Spatial averaging of streamwise and spanwise velocity measurements in wall-bounded turbulence using ∨- And ×-probes

Abstract

The effect of finite dimensions of ∨- and ×-probes is investigated for the measurement of mean and variances of streamwise and spanwise velocities in wall-turbulence. The probes are numerically simulated using a Direct Numerical Simulation database of channel flow at a friction Reynolds number (Reτ) of 934 by varying the probe parameters, namely, the wire-lengths (l), the angle between the wires (θ) and the spacing between the wires (Δs). A single inclined wire is first studied to isolate the effect of l and θ. Analytical expressions for the variances of the streamwise and spanwise velocities are derived by applying a linear-box-type filter to the unfiltered velocity field for both ∨- and ×-..