Fig. 2: Properties of time-delayed cross-correlation functions.

a Three snapshots of the field \(C\left({\bf{R}}={\bf{0}},{{\bf{R}}}^{\prime};\tau \right)\), whose peak flows downstream and broadens in time. Distances are given in mm and the center of the near-boundary is chosen as the origin. Panels b–e show mean values (symbols) and standard deviations (error bars) of variables computed from four non-overlapping subintervals, each of 1500 snapshots. b The downstream velocity of the peak (blue diamonds) is smaller than the convection velocity (red line). c The width of the peak, both in the flow direction (blue circles) and normal to it (red circles), grows linearly in time. d The peak P_z(τ) (flow direction: θ = 0, black diamonds) decays exponentially in time. e Velocity of the peak is nearly independent of the direction within a cone. The lines (shifted for clarity) show the peak locations as a function of time for the flow direction (black diamonds) and for directions θ = tan⁻¹(1/6) (blue circles), tan⁻¹(1/5) (green crosses), and tan⁻¹(1/4) (red squares) from the flow axis. However, as seen in d, the peak intensity decays faster away from the flow direction (red circles).