Rayleigh-Taylor instabilities (with animations) If a dense viscous layer rests on top of a less dense viscous layer, the lower layer will become unstable and form a Rayleigh Taylor instability. It will rise through the overburden in the form of diapirs. Examples are salt domes or magmatic diapirs. As example the figure shows a laboratory experiment by Hemin Koyi (1989, Dissertation, Uppsala) in which a light layer (PDMS,black) was overlain by a denser layer (bouncing putty). The faulted basement (plastillina) was camparably stiff. After centrifuging the buoyant layer becomes unstable and forms a series of diapirs. In the following animations of numerical experiments demonstrate the evolution of a Rayleigh-Taylor instability, and show how different viscosities and boundar conditions influence the style of the instability and the growth rates.

Model set up Density: 1 (kg/m 3 ) Viscosity: 1 (Pa s) Density: 0 (kg/m 3 ) Viscosity: 0.01, 1, 100 (Pa s) h: 1 (m) 0.1 (m) Perturbation 0.01 or 0.03 (m) Boundary condition: Free slip, no slip Free slip, no slip Symmetric at the sides Gravity 1 (m/s 2 )

Definitions: Characteristic wavelength char : A perturbation with this wavelenth is growing fastest Growth rate  describes the growth of a perturbation of initial amplitude A 0 : A Dominant wavelength: This wavelength dominates the final stage (often equal to the char. wavelenth, but sometime inherited from the initial wavelength)

Case 1: Same viscosities Free slip No slip Total run time: 4000 (s) Total run time: 8000 (s) char = 0.72 (m) char = 0.36 (m)

Case 2: Weak (0.01 Pa s) layer Free slip No slip Total run time: 140 (s) Total run time: 250 (s) char = 1.92 (m) char = 1.25 (m)

Case 3: Strong (100 Pa s) layer Free slip No slip Total run time: (s) Total run time: (s) char = 0.30 (m) char = 1.1 (m)

Comparison of growth rates of the cases Initial wavelength Weak layers grow faster than strong layers No slip boundary condition decreases the growth rate, especially for strong layers Initial wavelengths develop as dominant wavelengths because of the strong initial amplitude or the braod maximum in case 3 (f.s.) At later stages the characteristic wavelength becomes visible in the cases with very small char. Wavelengths (mostly no slip cases) Case 1 Case 2 Case 3