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3 - Basic Equations

Published online by Cambridge University Press:  22 August 2018

Alexander P. Khain  and
Mark Pinsky
Alexander P. Khain
Affiliation:
Hebrew University of Jerusalem
Mark Pinsky
Affiliation:
Hebrew University of Jerusalem
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Summary

Chapter 3 explains the thermodynamics of dry and moist air. The governing equations are derived on the basis of the laws of conservation of heat and moisture. Turbulence-related topics include the transition of laminar flow to turbulent flow, as well as the energy and statistic properties of turbulence in clouds and equations for turbulent kinetic energy for dry and cloud air. Atmospheric motions are represented as a sum of three types of motions (synoptic scale, convective and turbulent). As numerical atmospheric models deal with averaged equations, we focus on the approaches to estimating the averaging intervals basing on physical considerations. The closure hypotheses are formulated and serve as the basis for deriving equations for averaged quantities. We consider application of the closure approach using the K-theory for conservative and non-conservative quantities in cloud investigation. We analyze the averaged equations used in bin microphysics and bulk parameterizations. Chapter 3 ends with discussing the similarity of averaged and non-averaged equations, as well as similarities and differences between the turbulent and laminar Reynolds and Rayleigh numbers.

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Physical Processes in Clouds and Cloud Modeling , pp. 68 - 121
Publisher: Cambridge University Press
Print publication year: 2018

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  • Basic Equations
  • Alexander P. Khain, Hebrew University of Jerusalem, Mark Pinsky, Hebrew University of Jerusalem
  • Book: Physical Processes in Clouds and Cloud Modeling
  • Online publication: 22 August 2018
  • Chapter DOI: https://doi.org/10.1017/9781139049481.004
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  • Basic Equations
  • Alexander P. Khain, Hebrew University of Jerusalem, Mark Pinsky, Hebrew University of Jerusalem
  • Book: Physical Processes in Clouds and Cloud Modeling
  • Online publication: 22 August 2018
  • Chapter DOI: https://doi.org/10.1017/9781139049481.004
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  • Basic Equations
  • Alexander P. Khain, Hebrew University of Jerusalem, Mark Pinsky, Hebrew University of Jerusalem
  • Book: Physical Processes in Clouds and Cloud Modeling
  • Online publication: 22 August 2018
  • Chapter DOI: https://doi.org/10.1017/9781139049481.004
Available formats
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