The effect of acceleration on turbulent entrainment

A new class of self-similar turbulent flows is proposed, which exhibits dramatically reduced entrainment rates. Under strong acceleration, the rotation period of the large-scale vortices is forced to decrease linearly in time. In ordinary unforced turbulence, the rotation period always increases linearly with time, at least in the mean. However, by imposing an exponential acceleration on the flow, the vortex rotation period is forced to become the e-folding timescale of the acceleration. If the e-folding timescale itself decreases linearly in time, the forcing is ‘super-exponential’, characterized by an acceleration parameter α. Based on dimensional and heuristic arguments, a model suggests that the dissipation rate is an exponential function of α and the dimensions of the conserved quantity of the flow. Acceleration decreases the dissipation and entrainment rates in all canonical laboratory flows except for Rayleigh–Taylor. Experiments of exponential jets and super-exponential transverse jets are in accord with the model. As noted by Johari, acceleration is the only known means of affecting the entrainment rate of the far-field jet. Numerical simulations of Rayleigh–Taylor flow by Cook and Greenough are also consistent. In the limit of large acceleration, vortices do not move far before their rotation period changes substantially. In this sense, extreme acceleration corresponds to stationary vortices.