Modeling gravitational instabilities in the partially molten crust with a Volume-Of-Fluid method
Authors: Louis-Napoleon Aurélie , Gerbault Muriel , Bonometti Thomas , Vanderhaeghe Olivier , Martin Roland 
Published: March 2021

&lt;p&gt;&lt;span&gt;This work aims at &lt;/span&gt;&lt;span&gt;investigat&lt;/span&gt;&lt;span&gt;ing&lt;/span&gt;&lt;span&gt; the &lt;/span&gt;&lt;span&gt;thermo-mechanical&lt;/span&gt;&lt;span&gt; conditions required for the development of &lt;/span&gt;&lt;span&gt;convective&lt;/span&gt;&lt;span&gt; instabilities &lt;/span&gt;&lt;span&gt;and polydiapirism &lt;/span&gt;&lt;span&gt;in the partially molten root of orogenic belts. &lt;/span&gt;&lt;span&gt;F&lt;/span&gt;&lt;span&gt;irst, &lt;/span&gt;&lt;span&gt;we&lt;/span&gt; &lt;span&gt;test&lt;/span&gt;&lt;span&gt;ed &lt;/span&gt;&lt;span&gt;the &lt;/span&gt;&lt;span&gt;volume-of-fluid method (VOF) implem&lt;/span&gt;&lt;span&gt;ented in&lt;/span&gt;&lt;span&gt; codes &lt;/span&gt;&lt;span&gt;OpenFOAM &lt;/span&gt;&lt;span&gt;(open source) and Jadim (in-house IMFT code). &lt;/span&gt;&lt;span&gt;C&lt;/span&gt;&lt;span&gt;omparison &lt;/span&gt;&lt;span&gt;of&lt;/span&gt;&lt;span&gt; theoretical and numerical solutions of Rayleigh-Taylor and Ra&lt;/span&gt;&lt;span&gt;y&lt;/span&gt;&lt;span&gt;leigh-Benard instabilities show that Openfoam&lt;/span&gt;&lt;span&gt; is most satisfactory&lt;/span&gt; &lt;span&gt;in terms of speed and mass &lt;/span&gt;&lt;span&gt;conse&lt;/span&gt;&lt;span&gt;rvation&lt;/span&gt;&lt;span&gt; (Louis-Napoleon et al., 2020). &lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;Then, we applied the VOF method to investigate specifically the formation of &lt;/span&gt;&lt;span&gt;metamorphic &lt;/span&gt;&lt;span&gt;dome&lt;/span&gt;&lt;span&gt;s&lt;/span&gt;&lt;span&gt; in &lt;/span&gt;&lt;span&gt;Naxos, &lt;/span&gt;&lt;span&gt;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 &lt;/span&gt;&lt;span&gt;thermal cycles&lt;/span&gt;&lt;span&gt; (Vanderhaeghe et al., 2018). &lt;/span&gt;&lt;span&gt;W&lt;/span&gt;&lt;span&gt;e tried to show that the&lt;/span&gt;&lt;span&gt;se imbricated domes&lt;/span&gt; &lt;span&gt;could&lt;/span&gt;&lt;span&gt; result from a combination of convective and diapiric episode&lt;/span&gt;&lt;span&gt;s, &lt;/span&gt;&lt;span&gt;consider&lt;/span&gt;&lt;span&gt;ing&lt;/span&gt;&lt;span&gt; the hot orogenic crust as a system of horizontal layers with &lt;/span&gt;&lt;span&gt;power-law &lt;/span&gt;&lt;span&gt;temperature-&lt;/span&gt;&lt;span&gt;d&lt;/span&gt;&lt;span&gt;ependent &lt;/span&gt;&lt;span&gt;v&lt;/span&gt;&lt;span&gt;iscosities with internal heating.&lt;/span&gt; &lt;span&gt;I&lt;/span&gt;&lt;span&gt;n &lt;/span&gt;&lt;span&gt;both &lt;/span&gt;&lt;span&gt;2D &lt;/span&gt;&lt;span&gt;and&lt;/span&gt;&lt;span&gt; 3D, &lt;/span&gt;&lt;span&gt;small domes are systematically &lt;/span&gt;&lt;span&gt; destroyed by convection when it appears.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;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 &quot;average&quot; crustal domain. &lt;span&gt;P&lt;/span&gt;&lt;span&gt;arametric tests allow to define &lt;/span&gt;&lt;span&gt;the &lt;/span&gt;&lt;span&gt;conditions for &lt;/span&gt;&lt;span&gt;the development of &lt;/span&gt;&lt;span&gt;convection cells, diapirs and segregation-sedimentation of the inclusions&lt;/span&gt;&lt;span&gt;. &lt;/span&gt;&lt;span&gt;Two scenarios &lt;/span&gt;&lt;span&gt;are then found to potentially &lt;/span&gt;&lt;span&gt;explain the formation of the Naxos domes. &lt;/span&gt;&lt;span&gt;A&lt;/span&gt;&lt;span&gt; first &lt;/span&gt;&lt;span&gt;scenario in which melting viscosity is not accounted for, but the inclusions are initially &amp;#8220;active&amp;#8221;, generates&lt;/span&gt;&lt;span&gt; local convection cell&lt;/span&gt;&lt;span&gt;s around rising&lt;/span&gt;&lt;span&gt; clusters of inclusions. D&lt;/span&gt;&lt;span&gt;iapir&lt;/span&gt;&lt;span&gt;s&lt;/span&gt; &lt;span&gt;then&lt;/span&gt;&lt;span&gt; emerge above the local convective cells &lt;/span&gt;&lt;span&gt;and accumulate at the base of the upper crust&lt;/span&gt;&lt;span&gt;. The second scenario takes into account m&lt;/span&gt;&lt;span&gt;elting &lt;/span&gt;&lt;span&gt;vis&lt;/span&gt;&lt;span&gt;c&lt;/span&gt;&lt;span&gt;osity,&lt;/span&gt; &lt;span&gt;the inclusions&amp;#8217; properties are active only when&lt;/span&gt;&lt;span&gt; temperatures exceed&lt;/span&gt;&lt;span&gt; the melt front, and&lt;/span&gt; &lt;span&gt;basal heating is &lt;/span&gt;&lt;span&gt;progressively shut down&lt;/span&gt;&lt;span&gt;. &lt;/span&gt;&lt;span&gt;T&lt;/span&gt;&lt;span&gt;he light inclusions t&lt;/span&gt;&lt;span&gt;hen&lt;/span&gt;&lt;span&gt; rise and form domes above large&lt;/span&gt;&lt;span&gt;r&lt;/span&gt;&lt;span&gt; convection cells, if their rheological properties are frozen. &lt;/span&gt;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.&lt;/p&gt;