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Gravitational Viscoelastodynamics

In: Handbook of Geomathematics

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  • Detlef Wolf

    (German Research Center for Geosciences GFZ, Department of Geodesy and Remote Sensing)

Abstract

We consider a compositionally and entropically stratified, compressible, rotating fluid earth and study gravitational-viscoelastic perturbations of its hydrostatic initial state. Using the Lagrangian representation and assuming infinitesimal perturbations, we deduce the incremental field equations and interface conditions of gravitational viscoelastodynamics (GVED) governing the perturbations. In particular, we distinguish the material, material-local, and local forms of the incremental equations. We also demonstrate that their short-time asymptotes correspond to generalizations of the incremental field equations and interface conditions of gravitational elastodynamics (GED), whereas the long-time asymptotes agree with the incremental field equations and interface conditions of gravitational viscodynamics (GVD). The incremental thermodynamic pressure appearing in the long-time asymptote to the incremental constitutive equation is shown to satisfy the appropriate incremental state equation. Finally, we derive approximate field theories applying to gravitational-viscoelastic perturbations of isocompositional, isentropic, and compressible or incompressible fluid domains. Gravitational viscoelastodynamics (GVED)

Suggested Citation

  • Detlef Wolf, 2015. "Gravitational Viscoelastodynamics," Springer Books, in: Willi Freeden & M. Zuhair Nashed & Thomas Sonar (ed.), Handbook of Geomathematics, edition 2, pages 623-659, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-54551-1_10
    DOI: 10.1007/978-3-642-54551-1_10
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