Development of turbulence in subsonic submerged jets

The development of turbulence in subsonic submerged jets is reviewed. It is shown that the turbulence results from a strong amplification of the weak input noise that is always present in the jet nozzle exit section. At a certain distance from the nozzle the amplification becomes essentially nonlinear. This amplified noise leads to a transition of the system to a qualitatively new state, which depends only slightly on the characteristics of the input noise, such as its power spectrum. Such a transition has much in common with nonequilibrium noise-induced phase transitions in nonlinear oscillators with multiplicative and additive noise. The Krylov–Bogolyubov method for spatially extended systems is used to trace the evolution of the power spectra, the root-mean-square amplitude of the turbulent pulsations, and the mean velocity, with increasing distance from the nozzle. It is shown that, as turbulence develops, its longitudinal and transverse scales increase. The results coincide qualitatively and also, in specific cases, quantitatively, with known experimental data.