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Existence and positivity of a systemk-ε with a production term of the Rayleigh-Taylor type

Authors
Journal
Applied Mathematics Letters
0893-9659
Publisher
Elsevier
Publication Date
Volume
15
Issue
3
Identifiers
DOI: 10.1016/s0893-9659(01)00142-2
Keywords
  • Turbulence
  • Maximum Principle
  • Instability
  • Diffusion
  • Models
Disciplines
  • Physics

Abstract

Abstract In this paper, we study a modelization of the turbulence which allows us to have a control on the positivity of the kinetic turbulence energy k and the dissipation growth rate of the energy ε. We use for that purpose the maximum principle on a new system modelling the turbulence, written on the variables θ and φ first introduced by Lewandowski (θ = k/ε, φ = ε 2/ k 3). Estimates on θ and φ are given for a turbulent system with a Rayleigh-Taylor type term under a hypothesis of low compressibility of the mean flow, which is more general than the hypothesis of Lewandowski. In a second part, we study a simpler convection diffusion system (the diffusion is a constant) in which there is still the Rayleigh-Taylor term. We show that the presence of this term gives greater solutions of the k, ε system, hence proving that these terms are turbulent kinetic energy production terms.

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