Momentum and energy diffusion in the turbulent wake of a cylinder

Abstract A detailed experimental investigation of the turbulent motion in the wake of a circular cylinder, 0.953 cm. diameter placed in a n air-stream of velocity 1280 cm.sec.-1, has been carried out with particular reference to those quantities determining the transport of turbulent energy and mean stream momentum. At distances of 80, 120 and 160 diameters down-stream from the cylinder, direct measurements have been made of mean flow velocity, turbulent intensity , viscous dissipation, energy diffusion, scale, and form factors of the velocity components and their spatial derivatives.These observations show that, except close to the wake centre, the flow at a point fixed with respect to the cylinder is only intermittently turbulent, due to the passage of the point of observation through jets or billows of turbulent fluid emitted from the inner wholly turbulent core of the wake. Further consideration of the results indicates that the turbulent motion within the jets is solely responsible for the turbulent transfer of momentum , while diffusion of turbulent energy and of heat is carried out by the bulk movement of the jets. Most probably, the jets are initiated b y local fluctuations of pressure inside the turbulent core, and in the late r stages of their development that are slowed down by adverse pressure gradients. The existence of pressure-velocity correlations of sufficient magnitude is demonstrated by using the equation for the conservation of kinetic energy in the wake, all terms of which are know n excepting the one involving the pressure-velocity correlation, which is the n obtained by difference. While the conception of jets of turbulent fluid is more convenient for following the physical processes in the wake, the alternative but equivalent description that the turbulent motion consists of a motion of scale small compared with the mean flow superimposed on a slower turbulent motion whose scale is large compared with the mean flow may be used. A formal explanation of this two-stage turbulent structure in terms of the Fourier representation of the velocity field is suggested, which relates the structure to the presence of a quasi-constant source of energy of nearly fixed wave-number, and to the free boundary which allows an unlimited range of wave-numbers. It is expected that this type of motion will occur in all systems of turbulent shear flow with a free boundary, such as wakes, jets and boundary layers.