INSTANTANEOUS VELOCITY AND LENGTH
SCALES IN A TURBULENT SHEAR FLOW
P. J. SULLIVAN
Depurtmenr o/' Applied Muthematics
The Unirvrsity of Western Ontario, Lnndnn. Onturio, Canudu
1. INTRODUCTION
In an earlier paper (Sullivan, 1971b), the prospect of describing the longitudinal dispersion of marked fluid in an open channel flow using a numerical
simulation was explored. This approach consisted of recording the paths of
many particles as these traversed the simulating random field that was programmed on a digital computer. The resulting concentration patterns at
prescribed time intervals were compared with experimental measurements.
Very crude estimates based upon Eulerian measurements were used to construct the simulating random field. Although a quite reasonable qualitative
agreement between simulated and experimental results was achieved, it is
clear that progress with such a simulation depends critically upon the
acquisition of pertinent Lagrangian data. This is particularly true when the
dispersion of particles with other than unit specific gravity is to be considered. The particular statistics considered here (e.g. projection of motion
on a plane perpendicular to the mean flow vector) are those most relevant to
such a simulation model of dispersion in a turbulent shear flow.
Neutrally buoyant particles of approximately 4 mm diameter were injected, using an eyedropper, through the free surface of an open channel
flow. The 8.95-cm-deep flow within the glass walled flume was determined to
be homogeneous in the lateral direction y and streamwise direction x within
8 working section that was 0.46 m wide and 2.45 m long. When a particle
was injected, approximately mid-way across the working section, it was
allowed to travel approximately 10 depths before its motion was recorded. A
photographic system, suspended above the flow, travelled at the flow
discharge vclocity and recorded the three-dimensional coordinate positions
of the particle at discrete time intervals of 0.07 sec. The Reynolds number of
the flow was R = u,d/v = 620 where u,, is the friction velocity and d is the
flow depth. Approximately 150 particle trajectories over the channel length
were recorded and contained approximately 200 coordinate positions each.
213
SCALES IN A TURBULENT SHEAR FLOW
P. J. SULLIVAN
Depurtmenr o/' Applied Muthematics
The Unirvrsity of Western Ontario, Lnndnn. Onturio, Canudu
1. INTRODUCTION
In an earlier paper (Sullivan, 1971b), the prospect of describing the longitudinal dispersion of marked fluid in an open channel flow using a numerical
simulation was explored. This approach consisted of recording the paths of
many particles as these traversed the simulating random field that was programmed on a digital computer. The resulting concentration patterns at
prescribed time intervals were compared with experimental measurements.
Very crude estimates based upon Eulerian measurements were used to construct the simulating random field. Although a quite reasonable qualitative
agreement between simulated and experimental results was achieved, it is
clear that progress with such a simulation depends critically upon the
acquisition of pertinent Lagrangian data. This is particularly true when the
dispersion of particles with other than unit specific gravity is to be considered. The particular statistics considered here (e.g. projection of motion
on a plane perpendicular to the mean flow vector) are those most relevant to
such a simulation model of dispersion in a turbulent shear flow.
Neutrally buoyant particles of approximately 4 mm diameter were injected, using an eyedropper, through the free surface of an open channel
flow. The 8.95-cm-deep flow within the glass walled flume was determined to
be homogeneous in the lateral direction y and streamwise direction x within
8 working section that was 0.46 m wide and 2.45 m long. When a particle
was injected, approximately mid-way across the working section, it was
allowed to travel approximately 10 depths before its motion was recorded. A
photographic system, suspended above the flow, travelled at the flow
discharge vclocity and recorded the three-dimensional coordinate positions
of the particle at discrete time intervals of 0.07 sec. The Reynolds number of
the flow was R = u,d/v = 620 where u,, is the friction velocity and d is the
flow depth. Approximately 150 particle trajectories over the channel length
were recorded and contained approximately 200 coordinate positions each.
213