306
W. W. WILLMARTH AND S. S. LU
hot film probes in the region very near the wall where the level of turbulent
fluctuations is very high (tr'/V = 0.4) and the mean shear (SVI8y) is also
very high. Accordingly, it remains a subject for further research to determine
the reason for the difference between the present measurements and those of
Wallace et a/. (1972) near the wall.
3.7. Meun Ptv-iocls of Bursts and Sweeps
In the visual studies of Runstadler et al. (1963). Schraub and Kline (l965),
and Kim et al. (1968, 1971), the mean time intervals TB, between bursts were
measured by visual counting of the violent events of ejection near the wall in
a turbulent boundary layer. Kim et al. found that the mean time interval TB,
was nearly the same as the time lag required to obtain the second mild
maximum in the curve of the autocorrelation coefficient of the fluctuating
streamwise velocity R,. By a complex processing of a hot wire signal in a
turbulent boundary layer, Rao et al. (1969, 1971) were able to measure the
mean time interval between bursts. They showed, in a summary of their own
and otherZ data obtained over a wide range of Reynolds numbers, that the
mean burst period T,,, scaled with outer rather than inner boundary layer
flow variables. Among their summarized data, there was only one measurement of T for high Reynolds number flow (Ree = 38,000). This Was obtained
from the second mild maximum in R , measured by Tu and Willmarth
(1966). We have recently determined (Lu and Willmarth, 1974) that the
second mild maximum in R , in that data was produced by a low pass filter
used during our (1966) measurements of R,. Therefore the value of T at
Re, = 38,000 that is quoted in Rao er al. (1971) is not valid.
In any process of counting the number of bursts, a definitive identification
of bursts is required. In visual studies bursts of varying magnitude are observed embedded in a background of other turbulent fluctuations. When an
event is not extremely violent and/or coherent, it is up to the observer to
decide whether it is a burst or not. Very much greater difficulties are present
in the measurement of the mean burst period from a trace of a single hot
wire signal because only the velocity at one point in.a complex bursting
pattern can be observed.
In the hot wire measurements of Rao et al. (1969. 1971). the signal u was
passed through a band pass filter to make "bursts" stand out more clearly
(we are not certain from their paper whether or not the u signals were
differentiated before filtering. First, as pointed out by Kim et al. (1971), it
remains to be determined whether this process will show the phenomenon of
Rao et ul. (1971) summarizcd the resulis for the mean burst period T , obtained from papm
by Kim e/ a/. (1968), Schraub aad Kline (1965). Runstadlur et a/. (1963) and Laufer and Badri
Nerayanan (1971).
W. W. WILLMARTH AND S. S. LU
hot film probes in the region very near the wall where the level of turbulent
fluctuations is very high (tr'/V = 0.4) and the mean shear (SVI8y) is also
very high. Accordingly, it remains a subject for further research to determine
the reason for the difference between the present measurements and those of
Wallace et a/. (1972) near the wall.
3.7. Meun Ptv-iocls of Bursts and Sweeps
In the visual studies of Runstadler et al. (1963). Schraub and Kline (l965),
and Kim et al. (1968, 1971), the mean time intervals TB, between bursts were
measured by visual counting of the violent events of ejection near the wall in
a turbulent boundary layer. Kim et al. found that the mean time interval TB,
was nearly the same as the time lag required to obtain the second mild
maximum in the curve of the autocorrelation coefficient of the fluctuating
streamwise velocity R,. By a complex processing of a hot wire signal in a
turbulent boundary layer, Rao et al. (1969, 1971) were able to measure the
mean time interval between bursts. They showed, in a summary of their own
and otherZ data obtained over a wide range of Reynolds numbers, that the
mean burst period T,,, scaled with outer rather than inner boundary layer
flow variables. Among their summarized data, there was only one measurement of T for high Reynolds number flow (Ree = 38,000). This Was obtained
from the second mild maximum in R , measured by Tu and Willmarth
(1966). We have recently determined (Lu and Willmarth, 1974) that the
second mild maximum in R , in that data was produced by a low pass filter
used during our (1966) measurements of R,. Therefore the value of T at
Re, = 38,000 that is quoted in Rao er al. (1971) is not valid.
In any process of counting the number of bursts, a definitive identification
of bursts is required. In visual studies bursts of varying magnitude are observed embedded in a background of other turbulent fluctuations. When an
event is not extremely violent and/or coherent, it is up to the observer to
decide whether it is a burst or not. Very much greater difficulties are present
in the measurement of the mean burst period from a trace of a single hot
wire signal because only the velocity at one point in.a complex bursting
pattern can be observed.
In the hot wire measurements of Rao et al. (1969. 1971). the signal u was
passed through a band pass filter to make "bursts" stand out more clearly
(we are not certain from their paper whether or not the u signals were
differentiated before filtering. First, as pointed out by Kim et al. (1971), it
remains to be determined whether this process will show the phenomenon of
Rao et ul. (1971) summarizcd the resulis for the mean burst period T , obtained from papm
by Kim e/ a/. (1968), Schraub aad Kline (1965). Runstadlur et a/. (1963) and Laufer and Badri
Nerayanan (1971).