Fully three‐dimensional exact and ray asymptotic formulation of the characteristic wave fields on a spherical shell surface

1994 ◽  
Vol 95 (1) ◽  
pp. 265-285 ◽  
Author(s):  
J. M. Ho ◽  
L. B. Felsen
Keyword(s):  
Spherical Shell ◽  
Three Dimensional ◽  
Shell Surface ◽  
Wave Fields ◽  
Characteristic Wave ◽  
Asymptotic Formulation

scholarly journals Density Stratification Effects on the Thermal Convection in a Rotating Spherical Shell

2001 ◽  
Vol 203 ◽  
pp. 195-197
Author(s):  
N. Nishikawa ◽  
K. Kusano
Keyword(s):  
Spherical Shell ◽  
Thermal Convection ◽  
Structural Transition ◽  
Rotation Axis ◽  
Three Dimensional ◽  
Density Stratification ◽  
Nonlinear Convection ◽  
Solar Convection Zone ◽  
Solar Convection ◽  
The Stability

The density stratification effects on the thermal convection in a rotating spherical shell, which is the representative of the solar convection zone, are investigated by three dimensional numerical simulations. It is found that, the convection structure in the strongly stratified system is switched from parallel cells aligned to the rotation axis to zonal rolles dominated by the longitudinally averaged mode, as the Rayleigh number increases much larger than the stability threshold. Corresponding to this structural transition, the averaged kinetic helicity reverses the sign in each hemisphere (from negative to positive in the northern hemisphere). The results indicate that the density stratification is much important for the nonlinear convection process in the rotating spherical shell.

Migration of seismic data by phase shift plus interpolation

Geophysics ◽  
1984 ◽  
Vol 49 (2) ◽  
pp. 124-131 ◽  
Author(s):  
Jeno Gazdag ◽  
Piero Sguazzero
Keyword(s):  
Phase Shift ◽  
Wave Field ◽  
Seismic Data ◽  
Three Dimensional ◽  
Reference Wave ◽  
Second Step ◽  
Lateral Velocity ◽  
Wave Fields ◽  
Shift Method ◽  
Phase Shift Method

Under the horizontally layered velocity assumption, migration is defined by a set of independent ordinary differential equations in the wavenumber‐frequency domain. The wave components are extrapolated downward by rotating their phases. This paper shows that one can generalize the concepts of the phase‐shift method to media having lateral velocity variations. The wave extrapolation procedure consists of two steps. In the first step, the wave field is extrapolated by the phase‐shift method using ℓ laterally uniform velocity fields. The intermediate result is ℓ reference wave fields. In the second step, the actual wave field is computed by interpolation from the reference wave fields. The phase shift plus interpolation (PSPI) method is unconditionally stable and lends itself conveniently to migration of three‐dimensional data. The performance of the methods is demonstrated on synthetic examples. The PSPI migration results are then compared with those obtained from a finite‐difference method.

scholarly journals Coronal ejections from convective spherical shell dynamos

2011 ◽  
Vol 7 (S286) ◽  
pp. 154-158 ◽  
Author(s):  
J. Warnecke ◽  
P. J. Käpylä ◽  
M. J. Mantere ◽  
A. Brandenburg
Keyword(s):  
Magnetic Field ◽  
Spherical Shell ◽  
Large Scale ◽  
Convection Zone ◽  
Three Dimensional ◽  
Simplified Model ◽  
Spherical Coordinates ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Large Scale Magnetic Field

AbstractWe present a three-dimensional model of rotating convection combined with a simplified model of a corona in spherical coordinates. The motions in the convection zone generate a large-scale magnetic field which is sporadically ejected into the outer layers above. Our model corona is approximately isothermal, but it includes density stratification due to gravity.

scholarly journals Viscous dissipation by tidally forced inertial modes in a rotating spherical shell

2010 ◽  
Vol 643 ◽  
pp. 363-394 ◽  
Author(s):  
M. RIEUTORD ◽  
L. VALDETTARO
Keyword(s):  
Spherical Shell ◽  
Shear Layer ◽  
Viscous Dissipation ◽  
Inner Core ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Two Dimensional Model ◽  
Critical Latitude

We investigate the properties of forced inertial modes of a rotating fluid inside a spherical shell. Our forcing is tidal like, but its main property is that it is on the large scales. By numerically solving the linear equations of this problem, including viscosity, we first confirm some analytical results obtained on a two-dimensional model by Ogilvie (J. Fluid Mech., vol. 543, 2005, p. 19); some additional properties of this model are uncovered like the existence of narrow resonances associated with periodic orbits of characteristics. We also note that as the frequency of the forcing varies, the dissipation varies drastically if the Ekman number E is low (as is usually the case). We then investigate the three-dimensional case and compare the results to the foregoing model. The three-dimensional solutions show, like their two-dimensional counterpart, a spiky dissipation curve when the frequency of the forcing is varied; they also display small frequency intervals where the viscous dissipation is independent of viscosity. However, we show that the response of the fluid in these frequency intervals is crucially dominated by the shear layer that is emitted at the critical latitude on the inner sphere. The asymptotic regime, where the dissipation is independent of the viscosity, is reached when an attractor has been excited by this shear layer. This property is not shared by the two-dimensional model where shear layers around attractors are independent of those emitted at the critical latitude. Finally, resonances of the three-dimensional model correspond to some selected least damped eigenmodes. Unlike their two-dimensional counter parts these modes are not associated with simple attractors; instead, they show up in frequency intervals with weakly contracting webs of characteristics. Besides, we show that the inner core is negligible when its relative radius is less than the critical value 0.4E1/5. For these spherical shells, the full sphere solutions give a good approximation of the flows.

scholarly journals Simulated holographic three-dimensional intensity shaping of evanescent-wave fields

2008 ◽  
Vol 25 (5) ◽  
pp. 849 ◽  
Author(s):  
Laura C. Thomson ◽  
Graeme Whyte ◽  
Michael Mazilu ◽  
Johannes Courtial
Keyword(s):  
Evanescent Wave ◽  
Three Dimensional ◽  
Wave Fields
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