312
W. W. WILLMARTH AND S. S. LU
between the x probe. and detector probe forms an angle greater than approximately 10' with the stream direction. In addition, the contributions to ( u v 2 )
decay as one moves the x wire probe downstream at a constant small distance from the wall.
There is no doubt that these measurements indicate that an initially small
deterministic burst pattern is growing in scale and is distorted by the shearing motion as it is convected downstream. The question of how large the
evolving, deterministic bursting patterns ultimately become cannot
definitely be answered until someone devises (if it is 'possible) a more reliable
burst detection scheme. It seems likely that the effects of a violent ejection
near the wall can, after evolution and convection, reach a station remote
from the wall in the turbulent boundary layer. This conjecture is in agreement with the results of Grass (1971), the speculations of Kovasznay el al.
(1970). and present results which show that T . , is approximately constant
throughout the boundary layer.
Although definitive identification of bursts and sweeps is difficult, some
characteristic mean time intervals between bursts and sweeps have been
found. The scaling of the mean time interval between large bursts Fc3, with
the outer flow variables at Reynolds numbers RQ, of 4230 and 38,000 is
confirmed. As for the large sweep events, the mean sweep rates were also
obtained for Reynolds numbers Re,, of 4230 and 38,000. The mean time
interval between sweeps is roughly the same as that between bursts. There is
not enough data to allow us to draw a firm conclusion about the scaling of
the sweep rate, although at both Reynolds numbers we obtain roughly the
same value of about 30 for U, Ta/d*. However, if large bursting events are
indeed followed by large sweep events as suggested by Corino and Brodkey
(1969), the mean sweep period must also scale with the outer flow parameters and U, "
'
%
/6* = U, ?& fS" * 32.
It has been speculated that the bursts may have some bearing on the
turbulent "bulges" in the outer intermittent flow region. See, e.g., Kovasznay er al. (1970) and Laufer and Badri Narayanan (1971). The present measurements of the mean time interval between bursts seem to confirm this idea.
The mean burst period Ta, is approximately constant for most of the
boundary layer. This suggests that after a burst originates near the wall it
evolves into a larger convected disturbance with unchanged time interval
between bursts Ta. In addition, our measurements of contributions to uv
from different events as a function of H (Figs. 14-17) show that the contributions ;ui ( i = 1-4, h) are very similar throughout the boundary layer. This
again is consistent with the idea that the bursting events originating near the
wall continue to produce, as they evolve, relatively the same (but larger scale
and less intense) contributions to cur throughout the boundary layer.
The dominant feature of ejection near the wall in a turbulent boundary
layer can be constrasted with many well-known statistical characteristics of
W. W. WILLMARTH AND S. S. LU
between the x probe. and detector probe forms an angle greater than approximately 10' with the stream direction. In addition, the contributions to ( u v 2 )
decay as one moves the x wire probe downstream at a constant small distance from the wall.
There is no doubt that these measurements indicate that an initially small
deterministic burst pattern is growing in scale and is distorted by the shearing motion as it is convected downstream. The question of how large the
evolving, deterministic bursting patterns ultimately become cannot
definitely be answered until someone devises (if it is 'possible) a more reliable
burst detection scheme. It seems likely that the effects of a violent ejection
near the wall can, after evolution and convection, reach a station remote
from the wall in the turbulent boundary layer. This conjecture is in agreement with the results of Grass (1971), the speculations of Kovasznay el al.
(1970). and present results which show that T . , is approximately constant
throughout the boundary layer.
Although definitive identification of bursts and sweeps is difficult, some
characteristic mean time intervals between bursts and sweeps have been
found. The scaling of the mean time interval between large bursts Fc3, with
the outer flow variables at Reynolds numbers RQ, of 4230 and 38,000 is
confirmed. As for the large sweep events, the mean sweep rates were also
obtained for Reynolds numbers Re,, of 4230 and 38,000. The mean time
interval between sweeps is roughly the same as that between bursts. There is
not enough data to allow us to draw a firm conclusion about the scaling of
the sweep rate, although at both Reynolds numbers we obtain roughly the
same value of about 30 for U, Ta/d*. However, if large bursting events are
indeed followed by large sweep events as suggested by Corino and Brodkey
(1969), the mean sweep period must also scale with the outer flow parameters and U, "
'
%
/6* = U, ?& fS" * 32.
It has been speculated that the bursts may have some bearing on the
turbulent "bulges" in the outer intermittent flow region. See, e.g., Kovasznay er al. (1970) and Laufer and Badri Narayanan (1971). The present measurements of the mean time interval between bursts seem to confirm this idea.
The mean burst period Ta, is approximately constant for most of the
boundary layer. This suggests that after a burst originates near the wall it
evolves into a larger convected disturbance with unchanged time interval
between bursts Ta. In addition, our measurements of contributions to uv
from different events as a function of H (Figs. 14-17) show that the contributions ;ui ( i = 1-4, h) are very similar throughout the boundary layer. This
again is consistent with the idea that the bursting events originating near the
wall continue to produce, as they evolve, relatively the same (but larger scale
and less intense) contributions to cur throughout the boundary layer.
The dominant feature of ejection near the wall in a turbulent boundary
layer can be constrasted with many well-known statistical characteristics of