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Simulations of nonlinear pore-water convection in spherical shells
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10.1063/1.2839052
/content/aip/journal/pof2/20/2/10.1063/1.2839052
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/2/10.1063/1.2839052

Figures

Image of FIG. 1.
FIG. 1.

The marginal Raleigh number is plotted against the aspect ratio for different values of at the onset of hydrothermal convection.

Image of FIG. 2.
FIG. 2.

Sketch of the domain decomposition in spherical-shell geometry.

Image of FIG. 3.
FIG. 3.

Kinetic energies of nonlinear convection (a) at the aspect ratio for five different Rayleigh numbers and (b) at the aspect ratio for six different Rayleigh numbers are shown as a function of time.

Image of FIG. 4.
FIG. 4.

Isosurfaces of the temperature of nonlinear convection at : (a) for the Rayleigh number and (b) for . Red contours indicate positive temperature and blue contours correspond to negative temperature .

Image of FIG. 5.
FIG. 5.

Isosurfaces of the temperature of nonlinear convection at and obtained from four different initial conditions: (a) with , , (b) with , , (c) with , , (d) with , .

Image of FIG. 6.
FIG. 6.

Isosurfaces of of nonlinear convection for at , where , obtained with different initial conditions: (a) , (b) , (c) , (d) , (e) , (f) , (g) , and (h) .

Tables

Generic image for table
Table I.

Typical values of the marginal Rayleigh number as a function of for various values of . The most unstable mode is denoted by the bold number.

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Table II.

Dominant spherical harmonics in weakly nonlinear stationary convection solutions at with obtained by starting simulation from different initial conditions.

Generic image for table
Table III.

The accuracy of the numerical solutions at different spatial resolution, where , , and are the grid numbers in the azimuthal, latitudinal, and radial directions and denotes the time step in numerical simulations.

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/content/aip/journal/pof2/20/2/10.1063/1.2839052
2008-02-14
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Simulations of nonlinear pore-water convection in spherical shells
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/2/10.1063/1.2839052
10.1063/1.2839052
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