Turbulence and ‘coherent structures’
Soon after the first attempts by Lighthill and his successors to predict the sound radiated by turbulent jets a change occurred in the way turbulence is perceived. Turbulent flows were observed to be more ordered than had previously been believed, and a new conceptual flow entity was born, sometimes referred to as a ‘coherent structure’, or, alternatively, a ‘wave-packet’. Mollo-Christensen (1967) was one of the first to report such order in the case of the round jet: “…although the velocity signal is random, one should expect to see intermittently a rather regular spatial structure in the shear layer.”. A series of papers followed, confirming these observations and postulating on the nature of this order (Crow and Champagne (1971), Brown
Figure 4. Flash Schlieren images of jets (Re = 5 x 105; M = 0.83), taken from Moore (1977). Left: random ensemble average; middle: conditional average using axisymmetric nearfield pressure signature as trigger; right: conditional average using a single nearfield microphone as trigger (this educes the antisymmetric organisation).
and Roshko (1974) and Moore (1977) to cite just a few). Figure 3(b), taken from Crow and Champagne (1971), provides a visual sense of this underlying order: by changing visualisation technique, using sheet illumination and carbon dioxide fog, rather than the fine grained patterns revealed by the schlieren technique, an axially-aligned waveform with wavelength of the order of the jet diameter is observed.
A further illustration of the underlying organisation present in high Reynolds number jets is shown in figure 4, which shows the difference between time-averaged and conditionally-averaged images of round jets at high Reynolds and Mach numbers. We will discuss conditional averaging techniques later in more detail.