This article presents a numerical analysis of the instability developing in
horizontal plane Poiseuille flow, when stratification extends along the
direction orthogonal to the plane of shear. Our study builds up on the previous
work that originally detected the linear instability of such configuration, by
means of experiments, theoretical analysis and numerical simulations
\citep{G21}. We extend hereafter this former investigation beyond linear
theory, investigating nonlinear regimes with direct numerical simulations. We
notice a tendency for the flow to lose its vertical homogeneity through a point
of secondary bifurcation, due to harmonic resonances, and further describe this
symmetry-breaking mechanism in the vicinity of the instability threshold. When
departing away from this limit, we observe a series of bursting events that
break down the flow into disordered motions driven by localized shear
instabilities. This intermittent dynamics leads to the coexistence of localized
layers of stratified turbulence surrounded by quiescent regions of meandering
waves