LACRANGIAN-EULERIAN TIME-SCALE
RELATIONSHIP ESTIMATED FROM
CONSTANT VOLUME BALLOON FLIGHlS
PAST A TALL TOWER
I . I N T R O t ~ ~ ~ ~ T I O ~
Between September 25 and October 12, 1971, 56 free-floating constanl
volume balloons or tetroons (Fig. I ) were flown past the instrumented
460-m WKY television tower located on the northern outskirts of Oklahoma City. While the primary purpose of the experiment was to compare
Reynolds stress obtained from tetroons and tower, the experiment also
provided a unique opportunity to compare Lagrangian and Eulerian time
scales of motion in the vertical. Summaries of earlier attempts to define the
Lagrangian- Eulerian time-scale ratio fi have been presented in "Meteorology and Atomic Energy" (Slade, 1968).
In this paper the Eulerian and Lagrangian time scales of motion are
represented by the period or frequency of the vertical-velocity spectral peak
where, as is customary. the absolute spectral density S(n) has been multiplied
by the frequency t i (in cycles sec" '), and the spectral peak determined froni
the maximum in nS(n), as measured in mz sec-2. Inasmuch as the pertinent
theory deals with the integral time scale, there is some danger in this
procedure. but it is the most feasible one owing to the difficulty in determining representative Lagrangian and Eulerian integral scales from sampling
times of only I - 2 hr. In this connection, recall that the frequency of the nS(n)
spectral peak is proportional to the reciprocal of the integral time scale, with
the proportionality factor equal to 1/2n when the spectrum corresponds to a
simple exponential correlogram (Pasquill, 1963).
Figure 2 shows the location, with respect to Oklahoma City, of the WKY
lower. the tetroon-tracking radar. and the usual tetroon launch site. Because
of the prcvailing south-southwesterly winds in that area, in most of the
Eulerian L:iprangian comparisons the air moved across Oklahoma City
419
RELATIONSHIP ESTIMATED FROM
CONSTANT VOLUME BALLOON FLIGHlS
PAST A TALL TOWER
I . I N T R O t ~ ~ ~ ~ T I O ~
Between September 25 and October 12, 1971, 56 free-floating constanl
volume balloons or tetroons (Fig. I ) were flown past the instrumented
460-m WKY television tower located on the northern outskirts of Oklahoma City. While the primary purpose of the experiment was to compare
Reynolds stress obtained from tetroons and tower, the experiment also
provided a unique opportunity to compare Lagrangian and Eulerian time
scales of motion in the vertical. Summaries of earlier attempts to define the
Lagrangian- Eulerian time-scale ratio fi have been presented in "Meteorology and Atomic Energy" (Slade, 1968).
In this paper the Eulerian and Lagrangian time scales of motion are
represented by the period or frequency of the vertical-velocity spectral peak
where, as is customary. the absolute spectral density S(n) has been multiplied
by the frequency t i (in cycles sec" '), and the spectral peak determined froni
the maximum in nS(n), as measured in mz sec-2. Inasmuch as the pertinent
theory deals with the integral time scale, there is some danger in this
procedure. but it is the most feasible one owing to the difficulty in determining representative Lagrangian and Eulerian integral scales from sampling
times of only I - 2 hr. In this connection, recall that the frequency of the nS(n)
spectral peak is proportional to the reciprocal of the integral time scale, with
the proportionality factor equal to 1/2n when the spectrum corresponds to a
simple exponential correlogram (Pasquill, 1963).
Figure 2 shows the location, with respect to Oklahoma City, of the WKY
lower. the tetroon-tracking radar. and the usual tetroon launch site. Because
of the prcvailing south-southwesterly winds in that area, in most of the
Eulerian L:iprangian comparisons the air moved across Oklahoma City
419