Transition to chaos in a reduced-order model of a shear layer

The present work studies the non-linear dynamics of a shear layer, driven by body force and confined between parallel walls, simplified setting to study transitional turbulent layers. It was introduced Nogueira \& Cavalieri (J. Fluid Mech. 907, A32, 2021), is here studied using reduced-order model based on Galerkin projection Navier-Stokes system. By considering layer with free-slip boundary conditions periodic in streamwise spanwise directions may be used, simplifying system enabling use methods dynamical systems theory. A basis eight modes used projection, representing mean flow, Kelvin-Helmholtz vortices, rolls, streaks oblique waves, structures observed cited work, also layers jets. obtained, its transition chaos studied. Increasing Reynolds number $Re$ leads pitchfork Hopf bifurcations, latter limit cycle amplitude modulation as DNS Cavalieri. Further increase appearance chaotic saddle, followed emergence quasi-periodic attractors. attractors suffer merging crisis for higher $Re$, leading phase jumps vortices. This reminiscent observations coherent jets, suggesting that represents consistent features