After reviewing the experimental evidence for screech in a supersonic jet with and without a thin plate, we seek a minimal dynamical description capable of reproducing the observed changes in staging and spectral content. The experiments show that, in the unperturbed axisymmetric configuration, the classical sequence features an abrupt transition from mode B (flapping, standing-wave–like) to mode C (spinning, rotating-wave–like). When a plate is inserted parallel to the jet axis, this jump is suppressed and replaced by a continuous mixed response; in addition, in selected Mach number ranges the PSD exhibits two nearby spectral lines consistent with time-dependent mixed states. Motivated by these observations, we start from the resonant 1:1 Hopf normal form governing the azimuthal pair |m|=1associated with modes B and C, and introduce a symmetry-breaking perturbation representing the jet–plate interaction. The plate destroys continuous rotational invariance while preserving a reflection symmetry, thereby enabling coupling terms that are forbidden in the O(2)-equivariant case. We then classify the resulting solution branches (pure even/odd states and mixed states) and distinguish between phase-locked solutions, producing a single dominant tone, and phase-drifting (unlocked) solutions, producing a spectral line splitting through an Adler-type phase-drift mechanism. By comparing the qualitative bifurcation structure and predicted spectral signatures with the experimental PSDs, we show how the perturbed normal form naturally explains both the disappearance of the B→C jump and the emergence of mixed states. Finally, we highlight a possible amplitude-symmetry–breaking (pitchfork) bifurcation within the mixed family, providing a dynamical route to unequal-amplitude mixed states consistent with the asymmetric spectral weights measured by symmetric microphones
salle B266/B267 (Numa Manson)
1 avenue Clement Ader
86360 Futuroscope Chassenuil
Prochains évènements
Retour à l'agendaReinforcement Twinning and the Reciprocal Learning of Models and Control Policies
Miguel Alfonso Mendez, de du von Karman Institute (Belgique)
A statistical theory of disturbance growth in transitional flows
Intervenant : Aaron Towne, de l'University of Michigan
