It is critical to evaluate whether the flow has transitioned into turbulence because most of the impact of large-scale mixing occurs when the flow becomes fully developed turbulence. Hydrodynamic instability flows are even more complex because of their time-dependent nature; therefore, both spatial and temporal criteria will be introduced in great detail to demonstrate the necessary and sufficient conditions for the flow to transition to turbulence. These criteria will be extremely helpful for designing experiments and numeric simulations with the goal to study large-scale turbulence mixing. One spatial criterion is that the Reynolds number must achieve a critical minimum value of 160,000. In addition, the temporal criteria suggest that flows need to be given approximately four eddy-turnover-times. This chapter will expand on these issues.

In turbulent free-shear flows, fluid streams interact to generate regions of turbulence that evolve without being limited or confined by solid boundaries. Such interactions create mean shear, which is a source of turbulent kinetic energy that results in enhanced flow mixing. Far downstream, the flow retains little memory of its origins and exhibits self-similar behavior. Its mean velocity profile, turbulence intensities, and Reynolds stresses, when scaled appropriately, become independent of downstream distance as it freely expands into its surroundings. Free-shear flows occur in combustors, vehicle wakes, and jet engine exhaust. We focus our attention on three canonical categories of such flows: jets, wakes, and mixing layers. A detailed similarity analysis of the plane jet is provided alongside summarized results for the plane wake and mixing layer. We introduce examples involving turbines in wind farms and drag on wake-generating bodies. The notion of entrainment, which is central to the expansion of free-shear flows, is discussed. We also examine the scales and structural features of turbulent free-shear flows, including streamwise rib vortices and spanwise rollers.