The Slow Invariant Manifold of the Lorenz–Krishnamurthy Model

Jean-Marc Ginoux (1)

1 PROTEE - Processus de Transfert et d'Echanges dans l'Environnement - EA 3819

During this last decades, several attempts to construct slow invariant manifold of the Lorenz-Krishnamurthy five-mode model of slow-fast interactions in the atmosphere have been made by various authors. Unfortunately, as in the case of many two-time scales singularly perturbed dynamical systems the various asymptotic procedures involved for such a construction diverge. So, it seems that till now only the first-order and third-order approximations of this slow manifold have been analytically obtained. While using the Flow Curvature Method we show in this work that one can provide the eighteenth-order approximation of the slow manifold of the generalized Lorenz-Krishnamurthy model and the thirteenth-order approximation of the " conservative " Lorenz-Krishnamurthy model. The invariance of each slow manifold is then established according to Darboux invariance theorem.

Mots clés: Darboux invariance; Fenichel theory; Lorenz-Krishnamurthy model; Flow Curvature Method; slow invariant manifold

Domaines: Systèmes dynamiques [math.DS]; Géométrie différentielle [math.DG]; Dynamique Chaotique [nlin.CD]

Jean-Marc Ginoux. The Slow Invariant Manifold of the Lorenz–Krishnamurthy Model. Qualitative Theory of Dynamical Systems, 2014, 13 (1), pp.19 - 37. ⟨10.1007/s12346-013-0104-6⟩. ⟨hal-01856954⟩