The growth of Rayleigh–Taylor-type instabilities in the lithosphere for various rheological and density structures



Cold, dense mantle lithosphere overlying hotter, lighter, asthenosphere creates a potential instability that should be enhanced if mantle lithosphere is mechanically thickened. For timescales shorter than those during which significant heat diffuses, this instability can be treated as a Rayleigh-Taylor instability, whose basic condition consists merely of a heavy layer overlying a lighter one in a gravitational field. We have calculated growth rates of small-amplitude perturbations as a function of wavelength for several structures and boundary conditions of geological interest. In the absence of thermal diffusion, the wavelengths at which instabilities grow most rapidly are likely to be about eight times the characteristic depth scale for exponential viscosity decay, which, for typical lithosphere, yields wavelengths between 40 and 90 km. Thermal diffusion, however, smoothes out temperature-induced density perturbations and thus slows the growth of short-wavelength instabilities. As a result, wavelengths for realistic lithospheric structures are expected to increase to 100 to 200 km, with maximum values up to 300 km. As this is of the order of lithospheric thickness, a Rayleigh-Taylor instability should produce only small anomalies in topography and gravity at the Earth's surface above the downwelling. For plausible ranges of lithospheric parameters, perturbations exhibit exponential growth, with growth rates as large as 10−-14 s−-1. Such rapid growth rates correspond to e-folding times of three million years, for astheno-spheric viscosities of about 1019 Pa s. Viscosities greater than about 1021 Pa s allow thermal diffusion to slow growth rates to the point of stopping Rayleigh-Taylor growth completely. To simulate mechanical thickening of the lithosphere, we also include in our calculations non-zero horizontal strain rates, which can cause folding and boudinage instabilities. Folding instabilities will grow faster than those due solely to gravity when compression rates exceed about 10−-15 to 10−-16 s−-1, corresponding to shortening of 100 per cent in 30 to 300 million years. For strain rates of this magnitude, unstable growth occurs at wavelengths about 4 to 6 times the thickness of the lithosphere, as several others have previously shown. These wavelengths are significantly longer than those produced by the layered density structure alone.