Development of turbulence in subsonic submerged jets

Abstract

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.

The transition to turbulence in slowly diverging subsonic submerged jets

“…(11) and (12) can be solved approximately by a method similar to the Krylov-Bogolyubov method for spatially extended systems. 17,26 We therefore seek a solution in the form of a series in r (t, x, y) = 0 (t, x, y) + r 1 (t, x, y) + 2 r 2 (t, x, y) + . .…”

“…We have concluded 17 that the turbulence arises through strong amplification of the weak random disturbances that are always present in jets and, especially, within the nozzle exit section. Within the jet, at distances close to the nozzle, the turbulent pulsations are small, and for their calculation we can use a quasi-linear theory, e.g., the Krylov-Bogolyubov asymptotic method for distributed systems.…”

“…(1) and (2) into dynamical (regular) and random constituents. 17 It is clear that such approach is reasonable only where the level of turbulence is small. We now consider in turn the equations for the dynamical and random parts, in Secs.…”

“…14,15 Frequently, turbulence involves a cascade-like transfer of turbulent energy towards the high frequency domain, 14,16 which is where dissipation mainly occurs, but inverse cascades where the energy flows towards larger length scales (lower frequencies) can sometimes occur too. 15,17 Although turbulence has been studied for many years, and in many different contexts, the nature of the transition to turbulence has remained something of an enigma.…”

“…In Ref. 17, we used the same approach, but starting from the Navier-Stokes equations for the case a plane jet. For any given set of parameters this leads to a single eigenvalue for a given frequency and distance from the nozzle.…”