A new numerical technique using markers and a deformable Lagrangian mesh
is used to study the deformation of the surface above a rising diapir.
This method allows modelling of a free-surface boundary in a
self-consistent way. The method makes it possible to investigate many
different problems with non-regular geometry. The codes were verified
through comparison with analytical solutions for the initial stages and
with other numerical codes for mature stages.
Our simulations led to the following conclusions. (1) The growth rate of
the diapir is more strongly influenced by the viscosity contrast than
the wavelengths. This is due to the strong growth rate difference during
the initial stage. (2) The maximum elevation above the diapir linearly
increases with increasing wavelength and is approximately the same for
different viscosity contrasts. (3) The elevation will be considerably
higher for a low-viscosity diapir at a given depth than for an
isoviscous diapir.
Comparisons for different thicknesses of the buoyant layer showed that
the highest topography is produced when the two layers have equal
thickness.
We showed the dependence of the topographic behaviour on the parameter R
(the ratio of the density difference between two layers to the density
of the upper layer). It was found that topography behaves linearly up to
R = 0.15. It indicates that a posteriori estimation of topography for
traditional calculations using the free-slip boundary condition works
well within this limit.