Universitā degli studi di Roma “Tor Vergata” - ART - TORVERGATA ...

Below some the mixing problem within near-, mid- and far-fields is described.
Near-Field and Vertical Mixing
In this section the mixing phenomena near the dosage discharge point is explained. It is
called Near-Field, and it is within a distance from the tracer dosage point of 50 times the channel
width. In the near-field, the tracer is being mixing long x, y and z, if a damage is located within
this part the exfiltrated tracer is not proportional to the exfiltrated water, and the QUEST and
QUEST-C methods cannot be properly applied. If this length becomes negligible compared to
the total investigated length the error due to this part could be neglected. For reducing the effect
of this part either a propeller could be applied or a preliminary investigation of the sewer could
be done by means of CCTV and the dosage point should be located where the sewer walls appear
to be in good conditions.
The near field is the place where the vertical, transverse and longitudinal mixings occur.
The time scale for vertical mixing is shorter than for transverse and longitudinal ones. The
principal mechanism causing the vertical mixing is the turbulence due to velocity shear at the
bed.
Along the vertical direction the velocity profile in turbulent open channel for a nonbuoyant
tracer is:
u x ( y)
1 ⎛ y
= log
⎜ e
u * χ ⎝ yo
⎞
⎟
⎠
Eq. 2.2-18
where ux is the assemble longitudinal mean velocity [m s -1 ]; χ is a constant of proportional
(called Von Karman’s contant); yo is an arbitrary fixed depth; u* is the velocity shear defined as:
u * =
where τo is the bed shear stress [N m -2 ] at yo and ρ �is the water density [g m -3 ].
The shear stress profile is:
τ o
ρ
y
τ t = τ o ( 1−
)
h
Eq. 2.2-19
Eq. 2.2-20
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