a (Lagrangian) period of oscillation dp,. (wherc I is vortex diameter and 6,.
is the typical perimeter velocity). whereas a tixed instrument on thc track of
the vortex would ohscrve a (Eulerinn) p e r i d of oscillation ?/,:I., wherc I ' is
wind spccd. 'The ratio of ~hesc two periods. /L is ~ ' 3 .
where I is the \ertic;iI
intensity of turbulence f l W ! b ' . The light solid line in Fig. 6 is the cxprcssion of
this rclationship. aiid it is itpparcl1t lhat even the large (and presutnahlq
unreprescntativc) /j viilues determined when the tower was downwind of the
city and the tdtroons passed over the city are not this big, implying that the
"cartwheel ' ' concept of eddies is an unsatisfactory one.
This brings up the question of the cxtent of eddy decay and rebuilding
during the lime the cddy mows past the fixed point instrument and during
the time it takes the particle (tetroon) to move around the eddy perimeter.
'rhis problem hits becn considered by Gifford (1955) and Smith (1967). us
well as others, and thc light dashed lines in Fig. 6 represent the variation of /I
with turbulence intensity (i) derived from their theoretical work assuming a
nonstetidy cddy structure. GitTord obtained the expression /I = ( l . l i i ) + 1.
und while this expression agrecs well with the "urban" /I valucs found at
Oklahoma City. again these particular values are almost assuredly not
representative. Smith obtained several expressions for p depending on the
assumed form of the corrclogram, but in general they can be expressed by
[i z 0..5/i. This cxpression agrees well with the Oklahoma City data as normalized for city effects. Furthermore, note that the normalized Oklahoma
City data are in almost exact agreement with Pasquill's (1968) expectation,
based on similarity theory, that p = 0.44;i.
Finiilly. since /I exhibits such a strong dependence on vertical turbulence
intensity. the only satisfactory way to estimate the dependence of yon lapse
rate (which, of course, is highly correlated with vertical turbulence intensity)
is by means of a two-dimensional plot with coordinates of lapse rate and
turbulence intensity. Such a plot shows that, at a given turbulence intensity,
/ 1' tends to increase with decrease in lapse rate, with the increase becoming
quite rapid in near-isothcrmal conditions. For example, is found to incrCiisc: hy 60 ",, ;IS thc lapse rate changes from dry adiabatic to isothermal at
;I wrtical turhulence intensity of .lo. This result is in overall agreement with
Il1;it ohteinctt h?
I'rcvious cstirnatcs of /I hiivc usually been based on Taylor's diffusion
equation, ilt1tl thus involved determination of the Lagrangian autocorrelal i o i i cocflicicnc from it double diffcrentiation of the mass-tracer concentration in the lalcral (or vertical) direction, and comparison with the Eulerian
correlation oocfficient obtained from a fixed-point wind instrunienl. I t hlrs
is the typical perimeter velocity). whereas a tixed instrument on thc track of
the vortex would ohscrve a (Eulerinn) p e r i d of oscillation ?/,:I., wherc I ' is
wind spccd. 'The ratio of ~hesc two periods. /L is ~ ' 3 .
where I is the \ertic;iI
intensity of turbulence f l W ! b ' . The light solid line in Fig. 6 is the cxprcssion of
this rclationship. aiid it is itpparcl1t lhat even the large (and presutnahlq
unreprescntativc) /j viilues determined when the tower was downwind of the
city and the tdtroons passed over the city are not this big, implying that the
"cartwheel ' ' concept of eddies is an unsatisfactory one.
This brings up the question of the cxtent of eddy decay and rebuilding
during the lime the cddy mows past the fixed point instrument and during
the time it takes the particle (tetroon) to move around the eddy perimeter.
'rhis problem hits becn considered by Gifford (1955) and Smith (1967). us
well as others, and thc light dashed lines in Fig. 6 represent the variation of /I
with turbulence intensity (i) derived from their theoretical work assuming a
nonstetidy cddy structure. GitTord obtained the expression /I = ( l . l i i ) + 1.
und while this expression agrecs well with the "urban" /I valucs found at
Oklahoma City. again these particular values are almost assuredly not
representative. Smith obtained several expressions for p depending on the
assumed form of the corrclogram, but in general they can be expressed by
[i z 0..5/i. This cxpression agrees well with the Oklahoma City data as normalized for city effects. Furthermore, note that the normalized Oklahoma
City data are in almost exact agreement with Pasquill's (1968) expectation,
based on similarity theory, that p = 0.44;i.
Finiilly. since /I exhibits such a strong dependence on vertical turbulence
intensity. the only satisfactory way to estimate the dependence of yon lapse
rate (which, of course, is highly correlated with vertical turbulence intensity)
is by means of a two-dimensional plot with coordinates of lapse rate and
turbulence intensity. Such a plot shows that, at a given turbulence intensity,
/ 1' tends to increase with decrease in lapse rate, with the increase becoming
quite rapid in near-isothcrmal conditions. For example, is found to incrCiisc: hy 60 ",, ;IS thc lapse rate changes from dry adiabatic to isothermal at
;I wrtical turhulence intensity of .lo. This result is in overall agreement with
Il1;it ohteinctt h?
I'rcvious cstirnatcs of /I hiivc usually been based on Taylor's diffusion
equation, ilt1tl thus involved determination of the Lagrangian autocorrelal i o i i cocflicicnc from it double diffcrentiation of the mass-tracer concentration in the lalcral (or vertical) direction, and comparison with the Eulerian
correlation oocfficient obtained from a fixed-point wind instrunienl. I t hlrs