slender axisymmetric body of revolution by imposed nonlinear unstable helical modes

For a sufficiently slender axially symmetric body placed in a uniform stream, only convectively unstable modes are found in previous experiments. This work imposes theoretically and computationally a pair of most unstable helical modes, symmetrically and asymmetrically. The Reynolds stress modification of the developing laminar mean wake flow is modified into an elliptic-like cross section for symmetrical forcing; the consequences of unequal upstream amplitudes are also explored. Energytransfer mechanisms between the mean flow and the relevant dominant modes and between the modes through ‘triad interactions’ are studied. The results from dynamical considerations provide the physical understanding of the generation of a standing wave mode at twice the azimuthal wavenumber; it is necessary that the wave envelopes of participating modes, including that of the mean flow, overlap in their spatial development, which is a necessary supplement to kinematical conditions for such interactions to take place effectively. Standing wave motions, which are otherwise only found naturally in wakes behind blunt-trailing-edge axisymmetric bodies, can be rendered present through appropriate forcing and nonlinear interactions behind very slender axisymmetric bodies.