A plausible scenario for the existence of a persistent back-ground of turbulence in the free atmosphere is described. The MST radar technique is the only existing technique that can be used to describe the morphology of occurrence of turbulence as a function of altitude, wind speed, shear, weather conditions, geographical location, etc. This technique was used also to assess the degree of universality of shape and amplitude of the buoyancy wave spectrum and the relation between the buoyancy wave spectrum and turbulence

Vanzandt, T. E.

English

NASA Technical Reports Server

256 
4.3A EXISTENCE OF A PERSISTENT BACKGROUND OF TURBULENCE 
T. E. VanZandt 
Aeronomy Labor a tory 
National Oceanic and Atmospheric Administration 
Boulder, Colorado 80303 
Before the advent of VHF Doppler radars,  it w a s  generally believed, on the 
bas i s  of d i r e c t  measurements by balloons and a i r c r a f t  and ind i r ec t  measurements 
by incoherent radars,  t h a t  turbulent l aye r s  i n  the f r e e  atmosphere have median 
thicknesses of a t  least 100 m. Since it was a l so  believed t h a t  i n  the lower 
s t ra tosphere only about 3% of the atmosphere i s  turbulent on the average (LILLY 
e t  al.,  19741, then the mean separation between turbulent layers  had t o  be a t  
l e a s t  3 kilometers. I f  t h i s  were t rue,  then a radar with 1-km range ga te s  would 
detect  an echo only about one th i rd  of the time and the fading of the echo 
s t rength would be very deep. 
Instead, VHF Doppler radars  with 1-km resolut ion usually detect  echoes i n  
every range gate  up t o  the upper a l t i t u d e  of d e t e c t a b i l i t y .  I n  the troposphere, 
echoes a re  detected i n  every range gate  even with a resolut ion as small as  
150 m. These r e s u l t s  required t h a t  turbulence be much more uniformly d i s t r i -  
buted than had been thought. But since constraints  on the t o t a l  turbulent 
energy d i s s ipa t ion  rate make it impossible f o r  the e n t i r e  volume of the lower 
atmosphere to  be turbulent,  the turbulence must be d i s t r ibu ted  among many, thin,  
r e l a t ive ly  closely spaced layers.  This d i s t r ibu t ion  cons t i t u t e s  a pe r s i s t en t  
background of turbulence. 
The pr incipal  mechanism for the generation of turbulence i n  the f r e e  
atmosphere i s  thought t o  be shear i n s t a b i l i t y  i n  regions where the Richardson 
number R i  i s  less than 114. The existence of many t h i n  turbulent l aye r s  then 
requires many th in  regions of large shear. 
v e r t i c a l  shear p ro f i l e s  from smoke t ra i l s  (Figure 1) and high-vertical  resolu- 
t i o n  balloon ascents during the 1960s. 
very high resolut ion balloon data to  show t h a t  the turbulent  layers  do indeed 
occur i n  regions of large shear. 
I n  order t o  in t e rp re t  the ear ly  VHF Doppler radar measurements, VANZANDT e t  
Such regions were suggested by 
More recent ly ,  BARAT (1983) has used 
a l .  (1978) assumed t h a t  the t o t a l  shear i n  the denominator of R i  i s  the sum of 
the steady background shear and a f luc tua t ing  mesoscale shear, which they 
described by a probabi l i ty  d i s t r ibu t ion .  They then calculated the probabi l i ty  
of occurrence of regions where R i  5 114. Such regions occur more frequently 
where the background shear i s  large o r  where the background s t a b i l i t y  (Ng2, the 
numerator of Ri) i s  small. They assumed, lacking evidence t o  the  contrary,  t h a t  
the probabi l i ty  d i s t r i b u t i o n  i n  the troposphere i s  the same everywhere, inde- 
pendent of a l t i t u d e  or location, and s imilar ly  i n  the stratosphere.  
I n  t h e i r  model the mean thickness of turbulent layers  was taken t o  be 10 m. 
This value might be i n  e r ro r  due t o  def ic iencies  i n  the model o r  e r r o r s  i n  the 
absolute ca l ib ra t ion  of the radar. Nevertheless, 10 m was SO much smaller than 
the then generally accepted median thickness, t ha t  it did strongly suggest t h a t  
t h e  previous estimated thicknesses were too large.  
Later more d i r e c t  measurements confirmed tha t  the median turbulent layer  
WOODMAN (1980b1, using a 2380-MHz thickness i s  considerably less than 100 m. 
radar a t  Arecibo, found t h a t  the thickness of the echoing ( turbulent)  layers w a s  
usually not much Larger than the a l t i t u d e  resolut ion used, t h a t  is, with 150 m 
resolution, they were of ten 150 m thick,  with 60 m resolution, they were 60- 
200 m thick,  and with 30 m resolution, they were 30-60 m thick.  
https://ntrs.nasa.gov/search.jsp?R=19840019050 2020-03-22T09:43:49+00:00Z
25 7 
!O ‘ 0.1 
SHEAR (s-’) 
Figure 1. Superposition of e i g h t  vertical shear 
p r o f i l e s  from smoke trails wi th  25 m reso lu t ion .  
(Adapted from ROSENBERG and DEWAN, 1974.) 
Indeed, when the  e a r l i e r  r epor t s  of d i r e c t  measurements of tu rbulen t  layer  
thickness a re  examined, it i s  found t h a t  in almost every case the  median or m e a n  
th ickness  reported i s  c lose  t o  the r e so lu t ion  of the experiment. This suggests 
t h a t  the p robab i l i t y  of occurrence of a turbulen t  layer  of th ickness  i n  the  
range (L,dL) i s  a strongly decreasing func t ion  of L, a t  l e a s t  f o r  L l a rge r  than 
about 30 m. 
I n  a very high r e so lu t ion  balloon experiment i n  the  mid-stratosphere (27 .5  
t o  29.5 h), BARAT ( 1 9 8 2 )  found seven turbulen t  l aye r s  ranging i n  thickness from 
3 t o  240 m, with a median of 21 m and a mean of 56 m. 
258 
Although the VANZANDT e t  a l .  (1978) model provided a plausible scenario f o r  
the pe r s i s t en t  background of turbulence it did not attempt any explanation fo r  a 
pe r s i s t en t  f luctuat ing d i s t r ibu t ion  of mesoscale shears. Indeed, there was no 
generally accepted explanation for  such shears. 
Later VANZANDT (1982) showed t h a t  the mesoscale f luc tua t ions  of wind and 
temperature, hence of shear and s t a b i l i t y ,  i n  the troposphere and lower strato- 
sphere can be explained a s  the r e s u l t  of a spectrum of buoyancy ( in t e rna l  
gravi ty)  waves. The shape of t h i s  spectrum tends t o  be universal  and, indeed, 
can be described by a s l i gh t  modification of the GARRETT and MUNK (1972, 1975) 
model spectrum for  oceanic in t e rna l  gravi ty  waves. There a l so  appears t o  be a 
considerable degree of universal i ty  of the amplitude of t h i s  spectrum a s  a 
function of a l t i t ude ,  geographical location, etc., consistent with the assump- 
t i o n  i n  the VANZANDT e t  a l .  (1978) model t h a t  the probabili ty d i s t r ibu t ion  of 
the shear f luctuat ions i s  invariant.  
The universal  shape of the oceanic in t e rna l  waves spectrum is thought to  be 
maintained by weakly nonlinear resonant wave interact ions t h a t  cause a cascade 
of wave energy i n  frequency-wave-number space. 
i n  the atmosphere with some modifications. 
i l l u s t r a t e d  i n  Figure 2. Energy i s  put i n t o  the buoyancy wave f i e l d  a t  v e r t i c a l  
wave numbers smaller than $* (ve r t i ca l  wavelength I/$*). The sources of 
buoyancy wave energy a re  not wel l  understood. 
shear i n s t a b i l i t y ,  on the upper and lower sides of j e t  streams, fo r  e a p l e ,  
generation of waves by convective storms, extract ion of energy from lee waves by 
wave interact ion,  etc. 
not known even fo r  the sources t h a t  have been ident i f ied.  
The same process should operate 
The scenario fo r  energy flow i s  
They include wave generation by 
The order of magnitude of the r a t e  of energy input i s  
f 
Figure 2. Schematic scenario for energy flow in the 
buoyancy wave field. a is the horizontal wave 
number. (Adapted from McCOMAS and MULLER, 1981.) 
259 
The energy i s  cascaded through the constant energy f l u x  region by the wave 
interact ions.  McCOMAS and BRETHERTON (1977) showed t h a t  the dominant resonant 
wave in t e rac t ions  can be c l a s s i f i e d  as "e l a s t i c  scat ter ing,"  which simply 
reverses the v e r t i c a l  phase ve loc i ty  , and "induced diffusion" (ID) and "para- 
metric subharmonic i n s t a b i l i t y "  (PSI), both of which move energy i n  frequency- 
wave-number space toward the i n e r t i a l  frequency, f = s i n  ( l a t i t u d e I l l 2  hr,  and 
l a r g e  v e r t i c a l  wave numbers (small wavelenghs). Since the variance of the shear 
versus log 8 increases about as B1I2, as the energy moves t o  smaller and smaller 
v e r t i c a l  wavelengths the occurrence of shear i n s t a b i l i t y  (Ri 5 1/41 becomes more 
and more common. 
cascade from larger  wave numbers can no longer keep up with the turbulent dis-  
s ipa t ion  of wave energy. 
value i n  the atmosphere i s  unknown, but the observed spectrum of horizontal  wind 
versus $ does not show any breakdown t o  a t  least 20 m, the  shortest  scale  
observed (1. E. GOOD, p r iva t e  communication). 
The c r i t i c a l  wave number 8, i s  where the f l u x  of energy by 
I n  the ocean 8, Q1/10 m (GARGETT et  al.,  1981); i t s  
This scenario also automatically r e s u l t s  i n  long-lived, pancake shaped 
patches ( b l i n i )  of turbulence, consistent with observations (ROTTGER and 
SCHMIDT, 1979; WOODMAN e t  al.,  1981; SAT0 and WOODMAN, 1982; BARAT, 1983). 
Since the frequency spectrum i s  red, the dominant contribution t o  t h e  shear a t  
any pa r t i cu la r  scale  i s  l i k e l y  t o  be made by low-frequency waves, which have 
nearly horizontal  surfaces of constant phase and small v e r t i c a l  phase velo- 
c i t i e s .  Thus, most turbulent patches w i l l  be long-lived pancakes t h a t  move 
slowly upward o r  downward, as i n  Figure 3. 
According t o  t h i s  scenario, because the s t a b i l i t y  i s  greater  i n  the s t ra to-  
sphere than i n  the troposphere, the r a t e  of occurrence of turbulence should be 
2s. 
2.. 
1 6 23. 
W 
3 - 22. 9.. 
d 
21. 
20. 
19. 
80. la. 180. 1.0. SM). 
RECORD NUMBER 
Figure 3. Locus of echo power maxima observed by the Arecibo 
430-MHz radar with 150 m resolution. A turbulent layer  i s  
assumed t o  e x i s t  a t  every power maximum. (From WOODMAN e t  a l . ,  
1981). 
260 
less i n  the stratosphere.  
with increasing a l t i t u d e  due t o  the at tenuat ion of buoyancy waves by the 
increaasing kinematic viscosi ty .  
turbulent l aye r s  with increasing height. 
consistent with observations. 
i n  the troposphere turbulence occurred i n  every range gate,  but i n  the  s t ra to-  
sphere above 16 km there  were gaps. 
a l t i t u d e ,  t o  about 1 km a t  about 24 km. 
l en t  echo w a s  detected w a s  31 km. ( A t  the greatest  heights,  the de t ec t ab i l i t y  
of turbulence might have been strongly diminished by the approach of t he  inner 
s ca l e  of turbulence t o  the half-wavelength of the radar.) 
found t h a t  turbulent l aye r s  are sparse i n  the middle stratosphere.  
Also, the c r i t i c a l  wavelength of 1 / B ,  w i l l  increase 
T h i s  w i l l  r e s u l t  i n  fewer and fewer t h i n  
These predict ions are qua l i t a t ive ly  
With 150 m resolution, WOODMAN (19801 found t h a t  
The thickness of these gaps increased with 
The maximum height a t  which a turbu- 
BARAT (19821 a l so  
The foregoing cons t i t u t e s  a plausible  scenario f o r  the existence of a 
pe r s i s t en t  background of turbulence. 
have not been developed as f a r  as t h i s  one has. 
generally accepted as the explanation fo r  most, i f  not a l l ,  of the turbulence i n  
the deep ocean (MUNK, 1981; GARGETT e t  al.,  1981; DESAUBIES and SMITH, 1982). 
Nevertheless, many aspects of the scenario need t o  be quant i f ied,  not only i n  
the ocean but even more so i n  the atmosphere. The MST radar  technique can make 
c r u c i a l  contr ibut ions to  t h i s  study. It i s  the only ex i s t ing  technique tha t  can 
be used t o  describe the morphology of occurrence of turbulence as a function of 
a l t i t u d e  , wind speed, shear,  weather condi t ions,  geographical location, etc. It 
i s  a l so  the only technique t h a t  can describe the buoyancy wave spectrum versus 
frequency (BALSLEY and CARTER, 1982) and v e r t i c a l  wave number under a wide range 
of conditions. 
v e r s a l i t y  of the shape and amplitude of the buoyancy wave spectrum and the 
r e l a t i o n  between the buoyancy wave spectrum and turbulence. 
O t h e r  scenarios may be possible,  but they 
The present scenario i s  
Such observations a r e  e s s e n t i a l  t o  assess  the degree of uni- 
REFERENCES 
Balsley, B. B., and D. A. Carter (19821, The spectrum of atmospheric ve loc i ty  
f luc tua t ions  a t  8 km and 86 km, Geovhvs. Res. L e t t . ,  9, 465-468. 
Barat, J. (1982), I n i t i a l  r e s u l t s  from the use of i on ic  anemmeters under s t ra to-  
spheric balloons : 
spheric motions, J. Appl.  Meteorol.. 21, 1489-1496. 
Application t o  the high-resolution analysis  of s t ra to-  
Barat, J. (19831, The f i n e  s t ruc tu re  of the s t ra tospheric  flow revealed by 
d i f f e r e n t i a l  sounding, J. Geovhys. Res.. 88, 5219-5228. 
Desaubies, Y., and W. K. Smith (19821, S t a t i s t i c s  of Richardson number and of 
i n s t a b i l i t y  i n  oceanic i n t e r n a l  waves, J. Phvs. Ocean., 12, 1245-1259. 
Gargett, A. E., P. J. Bendricks, T. B. Sanford, T. R. Osborn, and A. J. W i l l i a m s  
111 (1981), A composite spectrum of v e r t i c a l  shear i n  the upper ocean, 
J. Phvs. Oceanographv. 11, 1258-1271. 
Garret t ,  C., and W. Munk (19721, Space-time scales  of i n t e rna l  waves, Geovhvs. 
Fluid Dynamics. 2, 225-265. 
Garret t ,  C., and W. Munk (19751, Space-time scales of i n t e rna l  waves: a 
progress report ,  J. Geovhvs. Res.. 80, 291-297. 
L i l l y ,  D. K., D. E. Waco, and S. I. Adelfang (19741, Stratospheric  mixing e s t i -  
mated from high-alt i tude turbulence measurements, J. A w ~ .  Meteorol.. 13, 
488-493. 
McComas, C. H., and F. P. Bretherton (19771, Resonant i n t e rac t ion  of oceanic 
261 
in t e rna l  waves, J. Geophvs. Res.. 82, 1397-1412. 
McComas, C. H., and P. Muller (19811, The dynamic balance of i n t e rna l  waves, 
J. Phvs. Oceanographv. 11, 970-986. 
Munk, W. (1981), Internal  waves and small-scale processes, i n  Evolution of 
Physical Oceanography, ed. B. A. Warren and C. Wunsch, pp 264-291. 
Rosenberg, N. W., and E. M. Dewan (19741, Stratospheric turbulence and v e r t i c a l  
e f f ec t ive  diffusion coeff ic ients ,  Proc. Third Conf. on the Climatic Impact 
Assessment Program, ed. A. J. Broderick and T. M. Hard, Rep. No. DOT-TSC- 
OST-74-15, pp 91-101; o r  AFCBL-TR-75-0519 (29 Sept. 19751, Hanscom AFB, M4. 
Rottger, J., and G. Schmidt (19791, High-resolution VHF radar  sounding of the 
troposphere and stratosphere,  IEEE Trans. Geosci. Electr . ,  GE-17, 182- 
189. 
Sato, T., and R. F. Woodman (1982), Fine a l t i t u d e  resolut ion observations of 
s t r a tosphe r i c  turbulent l aye r s  by the Arecibo 430 MHz radar,  J. Atmos. 
Sci., 39, 2546-2552. 
VanZandt, T. E. (1982), A universal  spectrum of buoyancy waves i n  the atmo- 
sphere, Geovhvs. Res. L e t t . ,  9, 575-578. 
VanZandt, T. E., J. L. Green, K. S. Gage and W. L. Clark (19781, Vertical  
p ro f i l e s  of r e f r a c t i v i t y  turbulence s t ruc tu re  constant: 
observations by the Sunset Radar with a new theo re t i ca l  model, Radio Sci., 
13, 819-829. 
Comparison of 
Woodman, R. F. (1980a), High-altitude resolut ion s t ra tospheric  measurements with 
the Arecibo 430-MHz radar,  Radio Sci.,  15, 417-422. 
Woodman, R. F. (1980b), High-altitude resolut ion s t ra tospheric  measurements with 
the Arecibo 2380-MHz radar,  Radio Sci., 15 423-430. 
Woodman, R. F., P. K. Rastogi, and T. Sat0 (19811, Evaluation of e f f ec t ive  eddy 
d i f fus ive  coeff ic ients  using radar observations of turbulence i n  the 
stratosphere,  i n  Handbook fo r  MAP, 2, Extended abs t r ac t s  from Intern.  
Symp. on Middle Dynamics and Transport, July 28-August 1, 1980, Urbana, 
Ill., ed. S. K. Avery. 


Existence of a persistent background of turbulence

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server