Quantification of the bias error induced by velocity gradients

A common aspect of intrusive and non-intrusive velocity instruments is that they sample the flow over a finite volume and report the time-averaged measurements in the volume's center. The presence of a velocity gradient in the measurement volume shifts the effective location of the reported quantity toward the high-velocity region. The reported quantity differs from the actual velocity in the measurement volume center commensurate with the size of the measurement volume, the direction and rate of the gradient, and the number of sample velocities. The paper analytically quantifies the bias in the location and magnitude of the mean velocity and turbulent intensities reported by instruments acquiring velocities in regions with velocity gradients. Procedures for bias removal/minimization and for estimating uncertainties due to the velocity gradient are described for several velocity distributions in open channel turbulent flows.