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

O.D. Lafitte
2002 Applied Mathematics Letters  
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 e. We use for that purpose the maximum principle on a new system modelling the turbulence, written on the variables 0 and ¢ first introduced by Lewandowski (O = k/e, ¢ = e2/k3). Estimates on O and ¢ are given for a turbulent system with a Rayleigh-Taylor type term uuder a hypothesis of low compressibility of
more » ... 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, e system, hence proving that these terms are turbulent kinetic energy production terms. (~
doi:10.1016/s0893-9659(01)00142-2 fatcat:r3wdeuangvelzc7ehq7yocwzz4