**3. Turbulent Flow
Structure**

The velocity data acquired using the LDV can be analyzed for turbulence in the wake. In order to estimate the turbulence intensity, velocity deviations are computed as

where *u* is a velocity vector and *u _{b}
*is a base velocity. As the bore passes the obstacle, there are large
changes in the flow structure. These changes represent gradually varying base
flow but not consider turbulence. Therefore defining

where *t* is time and Δ*t* represents
the length of the time interval the velocity is averaged over, does not solve
the problem, as the changes in the flow are very abrupt at the time of bore
impact. A single averaging interval Δ*t* provides
too much averaging in some portions of the velocity time history and does
not provide enough averaging in others. A different definition of a base velocity
*u _{b}* is needed. First the time of bore arrival,

where *i* is the step number in the repetition and *u _{0} = u*. Four repetitions are used so

a)

b)

Figure 3.1. Velocity data and the base
velocity in the wake of the circular column for *h*_{1} = 250 mm: a) *x*
= 350 mm, *y* = 0 mm, and *z* = 15 mm; b) *x* = 470 mm, *y* = 210 mm,
and *z* = 35 mm.

The turbulence intensity is then calculated as the root-mean-square average of the velocity deviations or

where the averaging interval is 20 times that used for the base velocity calculations or 20 Δt = 2 sec.

The LDV velocity
data for *u* and *v* are available at 24 points on a three-dimensional
rectangular grid at *x* = 210 mm, 350 mm and 470 mm, *y* = 0 mm,
70 mm, 140 mm and 210 mm, and *z* = 15 mm and 35 mm – the horizontal
and vertical coordinates of the measurement points are depicted in Fig. 3.2.

a)

b)

Figure 3.2. Locations of LDV measurements in the wake of the circular column: a) the horizontal coordinates, b) the vertical locations.

Figure 3.3 shows results of the
root-mean-square calculations starting 0.5 s after
the bore arrival. Away from the centerline there is a clear decrease in turbulence
intensity in time, in both the x and y-directions. The magnitudes of *u’ _{rms}* and

a)

b)

Figure 3.3. Root-mean-square average of
velocity deviations in the wake of the circular column for *h*_{1} = 250 mm: a) *x*
= 350 mm, *y* = 0 mm, and *z* = 15 mm; b) *x* = 470 mm, *y* = 210 mm,
and *z* = 35 mm

Using root mean square values
over the interval described above, we compute the relative strength *, where , and the results are listed in Table 2 and also plotted in Figs. 3.4 and 3.5. Generally the velocity fluctuation in the x-direction is greater at the lower elevation, but that does not hold for the y-direction. There the turbulence is greater at the lower elevation on the centerline, but it varies outside of it. On the centerline the turbulence intensity in the y-direction is considerably higher than that in the x-direction, while the magnitude is similar in either direction away from the centerline. Interestingly, these observations are true at the different downstream locations as shown in Figs. 3.4 and 3.5.*

**Recommendation:** Our LDV and DPIV data are available for validation of
turbulence models. Free-surface wake turbulence is a very challenging problem.

Table 2. Velocity deviation as a ratio
of the mean velocity in the wake of the circular column for *h*_{1} = 250 mm.

Figure 3.4. The flow-wise variations in the turbulence intensities.

Figure 3.5. The span-wise variations in the turbulence intensities.