optimization design of machine frame is done for low cost. Firstly, basing on the parameters designed with traditional ways, three-dimensional force model is set up with the soft of SolidWorks. Secondly, the statics and modal analysis for machine body have been done in Finite element methods (FEM), and then the optimization analysis of machine frame has been done. At last, the model of rebuild machine frame has been built. Result shows that the deformation angle value of machine frame increased from 0.72′ to 1.001′, the natural frequency of the machine decreased from 75.549 Hz to 62.262 Hz, the weight of machine decreased by 74.178 Kg after optimization. It meets the strength, stiffness and angel stiffness requirement of machine, reduces the weight and cost of machine.

Simulation of small-angle scattering curves by numerical Fourier transformation

2007 ◽  
Vol 40 (1) ◽  
pp. 16-25 ◽  
Author(s):  
Klaus Schmidt-Rohr
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Fourier Transformation ◽  
Three Dimensional ◽  
Power Laws ◽  
Numerical Approach ◽  
Peak Position ◽  
Two Dimensions ◽  
Correlation Peak ◽  
Scattering Intensity

A simple numerical approach for calculating theq-dependence of the scattering intensity in small-angle X-ray or neutron scattering (SAXS/SANS) is discussed. For a user-defined scattering density on a lattice, the scattering intensityI(q) (qis the modulus of the scattering vector) is calculated by three-dimensional (or two-dimensional) numerical Fourier transformation and spherical summation inqspace, with a simple smoothing algorithm. An exact and simple correction for continuous rather than discrete (lattice-point) scattering density is described. Applications to relatively densely packed particles in solids (e.g.nanocomposites) are shown, where correlation effects make single-particle (pure form-factor) calculations invalid. The algorithm can be applied to particles of any shape that can be defined on the chosen cubic lattice and with any size distribution, while those features pose difficulties to a traditional treatment in terms of form and structure factors. For particles of identical but potentially complex shapes, numerical calculation of the form factor is described. Long parallel rods and platelets of various cross-section shapes are particularly convenient to treat, since the calculation is reduced to two dimensions. The method is used to demonstrate that the scattering intensity from `randomly' parallel-packed long cylinders is not described by simple 1/qand 1/q4power laws, but at cylinder volume fractions of more than ∼25% includes a correlation peak. The simulations highlight that the traditional evaluation of the peak position overestimates the cylinder thickness by a factor of ∼1.5. It is also shown that a mix of various relatively densely packed long boards can produceI(q) ≃ 1/q, usually observed for rod-shaped particles, without a correlation peak.

Sign in / Sign up

Export Citation Format

Share Document