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| Titel |
Spatiotemporal waves caused by gravitational instability of an arbitrary stratified elasto-viscous rock massif |
| VerfasserIn |
Eugeny Ryzhak, Shamil Mukhamediev, Svetlana Sinyukhina |
| Konferenz |
EGU General Assembly 2015
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 17 (2015) |
| Datensatznummer |
250110480
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| Publikation (Nr.) |
 EGU/EGU2015-15232.pdf |
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| Zusammenfassung |
| The cause of the spatially-temporal wave-like out-of-plane distortions of originally horizontal
layers of the earth’s crust is still one of the most important and debated problems in solid
earth physics. Are these distortions originated due to action of the high horizontal
compressions applied to a massif or, contrary, they are the result of spontaneous deformation
of the massif under gravity without action of another pronounced external agents? The second
possibility is called the gravity instability. Understanding of the geodynamic evolution
of the region is crucially dependent on what the answer will be chosen from the
above alternative. Lord Rayleigh (1883) was the first who solved the problem of
gravity instability for the system of 2 infinite layers of ideal incompressible fluids and
showed that the system is gravitationally unstable when the upper fluid is denser
than the lower one (i.e. the density inversion exists). Since then numerous attempts
have been made to generalise the properties of constituents. 1961 till now were
the years of unsuccessful attempts to take into account the elastic properties of
fluids.
We used the principally new approach to the stability analysis of a system which is a
bounded 3D multi-layered fluid domain possessing cross-sections of arbitrary shape and
prescribed boundary conditions at all parts of the boundary. It is assumed that the fluid is
arbitrary stratified according to both density Ï and nonlinear elastic properties. By using a
static energy criterion for stability/instability alongside with the reference ("Lagrangian")
description of a continuum we succeeded in solving the problem completely, namely, we
obtained the necessary and sufficient condition for stability (violation of which is the
necessary and sufficient condition for instability). It was found that the system under study is
unstable if and only if 1) density inversion exists at least at one interface between the fluids
and/or 2) there exists a depth range h+dh for which the actual increase of Ï is less
than corresponding increase for hypothetical homogeneous fluid provided that both
possess equal densities anywhere inside h+dh. Both assertions are not obvious and are
proved by constructing the corresponding instability modes (IMs) satisfying the
kinematic boundary conditions. If the latter are of adhesion type, the constructed
IMs are suitable for a viscous fluid too. That allows to extend the results to the
case of elastic-viscous fluids, for which the very that type of kinematic boundary
conditions takes place. In the case of instability (both for an ideal elastic and for an
elastic-viscous fluid) we obtained lower bounds for the greatest exponent of the IMs growth.
Not less important for applications (in particular the geophysical ones) is the case
when one or both layers are formed not by fluids, but by solid elastic materials.
Thus, obtained above the necessary and sufficient conditions of stability for the
system of fluids in the case of solid elastic materials appear to be sufficient but not
necessary; it means that their violation is not a sufficient condition for instability. |
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