Scalings of the temporally developing turbulent planar jet and its turbulent/non-turbulent interface

We start with a first principles theoretical analysis of the temporally developing self-similar turbulent planar jet using mass, momentum and energy conservation laws which shows that the mean flow scalings are the same for equilibrium and non-equilibrium dissipation scalings in this very particular flow. The wake width, Taylor and Kolmogorov lengths all grow as the square root of time which makes this flow quite exceptional. The turbulent/non-turbulent interface (TNTI) propagation velocity and the mean centerline velocity vary in time in the same way, i.e. as inverse square root of time, but the TNTI velocity is also proportional to the global Reynolds number to a power which is inversely proportional to the fractal dimension of the interface. This fractal dimension remains constant in time during the self-similar regime, but depends on enstrophy threshold and therefore varies across the small TNTI thickness. The TNTI propagation velocity is observed to be lower at the highly contorted inner part of the TNTI and higher at the smoother outer edge of the TNTI in agreement with flux conservation.