Turbulent Modeling

  • Kolumban HutterEmail author
  • Yongqi Wang
Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM)


In this chapter a detailed introduction to the modeling of turbulence is given. Filter operations are introduced to separate the physical balance laws into evolution equations for the averaged fields on the one hand, and into fluctuating or pulsating fields on the other hand. The mathematical properties of the filter define the structure of the averaged equations. Reynolds introduced the steady statistical filter, leading to the Reynolds averaged NavierStokes equations. This procedure generates averages of products of fluctuating quantities, for which closure relations must be formulated. Depending upon the complexity of these closure relations, so-called zeroth, first and higher order turbulence models are obtained: simple algebraic gradient-type relations for the flux terms, one or two equation models, e.g., \(k-\varepsilon \), \(k-\omega \) models, in which evolution equations for the averaged correlation products for k and \(\varepsilon \) are formulated, etc. This is done for density preserving fluids as well as so-called Boussinesq and convection fluids on a rotating frame (Earth), which are important models to describe atmospheric and oceanic flows.


Statistical filter operator Reynolds averaged NavierStokes equations Closure relations for fluctuating correlation terms Open image in new window models Boussinesq, convection fluids 


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.c/o Versuchsanstalt für Wasserbau, Hydrologie und GlaziologieETH ZürichZürichSwitzerland
  2. 2.Department of Mechanical EngineeringTechnische Universität DarmstadtDarmstadtGermany

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