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| Titel |
Controlling thermal chaos in the mantle by positive feedback from radiative thermal conductivity |
| VerfasserIn |
F. Dubuffet, D. A. Yuen, E. S. G. Rainey |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 9, no. 3/4 ; Nr. 9, no. 3/4, S.311-323 |
| Datensatznummer |
250006544
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| Publikation (Nr.) |
 copernicus.org/npg-9-311-2002.pdf |
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| Zusammenfassung |
| The thermal
conductivity of mantle materials has two components, the lattice component
klat from phonons and the radiative component krad
due to photons. These two contributions of variable thermal
conductivity have a nonlinear dependence in the temperature, thus endowing
the temperature equation in mantle convection with a strongly nonlinear
character. The temperature derivatives of these two mechanisms have
different signs, with ∂klat /∂T
negative and dkrad /dT positive. This offers the
possibility for the radiative conductivity to control the chaotic boundary
layer instabilities developed in the deep mantle. We have parameterized
the weight factor between krad and klat
with a dimensionless parameter f , where f = 1 corresponds
to the reference conductivity model. We have carried out two-dimensional,
time-dependent calculations for variable thermal conductivity but constant
viscosity in an aspect-ratio 6 box for surface Rayleigh numbers between 106
and 5 × 106. The averaged Péclet < Pe > numbers
of these flows lie between 200 and 2000. Along the boundary in f
separating the chaotic and steady-state solutions, the < Pe >
number decreases and the Nusselt number increases with internal heating,
illustrating the feedback between internal heating and radiative thermal
conductivity. For purely basal heating situation, the time-dependent
chaotic flows become stabilized for values of f of between 1.5 and
2. The bottom thermal boundary layer thickens and the surface heat flow
increases with larger amounts of radiative conductivity. For magnitudes of
internal heating characteristic of a chondritic mantle, much larger values
of f , exceeding 10, are required to quench the bottom boundary
layer instabilities. By isolating the individual conductive mechanisms, we
have ascertained that the lattice conductivity is partly responsible for
inducing boundary layer instabilities, while the radiative conductivity
and purely depth-dependent conductivity exert a stabilizing influence and
help to control thermal chaos developed in the deep mantle. These results
have been verified to exist also in three-dimensional geometry and would
argue for the need to consider the potentially important role played by
radiative thermal conductivity in controlling chaotic flows in
time-dependent mantle convection, the mantle heat transfer, the number of
hotspots and the attendant mixing of geochemical anomalies. |
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