Correction to: Design and implementation of a hot-wire probe for simultaneous velocity and vorticity vector measurements in boundary layers

1 Correction to: Exp Fluids (2017) 58:148 https://doi.org/10.1007/s00348-017-2433-8

It has been discovered that the original manuscript presented data that had a sign error associated with the application of Taylor’s frozen turbulence hypothesis. The negative signs shown here in Eqs. 2 and 3 besides the $2U_c\varDelta t$ terms were not included in the original manuscript or the associated computational code. The affected figures are shown here in their updated form. While slightly better agreement between the synthetic and physical experimental results is observed, the differences do not warrant a revision of the original conclusions:

$$\begin{aligned} \omega _2 = \frac{\partial u_1}{\partial x_3}-\frac{\partial u_3}{\partial x_1} \approx \frac{u_{1_c}-u_{1_d}}{\varDelta x_3}-\frac{u_{3_a}+u_{3_b}}{-2U_c\varDelta t} \end{aligned}$$

(2)

$$\begin{aligned} \omega _3= \frac{\partial u_2}{\partial x_1}-\frac{\partial u_1}{\partial x_2} \approx \frac{u_{2_c}+u_{2_d}}{-2U_c\varDelta t}-\frac{u_{1_a}-u_{1_b}}{\varDelta x_2} . \end{aligned}$$

(3)

Fig. 13

a Inner-normalized existing and present RMS profiles of wall-normal vorticity fluctuations and predicted results. Inset highlights the effects of computing the $\partial u_1/\partial x_3$ gradient with a forward or backward difference (dark fill) as opposed to a central difference (light fill). b Simulated correlation coefficient between the measured $\partial u_1/\partial x_3$ gradient and its known value at the probe centroid as computed with a forward or backward difference (dark line) as opposed to a central difference (light line). Note that the dark fill symbols in the inset of a correspond to the poorer correlation coefficient, despite having RMS values closer to the fully resolved DNS

Fig. 16

Inner-normalized existing and present RMS profiles of spanwise vorticity fluctuations and predicted results

Fig. 19

Existing and present skewness profiles of $\omega _3$ and predicted results