Theoretical and Computational Fluid Dynamics

, Volume 24, Issue 6, pp 511–536 | Cite as

Two-fluid formulation of the cloud-top mixing layer for direct numerical simulation

  • Juan Pedro MelladoEmail author
  • Bjorn Stevens
  • Heiko Schmidt
  • Norbert Peters
Open Access
Original Article


A mixture fraction formulation to perform direct numerical simulations of a disperse and dilute two-phase system consisting of water liquid and vapor in air in local thermodynamic equilibrium using a two-fluid model is derived and discussed. The goal is to understand the assumptions intrinsic to this simplified but commonly employed approach for the study of two-layer buoyancy reversing systems like the cloud-top mixing layer. Emphasis is placed on molecular transport phenomena. In particular, a formulation is proposed that recovers the actual nondiffusive liquid-phase continuum as a limiting case of differential diffusion. High-order numerical schemes suitable for direct numerical simulations in the compressible and Boussinesq limits are described, and simulations are presented to validate the incompressible approach. As expected, the Boussinesq approximation provides an accurate and efficient description of the flow on the scales (of the order of meters) that are considered.


Stratocumulus clouds Multiphase Free convection Free turbulent flows 


Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  • Juan Pedro Mellado
    • 1
    Email author
  • Bjorn Stevens
    • 2
    • 3
  • Heiko Schmidt
    • 4
  • Norbert Peters
    • 1
  1. 1.Institut für Technische VerbrennungRWTH Aachen UniversityAachenGermany
  2. 2.Max Planck Institute for MeteorologyHamburgGermany
  3. 3.Department of Atmospheric SciencesUC Los AngelesLos AngelesUSA
  4. 4.Zuse Institute, FU BerlinBerlinGermany

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