## Secular gravitational instability of a compressible viscoelastic sphere

**Ladislav Hanyk** ** , **
**Ctirad Matyska** ** & **
**David A. Yuen**
### Abstract

For a self-gravitating viscoelastic compressible sphere
we have shown that unstable modes can exist by means
of the linear viscoelastic theory by both initial-value
and normal-mode approaches.
For a uniform sphere we have derived analytical expressions
for the roots of the secular determinant based on the asymptotic expansion
of the spherical Bessel functions.
From the two expressions, both the destabilizing nature
of gravitational forces and the stabilizing influences
of increasing elastic strength are revealed.
Fastest growth times on the order of ten thousand years are developed
for the longest wavelength.
In contrast, a self-gravitating incompressible viscoelastic model
is found to be stable.
This result of linear approximation suggests that a more general approach,
e.g., non-Maxwellian rheology or a non-linear finite-amplitude theory,
should be considered in global geodynamics.

### Whole paper

The paper is available in PDF (240 kB).

*Geophys. Res. Lett.*, **26** (1999), 557-560.