Triadic resonant modes: dynamical model and truncation criterion

Abstract

In the present paper we propose a three-dimensional model describing the local evolution of any two- or three-dimensional disturbance superimposed on a basic shear flow. A numerical investigation, using a truncated form of the evolution model, was performed to select resonant tree-dimensional disturbance in a transitional cylinder wake. A truncation criterion of non-linear triadic resonance, which is a generalisation of the standard linear-resonance condition, allowed us to locate some triadic sets of linear eigenmodes. Numerical integration of the corresponding low-dimensional dynamical systems showed interesting results that are in qualitative agreement with those performed by Williamson and Prasad [j. Fluid Mech. 256 (1993) 269]. This seems to validate the truncation criterion which, together with the theoretical model, proved to be an appropriate tool for describing the local evolution of large-scale structures in shear flows.