Modeling gravitational instabilities in the partially molten crust with a Volume-Of-Fluid method

<p><span>This work aims at </span><span>investigat</span><span>ing</span><span> the </span><span>thermo-mechanical</span><span> conditions required for the development of </span><span>convective</span><span> instabilities </span><span>and polydiapirism </span><span>in the partially molten root of orogenic belts. </span><span>F</span><span>irst, </span><span>we</span> <span>test</span><span>ed </span><span>the </span><span>volume-of-fluid method (VOF) implem</span><span>ented in</span><span> codes </span><span>OpenFOAM </span><span>(open source) and Jadim (in-house IMFT code). </span><span>C</span><span>omparison </span><span>of</span><span> theoretical and numerical solutions of Rayleigh-Taylor and Ra</span><span>y</span><span>leigh-Benard instabilities show that Openfoam</span><span> is most satisfactory</span> <span>in terms of speed and mass </span><span>conse</span><span>rvation</span><span> (Louis-Napoleon et al., 2020). </span></p><p><span>Then, we applied the VOF method to investigate specifically the formation of </span><span>metamorphic </span><span>dome</span><span>s</span><span> in </span><span>Naxos, </span><span>Greece. These domes are characterized by nested structures of 2 km sub-domes in a 10 km major dome, and contain zircon grains that recorded dissolution-recrystallization cycles of 1 to 2 Myrs attributed to </span><span>thermal cycles</span><span> (Vanderhaeghe et al., 2018). </span><span>W</span><span>e tried to show that the</span><span>se imbricated domes</span> <span>could</span><span> result from a combination of convective and diapiric episode</span><span>s, </span><span>consider</span><span>ing</span><span> the hot orogenic crust as a system of horizontal layers with </span><span>power-law </span><span>temperature-</span><span>d</span><span>ependent </span><span>v</span><span>iscosities with internal heating.</span> <span>I</span><span>n </span><span>both </span><span>2D </span><span>and</span><span> 3D, </span><span>small domes are systematically </span><span> destroyed by convection when it appears.</span></p><p>Therefore in a second step we accounted for the specific lower viscosities induced by partial melting as well as compositional small heterogeneities (inclusions). These inclusions are supposed to represent sub-scale clustering of partially molten heterogeneous material with light-soft and heavy-resistant density and viscosity with respect to the "average" crustal domain. <span>P</span><span>arametric tests allow to define </span><span>the </span><span>conditions for </span><span>the development of </span><span>convection cells, diapirs and segregation-sedimentation of the inclusions</span><span>. </span><span>Two scenarios </span><span>are then found to potentially </span><span>explain the formation of the Naxos domes. </span><span>A</span><span> first </span><span>scenario in which melting viscosity is not accounted for, but the inclusions are initially &#8220;active&#8221;, generates</span><span> local convection cell</span><span>s around rising</span><span> clusters of inclusions. D</span><span>iapir</span><span>s</span> <span>then</span><span> emerge above the local convective cells </span><span>and accumulate at the base of the upper crust</span><span>. The second scenario takes into account m</span><span>elting </span><span>vis</span><span>c</span><span>osity,</span> <span>the inclusions&#8217; properties are active only when</span><span> temperatures exceed</span><span> the melt front, and</span> <span>basal heating is </span><span>progressively shut down</span><span>. </span><span>T</span><span>he light inclusions t</span><span>hen</span><span> rise and form domes above large</span><span>r</span><span> convection cells, if their rheological properties are frozen. </span>Both these scenarios do not exclude the role of external lateral forces a posteriori to finalise the exhumation process. More generally, we found that the domes characteristics are determined by their mode of formation. We propose a dimensional analysis to distinguish suspension from sedimentation regimes.</p>