The Rayleigh‐Taylor instability of an embedded layer of low‐viscosity fluid

The properties of gravitational instabilities formed within two‐layer fluid systems are well known and have been applied to a variety of geophysical problems. We present theoretical and experimental results for the gravitational instability developed by a three‐layer system, comprising a thin low‐viscosity low‐density fluid layer sandwiched between two thick layers of equal properties. Linearized equations can be used to solve for the initial growth rates as a function of perturbation wavelength. As is the case for two‐layer systems, the results yield a fastest growing wavelength, termed the characteristic wavelength, whose value is much greater than the thickness of the low‐viscosity layer. The experimental results confirm the ability of the linearized equations to predict the dominant wavelength of the instability. However, for very thin layers or smaller viscosity ratios a second instability is also observed at a scale much greater than the characteristic wavelength. Numerical solutions show that the wavelength of this instability matches that of a fast growing but short‐lived mode arising from perturbations which predominantly involve thickening rather than translation of the buoyant layer. The analytical solution also shows that at the characteristic wavelength, the displacement of the lower interface will be initially a factor 2 − √3 = 0.268 that of the upper interface. As the instability develops the characteristic diapir structures, the experiments show that the relative magnitude of these displacements increase, with underlying fluid being drawn up into the head of the diapir.