Reynolds number effect on the flow statistics and turbulent–non-turbulent interface of a planar jet

We investigate the influence of the Reynolds number on the spatial development of an incompressible planar jet. The study relies on direct numerical simulations (DNS) at inlet Reynolds numbers between $500 \leqslant Re \leqslant 13\,500$ , being the widest range and the largest values considered so far in DNS. At the lowest $Re$ , the flow is transitional and characterised by large quasi-two-dimensional vortices; at the largest $Re$ , the flow reaches a fully turbulent regime with a well-developed self-similar region. We provide a complete description of the flow, from the instabilities in the laminar near-inlet region, to the self-similar regime in the turbulent far field. At the inlet, the leading destabilisation mode is sinusoidal/asymmetric at low Reynolds number and varicose/symmetric at large Reynolds number, with both modes coexisting at intermediate $Re$ . In the far field, the mean and fluctuating statistics converge to self-similar profiles only for $Re\geqslant 4500$ ; the flow anisotropy, the budget of the Reynolds stresses and the energy spectra are addressed. The spreading of the jet is quantified via the turbulent–non-turbulent interface (TNTI). We find that the thickness of the turbulent region, and the shape and fractal dimension of the TNTI become $Re$ -independent for $Re \geqslant 4500$ . Comparisons with previous numerical and experimental works are provided whenever available.