A New Model for Mixing by Double-diffusive Convection (Semi-convection). I. The Conditions for Layer Formation Mirouh, Giovanni Marcello Garaud, Pascale Stellmach, Stephan Traxler, Adrienne L. Wood, Toby S. convection hydrodynamics planets and satellites: general stars: interiors G.M. and P.G. were supported by funding from the NSF (NSF-0807672), and benefited from the hospitality of the ISIMA program at the Kavli Institute for Astronomy and Astrophysics (Beijing) during the summer of 2011. A.T., P.G., and T.W. were funded by the NSF (NSF-0933759). Part of the computations were performed on the UCSC Pleiades supercomputer, purchased with an NSF-MRI grant. Others used computer resources at the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the US Department of Energy under contract DE-AC03-76SF00098. Department of Applied Mathematics and Statistics, Baskin School of Engineering, University of California Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA The process referred to as "semi-convection" in astrophysics and "double-diffusive convection in the diffusive regime" in Earth and planetary sciences occurs in stellar and planetary interiors in regions which are stable according to the Ledoux criterion but unstable according to the Schwarzschild criterion. In this series of papers, we analyze the results of an extensive suite of three-dimensional (3D) numerical simulations of the process, and ultimately propose a new 1D prescription for heat and compositional transport in this regime which can be used in stellar or planetary structure and evolution models. In a preliminary study of the phenomenon, Rosenblum et al. showed that, after saturation of the primary instability, a system can evolve in one of two possible ways: the induced turbulence either remains homogeneous, with very weak transport properties, or transitions into a thermo-compositional staircase where the transport rate is much larger (albeit still smaller than in standard convection). In this paper, we show that this dichotomous behavior is a robust property of semi-convection across a wide region of parameter space. We propose a simple semi-analytical criterion to determine whether layer formation is expected or not, and at what rate it proceeds, as a function of the background stratification and of the diffusion parameters (viscosity, thermal diffusivity, and compositional diffusivity) only. The theoretical criterion matches the outcome of our numerical simulations very adequately in the computationally accessible "planetary" parameter regime and can be extrapolated to the stellar parameter regime. Subsequent papers will address more specifically the question of quantifying transport in the layered case and in the non-layered case. 2026-02-20T13:10:53Z 2026-02-20T13:10:53Z 2012-04-16 journal article Mirouh et al. A New Model for Mixing by Double-diffusive Convection (Semi-convection). I. The Conditions for Layer Formation. The Astrophysical Journal, Volume 750, Issue 1, article id. 61, 18 pp. (2012). DOI 10.1088/0004-637X/750/1/61 https://hdl.handle.net/10481/111325 10.1088/0004-637X/750/1/61 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional The American Astronomical Society