Novel and versatile numerical tools are used in association with normal forms deduced from symmetry breaking considerations, to compute rich sequence of bifurcation of complex real flows such as rotating and impinging jets, or 2D or 3D wakes. Receptivity to perturbation, to blowing and suction, and to base flow modification and nonlinear coupling between modes may be accessed by formulating the adjoint problem. Computation of the adjoint global modes shows that both the lift-up mechanism associated with the transport of the base flow by the perturbation and the convective non-normality (the so-called convective Modoki*) associated with the transport of the perturbation by the base flow explain the properties of the flow. In particular, a compact wave maker region may be rigorously defined where control will be efficient and nonlinear interactions take place. Application to the nonlinear dynamics of vortex breakdown in a swirling jet will be discussed showing that complex interactions between simple and double spiraling modes are well described and physically explained by the normal form analysis.
*Japanese for a similar but different thing.