Theoretical and Computational Fluid Dynamics

, Volume 33, Issue 1, pp 83–106 | Cite as

Homogeneous nucleation from an asymptotic point of view

  • Manuel BaumgartnerEmail author
  • Peter Spichtinger
Original Article


The major formation pathway of ice crystals in the low-temperature regime below \({235}\hbox { K}\) is homogeneous freezing of solution droplets. This mechanism is known to be very sensitive to environmental conditions, i.e., temperature and humidity. Nucleation events are characterized by an explosive increase in ice crystal number concentrations. For a better understanding of ice nucleation in this temperature regime, we have to analyze these nucleation events carefully. In this study, we consider the description of a single nucleation event using a slightly simpler system which features the same sharp increase in ice crystal number concentration. We analyze the simpler system with the help of asymptotic methods and construct a leading order approximation to the exact solution. This gives insight into a single homogeneous nucleation event from a mathematical perspective, without introducing further assumptions apart from the transition to the simplified system. In addition, we use the asymptotic approximation to construct a new parameterization, relating the updraft velocity to the homogeneously nucleated number of ice crystals, and compare the results with a widely used parameterization.


Moist processes Matched asymptotic expansions Nucleation Homogeneous nucleation 


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We thank Rupert Klein for pointing us toward the asymptotic methods in combustion processes. We also thank the anonymous reviewers for their comments which led to a significant improvement of the manuscript. Manuel Baumgartner acknowledges support of the “Deutsche Forschungsgemeinschaft (DFG)” within the project “Enabling Performance Engineering in Hesse and Rhineland-Palatinate” (Grant Number 320898076). Peter Spichtinger acknowledges support by the German Bundesministerium für Bildung und Forschung (BMBF) within the HD(CP)2 initiative, project S4 (01LK1216A) and by the DFG within the Transregional Collaborative Research Centre TRR165 “Waves to Weather,” subproject B7.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Data CenterJohannes Gutenberg UniversityMainzGermany
  2. 2.Institute for Atmospheric PhysicsJohannes Gutenberg UniversityMainzGermany

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