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On some problems in mathematical modeling of turbulent flow

Burnat M., Moszyński K.

Journal of Technical Physics

2007

Vol. 48, no 3-4

171-192

The paper presents a new, rather elementary mathematical model of turbulent fluid flow with intensive self-mixing. The flow is described in this model by the (in general non-invertible) mappings Φt,t0 : ω -->S(t, t0,ω), ω, S ⊂ R³, t > t0, such that ◛ ∩ ω² = ∅ in general not implies S(t, to, ◛) ∩ S(t, t0, ω²) = ∅. This modeling allows a new approach to certain problems of turbulent flow. For example, there are possibilities of describing the unpredictable explosions of turbulence in a calm, laminar flow.

Two-waves nonlinear interactions for hyperbolic systems of balance laws

Barbera E., Giambo S.

Journal of Technical Physics

2002

Vol. 43, no 2

165-185

In this paper we study the weakly nonlinear interaction of two waves whose propagation is governed by hyperbolic systems of balance laws. The method used here makes use of nonlinear phase variables and consists in a perturbation analysis. It is applied to an Eulerian gas and to a gas described by extended thermodynamics with thirteen moments.