The effect of variable viscosity in the Earth’s mantle on the stress field of the mantle and an overlying continent, moving self-consistently due to mantle flow
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Інститут геофізики ім. С.I. Субботіна НАН України
2010
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| Назва видання: | Геофизический журнал |
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| Цитувати: | The effect of variable viscosity in the Earth’s mantle on the stress field of the mantle and an overlying continent, moving self-consistently due to mantle flow / A. Bobrov, A. Baranov // Геофизический журнал. — 2010. — Т. 32, № 4. — С. 17-18. — Бібліогр.: 2 назв. — англ. |
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irk-123456789-1012112016-06-01T03:03:14Z The effect of variable viscosity in the Earth’s mantle on the stress field of the mantle and an overlying continent, moving self-consistently due to mantle flow Bobrov, A. Baranov, A. 2010 Article The effect of variable viscosity in the Earth’s mantle on the stress field of the mantle and an overlying continent, moving self-consistently due to mantle flow / A. Bobrov, A. Baranov // Геофизический журнал. — 2010. — Т. 32, № 4. — С. 17-18. — Бібліогр.: 2 назв. — англ. 0203-3100 http://dspace.nbuv.gov.ua/handle/123456789/101211 en Геофизический журнал Інститут геофізики ім. С.I. Субботіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| format |
Article |
| author |
Bobrov, A. Baranov, A. |
| spellingShingle |
Bobrov, A. Baranov, A. The effect of variable viscosity in the Earth’s mantle on the stress field of the mantle and an overlying continent, moving self-consistently due to mantle flow Геофизический журнал |
| author_facet |
Bobrov, A. Baranov, A. |
| author_sort |
Bobrov, A. |
| title |
The effect of variable viscosity in the Earth’s mantle on the stress field of the mantle and an overlying continent, moving self-consistently due to mantle flow |
| title_short |
The effect of variable viscosity in the Earth’s mantle on the stress field of the mantle and an overlying continent, moving self-consistently due to mantle flow |
| title_full |
The effect of variable viscosity in the Earth’s mantle on the stress field of the mantle and an overlying continent, moving self-consistently due to mantle flow |
| title_fullStr |
The effect of variable viscosity in the Earth’s mantle on the stress field of the mantle and an overlying continent, moving self-consistently due to mantle flow |
| title_full_unstemmed |
The effect of variable viscosity in the Earth’s mantle on the stress field of the mantle and an overlying continent, moving self-consistently due to mantle flow |
| title_sort |
effect of variable viscosity in the earth’s mantle on the stress field of the mantle and an overlying continent, moving self-consistently due to mantle flow |
| publisher |
Інститут геофізики ім. С.I. Субботіна НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/101211 |
| citation_txt |
The effect of variable viscosity in the Earth’s mantle on the stress field of the mantle and an overlying continent, moving self-consistently due to mantle flow / A. Bobrov, A. Baranov // Геофизический журнал. — 2010. — Т. 32, № 4. — С. 17-18. — Бібліогр.: 2 назв. — англ. |
| series |
Геофизический журнал |
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| first_indexed |
2025-07-07T10:35:58Z |
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2025-07-07T10:35:58Z |
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1836984104095055872 |
| fulltext |
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The effect of variable viscosity in the Earth’s mantle
on the stress field of the mantle and an overlying continent,
moving self-consistently due to mantle flow
A. Bobrov, A.�Baranov, 2010
Laboratory of Theoretical Geodynamics, Institute of Physics of the Earth, RAS, Moscow, Russia
bobrov@ifz.ru
baranov@ifz.ru
In numerical two-dimensional experiments we
investigate the spatial field of stresses in the man-
tle and continent and its evolution. A continent moves
self-consistently with changing mantle flows. Ve-
locity of a continent in the process of movement
varies in accordance with time-dependent forces
which act from underlying viscous mantle as well
as with mantle forces acting on the end faces of
continent. This model is described in [Bobrov, Tru-
bitsyn, 2008]. Continent viscosity is equal to 1e5
with respect to average viscosity of the mantle. For
convection modeling we used Citcom code with high
Rayleigh numbers, strong viscosity variations and
active markers for simulating continent [Moresi,
Gurnis, 1996]. We consider three model laws for
viscosity: isoviscous mantle case; P,T�dependent
viscosity case and viscosity= f(P,�T, stress_ invari-
ant). For these three models we analyze how a form
of viscosity.
law can change stress fields in the mantle and
continent. We research what model law gives the
results more close to actual data. The horizontal
stress field in moving continent greatly depends on
variations of horizontal velocity in the underlying
mantle, and also on continent position between the
ascending and descending mantle streams. Sub-
continental upwelling mantle flows have the exten-
sive effect; sub-continental downwelling ones- the
compressive effect. Mantle plumes near continent‘s
borders demonstrate compressive effect on conti-
nent, ��
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�����mantle model leads to strongly overestimated
stresses and is not representative in this aspect.
Mantle model with variable viscosity has typical
horizontal stress values in the major portion of man-
tle ' (2 6)�MPa; in continent at different stages of
its movement ' (2 15)�MPa.
It should be noted that all examined models should
give approximately equal Nusselt number (i.�e., should
have the same efficiency of bearing-out of heat, as
surface heat flow is the observational value). For this
reason, the values of the adopted Rayleigh number
Ra, in all computations, were different.
Figure presents a comparison of temperature and
stress fields for the isoviscous mantle case and for
the variable viscosity case. All values are given in
dimensionless form. This comparison allows identi-
fication of a number of interesting effects.
Results. The models in this work are simplified
in several aspects. However our purpose was to re-
veal only the main features and patterns of the pro-
cess of mantle flow in the presence of floating con-
tinental material. From the numerical results, the
following conclusions can be derived.
1.�The distribution of horizontal stress in a mo-
ving continent over a viscous mantle greatly depends
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on the spatial variations of mantle velocities in the
subcontinental mantle and also on continent posi-
tion between the ascending and descending man-
tle streams at the given moment. Subcontinental
upgoing currents have an extensive effect on the
continent, while subcontinental downgoing ones a
compressive effect. On the contrary, suboceanic
upgoing mantle plumes near continent’s borders
result in compressive actions on the continent, while
downwellings result in its extension.
2.�If the horizontal stresses are expressed in
non-dimensional units for the three cases consi-
dered here (constant and variable viscosity), they
show considerable, but not fundamental differences
(Figure). It should be noted that the stress values in
the case of variable viscosity are higher.
3.�Transition to dimensional stresses (that is,
to the stresses measured in MPa or bars) shows
that for the isoviscous model the stress values are
significantly higher than in the case of variable vis-
cosity. This arises from the imposed condition of
equality of the surface heat flow in both models. If
we would not equalize the models by heat flow, but
simply calculate them using the same Rayleigh
number ' that is, with the same intensity of con-
vection — then we wouldn’t have such significant
difference. However, the difference in Rayleigh num-
ber values (namely, for account of increasing of vis-
cosity in isoviscous model) leads to a difference of
dimensional stresses. As a result, the isoviscous
mantle model leads to overestimated dimensional
stresses. This model, however, is necessary for
comparison, as it allows to evaluate the effect of
the variable viscosity on the final results.
4.�For the considered model of variable mantle
viscosity the following typical horizontal stress va-
lues are found: for the largest part of the mantle
values between 2 to 5�MPa (that is 20'50�bars); in
continent at different stages of its movement and in
different areas 2'10�MPa, depending on the im-
pact of the mantle these stresses may be com-
pressive or tensile.
Moresi L. N., Gurnis M. Constraints on the lateral
strength of slabs from three-dimensional dynamic
flow models // Earth Planet. Sci. Lett. ' 1996. '
138. '�P.�15'28.
References
Dimensionless horizontal stress fields xx(x, z) for isoviscous model (upper panel) and P,T-dependent viscosity model (lower
panel). Light grey depicts positive values, dark grey — negative values. The stresses xx(x, z) are determined by the relation
xx(x,z)= p(x, z) 2 vx(x, z) x, i. e., compressive stresses are considered to be positive. White isolines show the non-
dimensional temperature field. The position of the continent is shown with a rectangle on the upper surface.
Bobrov A. M., Trubitsyn A. P. Numerical model of the su-
percontinental cycle stages: integral transfer of the
oceanic crust material and mantle viscous shear
stresses // Stud. Geophys. Geod. '�2008. '�52. '
P.�87'100.
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