An analytical approach for modeling the initiation and early development of the Rayleigh-Taylor gravitational instability in subduction settings

In the past decades, the comprehension of major geodynamic processes has mostly been dominated by computational and numerical models, with researchers generally avoiding the usage of analytical methods. The main reason for the latter lies in the fact that geodynamic systems and processes can be very challenging, and sometimes even impossible, to model analytically due to their high complexity and unknown factor. However, with the proper assumptions, the processes can be simplified in a way that analytical approaches can be utilized to model the occurring phenomenon, without compromising accuracy and realism. Overall, a subject that has been studied by various researchers, and as a result a great number of computational models have been proposed in the last two decades, is the development of the Rayleigh-Taylor gravitational instability in the interface between the subducting plate and the flowing mantle. This instability is induced by the density contrast between the two aforementioned layers, and particularly the fact that a denser fluid, in this case the flowing mantle, overlies a lighter fluid, the subducting plate. It has been illustrated that overtime with the development of the instability, characteristic plume-like shapes are formed that enter the hot flowing mantle and at some point even detach completely from the subducting plate. These plumes are then subjected to high, or even ultra high, pressure and temperature conditions making them newly formed metamorphic rocks that at some point in time are likely to get exhumed. The initiation and early development of the above discussed phenomenon was modeled in the present work by using linearised Navier-Stokes equations for two viscous fluids, with different density and viscosity values. From this analytical approach a basic methodology is proposed, capable of estimating the required growth rate of the instability in its early stages and also the critical wavelength, after which the plume is considered to have been fully formed and probably even detached from the plate. Additionally, the introduced function for the amplitude of the instability was correlated with the detachment potential of the plume from the downgoing plate. Furthermore, the proposed model was applied to the subduction setting of the Mediterranean ridge, located south of the island of Crete. Lastly, macroscopic observations from the broader Hellenides region were employed, by mostly examining the existing literature, to ascertain whether any such metamorphic rocks had indeed surfaced, thus confirming their exhumation.