Rayleigh–Taylor instability in impact cratering experiments

Abstract

When a liquid drop strikes a deep pool of a target liquid, an impact crater opens while the liquid of the drop decelerates and spreads on the surface of the crater. When the density of the drop is larger than the target liquid, we observe mushroom-shaped instabilities growing at the interface between the two liquids. We interpret this instability as a spherical Rayleigh–Taylor instability due to the deceleration of the interface, which exceeds the ambient gravity. We investigate experimentally the effect of the density contrast and the impact Froude number, which measures the importance of the impactor kinetic energy to gravitational energy, on the instability and the resulting mixing layer. Using backlighting and planar laser-induced fluorescence methods, we obtain the position of the air–liquid interface, an estimate of the instability wavelength, and the thickness of the mixing layer. We derive a model for the evolution of the crater radius from an energy conservation. We then show that the observed dynamics of the mixing layer results from a competition between the geometrical expansion of the crater, which tends to thin the layer, and entrainment related to the instability, which increases the layer thickness. The mixing caused by this instability has geophysical implications for the impacts that formed terrestrial planets. Extrapolating our scalings to planets, we estimate the mass of silicates that equilibrates with the metallic core of the impacting bodies.

Equilibrated crater: fragmentation and mixing

“…This is actually what happens, as Lherm et al. (2022) have nicely shown (see figure 1 b ) by documenting and analysing step by step the many concomitant, interconnected processes at play in this phenomenon, which is simple in its principle, but turns out to be complicated (as the author's analysis is) when all the imbricated details are handled quantitatively. Elements of the phenomenology had been identified long ago (Thomson & Newall 1885; Arecchi et al.…”

“…According to this principle, when a deformable object (a liquid drop) impacts a deformable substrate (a pool of another liquid), a Rayleigh-Taylor instability is likely to occur if the impacting drop is denser than the pool, a consequence of the drop/pool interface deceleration consecutive to the impact. This is actually what happens, as Lherm et al (2022) have nicely shown (see figure 1b) by documenting and analysing step by step the many concomitant, interconnected processes at play in this phenomenon, which is simple in its principle, but turns out to be complicated (as the author's analysis is) when all the imbricated details are handled quantitatively. Elements of the phenomenology had Lherm et al (2022) clearly demonstrate here that, when ρ 1 /ρ 2 < 1, the cavity is smooth while, for ρ 1 /ρ 2 > 1, corrugations have developed at its surface, which are more pronounced for larger ρ 1 /ρ 2 .…”

“…This is actually what happens, as Lherm et al (2022) have nicely shown (see figure 1b) by documenting and analysing step by step the many concomitant, interconnected processes at play in this phenomenon, which is simple in its principle, but turns out to be complicated (as the author's analysis is) when all the imbricated details are handled quantitatively. Elements of the phenomenology had Lherm et al (2022) clearly demonstrate here that, when ρ 1 /ρ 2 < 1, the cavity is smooth while, for ρ 1 /ρ 2 > 1, corrugations have developed at its surface, which are more pronounced for larger ρ 1 /ρ 2 . (c) Collapse of a hydrogen-oxygen mixture ignited in a bubble immersed in a liquid, and Rayleigh-Taylor corrugations of its interface as it rebounds on the compressed burnt gases (adapted from Duplat & Villermaux 2015).…”

“…We have known since Newton that in order to move a massive object from rest, or slow it down to immobility, a force must be applied to it (Newton 1687, Law 1). In fluids, forces are measured by pressure gradients, and Lherm et al (2022) recall that when the density and pressure gradients are in opposite directions at an interface between two fluids of different densities, then the interface is unstable. This is the Rayleigh (1883)- Taylor (1950) instability paradigm, a ubiquitous phenomenon with an immense range of applications when it comes to understanding how different phases interpenetrate, mix or fragment in non-Galilean (i.e.…”

“…(a) A drop of heavy liquid deposited at the surface of a lighter pool forms a vortex ring which soon fragments into secondary rings; it would not do so if it were lighter than the pool, as first noticed by Thomson & Newall (1885). (b) Patterns of the cavity (crater) at maximal extension following the impact of a drop of density ρ 1 with radius R 0 on a pool with density ρ 2 at velocity u, defining the Froude number Fr = u 2 /gR 0 Lherm et al (2022). clearly demonstrate here that, when ρ 1 /ρ 2 < 1, the cavity is smooth while, for ρ 1 /ρ 2 > 1, corrugations have developed at its surface, which are more pronounced for larger ρ 1 /ρ 2 .…”