Figure 2
Comparison of experimentally (top) and numerically (bottom) observed streak patterns.
Velocity components in the plane are indicated by arrows, and the downstream component is indicated by colour coding, where red or blue signifies velocities faster or slower than that of fully developed laminar flow. The colour coding for the experimental flow patterns (top row) ranges from plus (dark red) to minus (dark blue) 0.6U, where U is the mean (or bulk) flow speed; the numerical flows (bottom row) range from plus (dark red) to minus (dark blue) 0.4U. The maximum in-plane velocities are one order of magnitude smaller than the maximum out-of-plane components.
(A) Experimentally observed state in turbulent "puff" (a localised turbulent structure) at Reynolds number, Re = 2000 (Re is used as a measure of turbelence and equals UD/ν), where D is the pipe diameter and ν is the kinematic velocity of the fluid. Flows with small Re are dominated by viscosity and are smooth and laminar. Instabilities in the flow appear as Re increases, and all flows become turbulent at sufficiently large Re
(B) Cross-sectional slice through a C3 symmetric streamwise travelling wave observed numerically at Re = 1250. Cm specifies an m-fold rotational symmetry
(C) C2 symmetric state observed in a turbulent puff at Re = 2500
(D) Corresponding numerical C2 travelling wave (Re = 1360)
(E) C6 symmetric state found in the experiment at Re = 5300 for fully turbulent flow. The streak configuration in the near-wall region resembles that of a numerical C6 travelling wave (F) (Re = 2900). The dominance of the low-speed streak in the central part of (E) is more characteristic of a C3 travelling wave, suggesting that (E) may result from nonlinear interactions of C3 and C6 travelling waves.