In order to improve the closure of the turbulent energy dissipation epsilon whose equation appears in almost all modern turbulent models, it appears necessary to better understand some fundamental aspects of turbulence relaxation. This old problem still leaves some open issues even in the simplest case of homogeneous isotropic turbulence. An analysis is presented here based on the approach initially proposed by Landau in 1944 of angular momentum invariance at large scales. It is shown how this fully defines turbulent relaxation in common regimes, and how this concept can be extended (in simplified form using Saffman's impulsive approach) to turbulent slab, tube and spot of turbulence in an infinite fluid at rest. Application of the standard k-epsilon model, to which most models reduce in these situations, reveals the major influence of initial conditions and dimensionality over its mediocre response, and suggests new approaches to improve its behavior.
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