WINE

Journal

of Armospherrc

and Terreslrial

Physics,

PnntedinGreatBritain.

OOZI-9169/X7$3.00+ .oO Pergamon Journals Ltd.

Vol.49,Nos.7/S,pp.763-775, 1987.

In situ measurements of turbulent energy dissipation rates and eddy diffusion coefficients during MAP/WINE F.-J. Physikalisches

Institut,

L~~BKEN, U.

UniversitHt

E. V. Norwegian

Defence

Research

THRANE,

Establishment,

G. A. KOKIN and Central

Aerological

Observatory,

VON ZAHN

Bonn, Nussallee T.

12, 5300 Bonn 1, F. R. G.

BLIX

PO Box 25, N-2007 Kjeller, Norway

S. V. PACHOMOV

141700 Dolgoprudny,

Moscow

Region,

U.S.S.R.

(Receivedfor publication 14 January 1987) Abstract-Zn situ measurements of turbulent energy dissipation rates E and eddy diffusion coefficients in the 65120 km altitude range using mass spectrometers, positive ion probes and foil clouds are presented. The mass spectrometer and the ion probe data were both analyzed with two independent theoretical approaches to derive E. In general, the derived quantities agree with the values discussed in the literature, although noticeable differences occur in certain rocket flights. An intercomparison of the spectral power densities derived from the observed neutral gas and positive ion density fluctuations supports the assumption that under certain circumstances positive ions can be used as passive tracers for neutral gas number density fluctuations. The observed E profiles exhibit a local minimum around 80 km altitude.

1. INTRODUCTION

sipation rates from the relative density fluctuations. The data reduction reflects the constraints of the applied formulas, especially concerning the spectral scales and the spectral index of the power spectrum of the relative density variations. The results of seven sounding rocket flights during the MAP/WINE campaign are shown, while combined measurements with the two aforementioned techniques were only performed during two flights. One of the results of the intercomparison between two entirely different experimental methods is that the positive ion fluctuations can indeed be considered a passive tracer for neutral gas variations, a plausible but not yet verified assumption made in most of the recent papers about turbulent ion density fluctuations. A comparison with other measurements shows reasonable agreement, although some features turn out to be perceptibly different.

The study of turbulent phenomena in the mesosphere and lower thermosphere is one of the main goals of the international program MAP/WINE, the scientific aims of which are described in more detail elsewhere (see VON ZAHN, 1983, 1987). This report concentrates on the results of in situ experiments performed during this campaign to detect turbulent features. These are a neutral gas mass spectrometer from the University of Bonn, called BUGATTI (Bonn University Gas Analyzer for Turbulence and Turbopause Investigations) and a positive ion probe (PIP) experiment of the Norwegian Defence Research Establishment (NDRE). Both instruments were mounted on the same rockets, which gave a unique opportunity for data comparison, even though PIP measures on the upleg and BUGATTI on the downleg of the rocket trajectory. Furthermore, energy dissipation rates were derived from the observed spreading of foil clouds injected into the middle mesosphere. The latter experiments were performed by the Central Aerological Observatory (CAO), Moscow. After a brief description of the experimental techniques and the performed flights, two independent methods are presented to derive turbulent energy dis-

2. THE TECHNIQUES 2.1. The neutral gas mass spectrometer

Both the BUGATTI mass spectrometer and the PIP ion probe are instruments specially designed for the investigation of the influence of turbulence on neutral gas and positive ion densities, respectively. Com763

164

F.-J.LOBKEN et al.

prehensive descriptions of these two instruments can be found in VON ZAHYNet al. (1987) and in THRANE (1981), respectively. Only those principles of their operation which are relevant for turbulence analysis will be described below. The BUGATTI instrument consists of a double focusing neutral mass spectrometer of MattauchHerzog type with a detection system capable of measuring simultaneously absolute number densities of atmospheric nitrogen and argon with high precision (better than a few per cent). Measurement of the relative number density fluctuations performed to obtain turbulent parameters does not make use, however, of the absolute sensitivity of the mass spectrometer. As pointed out by VONZAHN et al. (1985), the Ar/N, ratio reflects large temporal and spatial scales of turbulent mixing, rather than the locally present intensity of turbulence. Therefore, and because of a better signal to noise (S/N) ratio, this paper concentrates on the nitrogen number densities. The overall time constant of the ion source, the analyzing system, the detectors (electrometers) and the subsequent electronics is about a few milliseconds only, which is smaller than the effective sampling time (N 10 msec). With a typical rocket velocity of - 700 m s- ’ at 95 km the spatial resolution becomes a few meters. An extension of the operational range of the BUGATTI instrument towards higher ion source pressures (up to N 1 x lO_‘mbar) is achieved by a special ion source design, effective ion extraction out of the ion source and by differential pumping of the analyzing section. Towards higher altitudes the capability of the instrument to detect small relative density fluctuations is restricted due to the increasing influence of instrumental noise caused by the decreasing densities. Altogether, an altitude range from about 110 km down to about 90 km is covered.

2.2. The positive ion probe (PIP) The PIP instrument measures the ion current in the lower ionosphere as caused by positive ions, collected during the flight with a system of grids. For high Mach numbers, M > 3, a simple transformation to atmospheric positive ion densities can be performed, using the rocket velocity, the ionic charge and the effective cross-section of the probe. With the assumption that these quantities vary slowly with time (compared to ion current fluctuations), the relative ion current variations equal the relative ion density variations. The determination of the appropriate reference value is described in Section 5. Since, in the altitude regime of interest, the lifetime of an ion against recombination is considerably longer than that of turbulent

small scale eddies and, on the other hand, the collisional coupling time between neutrals and ions is small compared to these time scales, the positive ions can be regarded as tracers for neutral gas fluctuations caused by turbulent motions. The good coupling between neutrals and ions is demonstrated in Section 6. The high sampling rate (2441.4 Hz), together with the small time constant of the probe and the subsequent electronic components (over all < OSms) allows detection of density variations with a spatial resolution of 0.5 m or better. 2.3. The foil clouds A detailed description of this experiment is given in et al. (1981). The principle of the measurements presented here is the observation of the timespace evolution of chaff clouds using a radar system. The chaff was released from the metrockets at about 80 km. After release the cloud spread quickly, due to a high horizontal ballistic velocity. After the ballistic inertia was damped, some spreading still continued, due to small scale turbulence. The radar tracked the chaff cloud automatically. Simultaneously, a quick periodic ultra-narrow gating was performed along the antenna beam, enabling recording of the echo power P from the chaff as a function of distance d (P is proportional to the chaff density). A geometry for the experiment was used such that all observations were carried out along an almost horizontal axis. The P(d) records were used for further processing.

GALADIN

3. THE FLIGHTS

A summary of the experimental set-up is given in Table 1. The listed M-T flights were part of rocket salvoes, which are described in more detail by VON ZAHN (1987). Due to the restriction of some ground-based and rocket-borne experiments to dark conditions, all salvoes took place during night-time. The time schedule of the launchings obviously does not permit continuous observation of the temporal behaviour of the turbulent upper atmosphere. It rather gives a number of snap shots with comprehensive case studies of turbulent phenomena. During two of the M-T flights (M-T5 and M-T6) almost of the PIP and measurements simultaneous BUGATTI instruments were performed and offer the unique possibility of intercomparison. To derive quantitative turbulent parameters, such as the energy dissipation rates, from the detected density fluctu-

Turbulent energy dissipation and eddy diffusion

165

Table 1. Summary of M-T flights during the MAP/WINE campaign, together with information on PIP and BUGATTI measurements

Flight label

Apogee

M-T2

127.2 km

M-T3

121.9 km

M:T4

118.3km

M-T5

115.3km

M-T6

Launch date and time (UT)

Altitude range of PIP measurements

Altitude range of BUGATTI measurements

Sources for temperature profiles

6 Jan. 1984 21:55 13 Jan. 1984 20:oo 25 Jan. 1984 16.39 31 Jan. 1984 18:31

65.7-I 19.9 km

USSA 76

63.9-l 19.9 km

USSA 76

63.7-l 18.0 km

USSA 76

61.7-115.0km

114.&91.0km

117.9km

10 Feb. 1984 2:40

63.9%117.0km

117.&92.0 km

M-T7

117.7km

69.4117.0 km

M-T8

113.3km

16 Feb. 1984 1:20 18 Feb. 1984 0:22

61.1-113.0km

Falling sphere USSA 76 : BUGATTI : USSA 76 : Falling sphere USSA 76 : BUGATTI : Falling sphere USSA 76 : Falling sphere USSA 76 :

:

61.7-89.9 km 90.0-93.0 km 93.0-t 10.0 km 110&115.0km : 63.9-90.5 km 90.5-95.0 km 95.&l 15.0 km : 69.4-89.9 km 90&l 17.0 km : 61.1-90.4 km 90.4-l 13.0 km

All launches took place from the Andaya Rocket Range (69”N. 16”E).

ations one has to know the status of the background atmosphere, particularly the altitude profiles of temperature, temperature gradient and scale heights of pressure and number density. As indicated in Table 1, the utilized temperature profiles to deduce E and K values were taken by one of the following techniques : (1) downward integration of the BUGATTI nitrogen densities ; (2) almost simultaneous soundings of passive falling spheres (see VON ZAHN 1987); (3) if no measurements were available, from a model atmosphere (U.S. Standard Atmosphere 1976). The scale heights of positive ion number densities were derived directly from the ion probe measurements. During three of the M-T flights the PIP probes detected a peculiar white noise-like increase in the ion density fluctuations in the high wave number part of the spectrum. It was detected both on the upleg and downleg from 92 km until apogee, from 104 to 108 km, and 93 km until apogee by the PIP probes aboard the M-T4, M-T5 and M-T8 payloads, respectively. This we tentatively explain as an aurora1 electrojet. No attempt has been made to extract turbulent parameters in this altitude regime from PIP data. However, since the status of the neutral atmosphere is presumed to be less affected by an electrojet than the ionized components, the BUGATTI data were still interpreted in these altitude ranges in terms of turbulent density variations. This approach is in part based on the low degree of ionization in the lower ionosphere, typically less than lo- ‘, and the collision

frequency, typically lo3 s- ‘, which gives a ‘lifetime’ of a neutral gas particle for collision with a postive ion of the order of hours. Furthermore, no significant increase in neutral gas density fluctuations were observed at these altitudes. 4. TURBULENT ENERGY DISSIPATION RATES AND EDDY DIFFUSION COEFFICIENTS FROM An/n

We have used the following two different theoretical approaches to derive turbulent energy dissipation rates E from measured density variations : (1) first deduce the mean turbulent velocity from the integrated power spectrum and then calculate E (referred to below as the ‘u, method’) ; (2) first deduce the structure function constant C, from the absolute value of the power spectral density at a certain wave number and then calculate E from C, (referred to below as the ‘C,, method’). In the following the two theoretical methods are described and their differences discussed. We will present results derived from both theoretical approaches, since they are both used in the literature and there is at the moment no theoretical or experimental evidence as to which one is more appropriate. This point needs clarification in future studies since, as is shown later, the results of these two methods are not identical. Possible reasons for observed differences are presented later.

766

F.-J.

LOBKEN et al.

4.1. The u, method The basic approach of this method has been presented by THRANE et al. (1985). They interpret the observed density fluctuations in terms of fluctuations of potential energy per unit mass and derive a mean turbulent velocity from the assumption of equipartition between the total kinetic and the potential energy. The expressions applied for neutral gas and positive ion fluctuations, respectively, are, for BUGATTI

for PIP

l&E z

pot = -_g’

(2) where u2 is the mean square turbulent velocity of the air elements, E,,, is the mean potential energy of the density fluctuations, HN2, HP and Hi are the scale heights of nitrogen number densities, pressure and positive ion density, respectively, (AnN2/nNlref)r.m,s,and (ANJAN,,,J,,,,, are the root-mean-square (r.m.s.) intensities of the nitrogen number density and positive ion fluctuations, respectively (the fluctuations are taken relative to a reference value, which represents the undisturbed situation), g is the acceleration due to gravity, y is the ratio of specific heats CJC, (= 1.4 for air) and F = (An/n~ef)/(Alvi/Ni\ri,f> is a conversion factor between the relative fluctuations of the number densities of neutral gas and positive ions. With the assumption that the ions are passive tracers for neutral gas variations and that the involved scale heights are constant in the considered altitude segments, Fis given by F

=

1 YH,IH, - 1’

YH,IK

-

(3)

where, in the case of a well mixed atmosphere, H, = HN,. Order of magnitude values for F are (-O.OlE( -0.1). This indicates that the ion density variations are expected to be stronger and have opposite sign compared to the neutral gas fluctuations. There has been some discussion at to whether the assumption of equipartition between potential and total kinetic energy is appropriate or whether instead the kinetic energy of the vertical component only should be used. We do not intend to discuss this question here and have used the former assumption

in order to facilitate comparison with the earlier measurements of THRANE et al. (1985). The derivation of turbulent energy dissipation rates from mean turbulent velocities has been discussed in a number of articles in the literature. We used the expression as given by WEINSTOCK(198 1) E = 0.4*u,2.w,,

(4)

.. . .. where uf = l/3 u2 and oB is the Brunt-Vaaala frequency derived from the temperature profiles as noted in Table 1. It is important in this context to note that (4) implicitly assumes the existence of an inertial subrange in the power spectral density of the turbulent velocity fluctuations. Therefore, E is only calculated at altitudes where the spectral index of the number density fluctuations is compatible with -5/3 (the value expected in the inertial subrange), considering the uncertainties of the experimental method. As described in more detail in Section 5, the r.m.s. values of the number density fluctuations are determined by integrating the power spectral density between two wave numbers, k, and k,. In the ideal case, k, should mark the transition between the inertial subrange and the viscous subrange at higher wave numbers, where the molecular dissipation of turbulent energy into heat becomes important. On the other side, k, should represent the transition wave number towards higher k values (also called k,), where buoyancy forces become dominant. In practice k, is given by experimental constraints, mainly due to the noiseequivalent-power (NEP) of the instrument noise and k, is given either by the influence of the rocket trajectory on the number densities (e.g. spin modulation) or by theoretical considerations of k,. Since the spectral index in the buoyancy subrange does not differ much from -5/3 (if at all), k, cannot be determined with our experimental techniques. Nevertheless, the value chosen for k, is very important for the derived u2 value, since for a km ‘I3 power spectrum most of the spectral power density is found at low wave numbers. We have chosen k, - l/l00 m (or L, E 3,, = 2n/kB = 630m for the corresponding length scale and wavelength) throughout this paper, as estimated by GELLER (1972). There are, however, experimental indications that a smaller value of k, (a larger value for the outer scale LB) is more appropriate (see, for example, HOCKING, 1985a). If this holds true, E values derived with k, N 1/ 100 m must be considered lower limit estimations. If, for example, a value of k, = l/500 m (L, = i, = 3 100 m) where chosen, as is believed to be still realistic for regions of strong turbulence, E as derived from (1) and (2) would be increased by a factor of - 3.

Turbulent energy dissipation and eddy diffusion It should be noted, however, that L, itself is a function of the intensity of turbulence (L, a &), which can be very variable, as shown in this study. Thus the presented considerations concerning the L, value must be taken with care. 4.2. The C, method As has been shown by different authors (e.g. TATARSKII, 1971, and references therein) and summarized in a review article by HOCKING (1985a), the structure function constant Ci of a passive tracer [ is related to the power spectral density S&) for isotropic turbulence in the inertial range as &(k__) = 0.25. C;Z.kzm5’3,

(5)

where k, is the z component of wave number. S,(k,) is the power spectral density as measured with an instrument probing the turbulent region along the z-axis. Number density is, however, not a passive tracer, because vertical movement of an air parcel does change its density. However, since the time scales of turbulent motions are considerably smaller than those of molecular heat conduction, this alteration can be described in terms of an adiabatically moved air parcel. An expression analogous to potential temperature can be introduced for number densities and this ‘potential number density’ is a conservative passive tracer. If the structure function constant C, of the quantity [ is determined from the spectral analysis of the variations of [, applying (5), the turbulent energy dissipation (E) can be obtained from

E=

cf (aujaz)’ 3’2 i&‘(grad1)2> ’

(

(6)

where a2 is a constant, - 2.8 (e.g. VANZANDT et al., 1978), a = Kc/Km is the ratio between the eddy diffusion constants for the quantity [ and for momentum (if [ = 0 is the potential temperature, l/a = Pr = Km/K, is called the ‘Prandtl number’), &_i/az is the mean wind shear and grad cis the gradient of the ‘background’ field of [. The derivation of (6) is reviewed in HOCKING (1985a). Here it will be briefly performed in a modified form, which does not make use of the outer scale of turbulence. The basic idea is that for steady state conditions the amount of inhomogenity transferred per unit time from the largest to the smallest eddies is constant and is equal to the rate at which the inhomogenity is dissipated at the smaller scales. This allows expression of the structure function constant Ci in terms of the characteristics of the mean profile of ?, (TATARSKII, 1961)

Here Kc is a proportional constant between the gradient of c and the mean turbulent flux of the quantity [. Most of the utilized expressions can be found with more explanations in TATARSKII (1961, 1971). Since E is related to the shear in the mean wind as

(8) expression (6) can be obtained from the combination of (7) and (8). Different authors (e.g. VANZANDT et al., 1978 ; GAGE et al., 1980) have replaced (&/az)’ by wi/Ri (Ri is the Richardson number) in (6) and used Ri = Ri, = l/4, where Ri, is the critical Richardson number. Turbulence is believed to be produced if the actual Richardson number is smaller than l/4. This substitution does, however, introduce uncertainties, since turbulence can persist at Richardson numbers as high as 1 and the actual value of Ri cannot be measured with the experimental set-up presented in this paper. A selection of Ri = 1 instead of Ri = l/4 would decrease the derived E values from C,’ by a factor of 8. With the substitution mentioned above, equation (6) reads, for neutral gas number densities, E

=

(Ri.

a2a

a)-

312.

where grad 1 has been replaced dn/dz = n*(l/H”-

by dnldz, llyH,)

(dn is the difference in number densities between the environment and the air parcel, the latter having been adiabatically moved by a vertical distance dz from its equilibrium altitude). Again, it should be noted that the application of (9) requires the existence of an inertial subrange. Therefore, expression (9) was used only at altitudes where the measured spectral index is compatible with - 5/3, considering the uncertainties of the experimental method. Obviously, this (- 5/3) criteria is a necessary but not sufficient condition. JOHNSON (1975) has discussed the possibility of Km > K8, i.e. Pr > 1 (K, is the eddy coefficient for turbulent heat conduction). His arguments are also applicable for K,,, > K,, and if values as high as K,,,/X;, = 7 are taken, as discussed by Johnson, this would increase the E values derived from C,’ by a factor of 20. Evidence for Pr > 1 has also been given by JUSTUS (1967) STROBELet al. (1985) FRITTS et al. (1985) and others, but not all of these studies are applicable here, due to different temporal and spatial

F.-J.

768

L~~BKEN et ai.

scales involved. For comparison reasons we have chosen Km = K, (a = 1) and Ri = Ri, = l/4. In the following K, is simply written as K. The relationship between the energy dissipation rate and the eddy diffusion coefficient has been extensively discussed in the literature (see, for example, WEINSTOCK,1978a, b; LILLYet al., 1974; ZIMMERMAN and MURPHY, 1980) and will not be reviewed here. Following WEINSTOCK(1978a), we have used K = 0.81 *F/W;.

(10)

In contrast to the ‘u, method’, the ‘C,, method’ does not require any jnformation about the actual value of the outer scale, which substantiall~~ facilitates the derivation of E with the latter method. 5. DATAREDUCTION The first step in both the BUGATTI and the PIP data reduction was to obtain relative fluctuations of neutral gas and positive ion number densities (both called ‘residuals’). After that, the r.m.s. intensity was calcuIated by integrating the power spectral density of the residuals between the appropriate scales. The structure-function constant was obtained from the absolute value of the spectral power density. Energy dissipation rates (E) and eddy diffusion coefficients (K) were deduced, applying equations (l)-(4) and (10). In the subsequent chapters some specific details of the data analysis for the two instruments are discussed. 5.1. Data reduction for BUGATTI The deduction of ambient nitrogen number densities from the measured electrometer current is described by VONZAHN et al. (1987). The data stream was split into sections of 1 km height centered at integer altitude numbers and then averaged over N 10ms. Large scale variations greater than about 0.5 km and a small modulation with the frequency of the spinning rocket are removed by means of a 3rd order polynomial and a sinosoidal fit. The fit to the large scale variations was used as reference value nNzreF.The relative density variations are defined as (11) A spectral analysis of TN,(z) is performed, using a Fast Fourier Transform program (FFT) yielding the power spectral density SP(v). Temporal scales were converted to spatial scales, using the relation between frequencies (v), wave numbers (k), wavelength (2) and length scales (L)

1 = vRjv = 2njk = L,

(12)

where vR is the velocity of the rocket, which is almost constant (deviation N 2%) within the 1km altitude bins. As described by L~YJBKEN and VON ZAHN (19&3), the instrument-induced noise equivalent power is obtained from in flight measurements and is subtracted from the spectral power densities. The spectral index 5 of the power spectrum is obtained from the approximation SP(v) = const - 4,

(13)

where SP(v) is the power spectral density. l is derived from a straight Iine fit to SP(v) in a log-log plot. The root-mean-square (r.m.s.) value of the fluctuation is calculated by integrating the power spectrum between 1 and 20Hz, corresponding to length scales of N 600-30m at 95 km. Then E and K are calculated, following the expressions discussed in Section 4. For the calculation of C,, the power spectral density at an arbitrary wune bobber inside the inertial subrange is needed. Therefore, the frequewy spectrum SP(v) was transformed to a wane number spectrum SP(k), using SP(k) = &sP(v)*(v,/2n).

(14)

In altitude bins where the spectral index (0 does not equal -5’3, but upper and lower limits of r include a -5/3 value, a redistribution of the spectrum, has been performed, keeping the integrated power spectrum in the frequency regions mentioned above constant and making the modified spectrum obey a -S/3 power law. Since the structure function constant in (9) is defined for absolute number density fluctuations, the r.m.s. value derived from the spectrum of the relatiue number density fluctuations were multiplied by F$++ which is almost constant in the altitude bin of interest. 5.2. Dafa reduction for PIP In principle, the data reduction for the ion probe measurements is very similar to that described in the previous section, except for the following details (see also TIZRANEet al., 1985). Positive ion number densities (NJ are obtained from the observed ion current I using (15) where e is the ionic charge, vR the rocket velocity and CTthe effective probe cross-section. Since we can assume ~1~and CJto be constant in the

Turbulent energy dissipation and eddy diffusion limited height interval,

we may write AN,

AI

N , ref

J,r’

Length

Wavenumber

It has been found that the P(d) curves have nearGaussian shapes until 20&300 s after release. Hence, the dispersion o* of the chaff may be determined for each data segment. Plotting a* vs. time t showed that this curve had quadratic, cubic and linear parts (see BATCHELOR, 1950). It is known from theoretical considerations that such a sequence of diffusion regimes is typical only for turbulent diffusion. Therefore, the shape of a*(t) was also used as a criteria of data reliability. Then the following procedure of calculation was used : from the cubic part of the curve

is obtained

(17)

; from the linear part K= ;+r*(t)

(18)

is derived (c = constant). There is an uncertainty to the E determination by this method, because the ‘zero point’ of the time scale does not correspond to the time of release, due to initial non-turbulent (ballistic) diffusion. To eliminate this uncertainty we have used the procedure of E and K comparison at the point where the cubic regime

I o-7

^

10-e

( k=2nv/vRl

10-Z ,,,,

10-E

CL=11 10’ ,““I”

1

(16)

5.3. Data reduction far the foil cloud experiments

CT* c-t

Scale

10’ ,““-I

The reference profile Ircf was obtained from a spline fit procedure, which effectively acts as a high pass filter. The cut-off frequency towards lower frequencies was dependent on the degree of disturbance of the spectra by the spin frequency of the rocket. Typically, a frequency range of 20-200 Hz was used. Estimations of the instrument-induced noise equivalent power (NEP) show that a ‘flattening’ of the power spectra, obtained for frequencies greater than - 100 Hz, is an instrument caused effect. The r.m.s. values were obtained as follows. First the power spectrum was integrated from - 20 to 100 Hz, then a redistribution of the power spectrum according to a -S/3 law was performed (see Section 4. l), than the r.m.s. value was calculated by extending the power spectrum towards lower frequencies down to a lowest frequency of v,,, = v,/400 m. For altitudes greater than N 90 km no spectral indices in the low wave number domain of the spectra were determined, due to enhanced disturbances in the spectrum at the frequency of the spinning rocket and at some harmonics.

&=j

769

v-l

[ml 10’ ,‘IIlII

[l/ml

10-l ,,,,

100 ‘1

10-6

lo-'

n

t

10-9t

_ --

BUGA PIP

M- T6 VR.’ 645. Height:

Frequency [Hz1 Fig. 1. An example of a combined power spectrum of nitrogen (solid line) and positive ion (dashed line) number density fluctuations. The ordinate scale is correct only for the frequency spectrum. No adjustments at all have been made between BUGATTI and PIP power spectral densities.

turns over to the linear one K=a.E”3.14,‘3,

(19)

with a = constant and I the scale of diffusion at this point. All results are obtained for a spatial scale about lo3 m and for heights around 75 km. 6. RESULTS AND DISCUSSION 6.1. Power spectra and spectral indices from density fluctuations Typical examples of a combination of power spectra from BUGATTI and PIP are shown in Figs. 1 and 2. Since PIP measured on the upleg and BUGATTI on the downleg, the horizontal separation of the probed atmosphere was typically 40 km at 95 km altitude. The power spectral densities of the mass spectrometric and ion probe number density fluctuations are plotted in one figure for a common altitude bin and M-T flight. It is important to note that no normalization of the power spectra obtained from one experimental technique to the other one was performed. The ion fluctuation spectrum continues the neutral gas power

F.-J. LCJBKENet

770

Wavenumber 10-2 , ,,I,/,

10-S

[ k=2nv/vR)

[l/ml

IOI/,,,,

100 I ma,,

10-S

10-E

10-l

10-e

10-g

10-‘0

_

BUGA

TTI

I/~.. Height

678.

9 Im/secl 91.010.5

lo-” :

Frequency

Fig. 2. As Fig.

1,

[km1

[Hz1

but for flight M-T5. A pronounced bend is seen around 20 Hz.

spectrum towards larger wave numbers without any noticeable offset. This is taken as an indication of the close coupling between the positive ions and the neutral gas and supports the basic assumption of the PIP experiment, to use ion density fluctuations as a passive tracer for neutral gas fluctuations. In Fig. 1 the spectral power may be approximated by a straight line in a double-logarithmic plot (corresponding to a spectral index of 5 - -2). The combined power spectrum in Fig. 2 shows, however, a distinct bend at a scale length of N 35m, which is of the same order of magnitude as the inner scale of turbulence I,, which marks the transition from the inertial to the viscous subrange in the spectrum. The inner scale is related to the Kolmogoroff microscale ‘1by (HILL and CLIFFORD, 1978) I, N 7.4-r/,

(20)

‘1 = (V’/&)“”

(21)

where

and If (E = with U.S.

v is the kinematic viscosity. the E value from the ‘C, method’ 0.021 m* ss3) is used (see Section 6.2) together the kinematic viscosity (v N 3m*s- ‘) from the Standard Atmosphere 1976, the obtained inner

al

scale is I,, N 44m, which is in reasonable agreement with the scale at which the power spectrum in Fig. 2 exhibits a ‘bend’. It should be noted, however, that the break in the shape of the spectrum occurs at 24 times I, (HOCKING, 1985a). The agreement between observed and calculated inner scale should not be overinterpreted, since on the one hand the relative error of the calculated 1, is estimated as of the order of 50% and on the other hand the relationship between the Kolmogoroff microscale ‘1 and the length scale where the ‘bend’ is seen in the spectrum is not obvious. Even the conversion from wave numbers (k) to scale lengths (L) is not uniformly used in the literature, some use L = l/k, others L = 2n/k. It is therefore not surprising that a bend is not seen in Fig. 2, although the energy dissipation rates are approximately the same in both cases, which in turn gives similar value for I,. The coherence of the BUGATTI and PIP power spectra has been observed over the whole altitude region of overlapping data, except where an electrojet or artificial spikes in the data stream complicate interpretation of the PIP power spectra. Figure 3 shows a summary of all spectral index profiles obtained during the MAP/WINE campaign. Furthermore, estimations of upper and lower limit values are marked as hatched areas. At altitudes where a sharp bend is seen in the PIP power spectra, a second spectral index is estimated in the high frequency range of the spectrum. These quantities are also shown in Fig. 3. As mentioned in Section 4, the expressions used to obtain turbulent energy dissipation rates assume the existence of an inertial subrange with a spectral index of -513. Thus the subsequent quantities, such as E and K, were only calculated at altitudes where the hatched area shown in Fig. 3 includes a - 513 value. 6.2. Turbulent energy dissipation rates and eddy d@ision coeflcients Individual profiles of the turbulent energy dissipation rates derived from the ‘uz method’ (see Section 4) are shown in Fig. 4 for the positive ion probe (solid line) and the BUGATTI data (dashed line). For altitudes higher than - 90 km no spectral index could be observed from the power spectra of PIP data, due to large disturbances at the frequency of the spinning rocket and higher harmonics. Here E was calculated disregarding the spectral index criterium. The broad line extending above 91 km exhibits an average over all M-I flights, although single values and the detailed behavior of the altitude profile may be questionable in this altitude regime.

Turbulent

energy dissipation

-6 I! w

PIP-DATA: t in high range

0

‘I!” 110

M-

frequency

BUGATTI-DATA: upper and Lower

-2

-4

“I

PIP-DATA: upper and Lower Limit of 5 in Low frequency range

p

771

and eddy diffusion

TZ

100

so

90

80

80

Limit 70

-6

-rc

-2

0

I

T

I'(

'#I'# 110

110 -

M-T3

j

.- / M-T4

100 -

100 90

90 -

60

1

80

7

70

70-

110 -

110

loo-

100

go-

90

ED===

EO

70-

70

110-

110

loo-

100 90

so e

80

flo-

70-

i= f-

70

L

Spectra Fig. 3. Spectral indices of all M-T flights. For more The dashed lines indicate a spectral index of r = of the PIP power spectra for altitudes greater than by major disturbances in the spectra at the

In addition, turbulent energy dissipation rates as measured with foil clouds at Volgograd (48”N/46”E) and Heiss Island (8 1“N/58”E) during the MAP/WINE campaign are shown in Figs. 4 and 5 as stars. They denote an average of the available measurements during the period of the M-T flights (6 Jan.-l 8 Feb. 1984). The size of the symbols approximately reflects the variance of the measurements (see also Fig. 8). For comparison, the region between the 16th and

1

Index

specifications on the frequency ranges used, see text, 7 and 5 = - 5/3, respectively. The spectral indices (5) 90 km are not shown, due to large errors in 5 caused rocket spin frequency and higher harmonics.

84th percentiles of a summary of E measurements as presented by HOCKING (1985b) is also shown in Fig. 4. The original measurements used rocket techniques (e.g. chemoluminescent clouds) and radar techniques (e.g. observations of radar fading time). The E values obtained from the M-T flights are on average considerably smaller than those summarized by Hocking and the chaff measurements. As can be seen in Fig. 5, energy dissipation rates

712

F.-J. 0 :M-T2 0 :M-T3 0 : M-T4 . :M-T5 l

:

I&KEN

0 :M-T2 0 :M-T3 0 : M-T4 A :M-T5

= :M-T6 + :M-T7 * :M-T8

: BUGATTI

FROM

CHAFF-CLOUDS

Heating

Rate 10-l

et al.

l

: BUGATTI

: FROM

CHAFF-CLOUDS

Heating

[K/d1 100

= :M-16 + :M-T7 * :M-T8

Rate

[K/d7

IO’

10-l E

from

u,

[W/kg1

E

Fig. 4. Turbulent energy dissipation rates of all M-T flights as derived with the ‘u, method’ (see Section 4). The hatched area represents measurements summarized by HOCKING (1985). The larger stars denote measurements from Volgograd and Heiss Island (KOKIN, 1985) averaged over the

period of the MAP/WINE campaign (individual results ; see Fig. 8). The broader line for z > 90 km represents an E value from PIP averaged over all M-T flights and calculated altitudes, regardless of whether the obtained spectral is compatible with - 5/3 or not (see text).

at all index

derived from the structure function constant are noticeably larger than those determined from the turbulent velocities, by up to a factor of 10-20. Since this difference vanishes if a larger L, value is chosen (see Section 4.1), this could indicate that the outer scale of turbulence is noticeably larger than the assumed - 600m. In the altitude range of overlap, the energy dissipation rates derived from C, in general agree with the measurements summarized by Hocking, although some flights show significantly smaller numbers by more than a factor of 50, especially for the M-T5, M-T6 and M-T7 flights around 85 km. It should be noted, however, that Hocking’s compilation presents E values averaged over the entire globe, whereas he shows in his Fig. 1 that they are extremely variable and can be

from

Cn

100

10’

[W/kg1

Fig. 5. As Fig. 4, except that the ‘C, method’ is applied (see Section 4).

small on occasions, especially in polar regions. At 75 km the data are of the same order of magnitude as the chaff data. The E values around 70 km correspond to heating rates of more than 1OOK day-‘, which is comparatively high, but still may be possible in nonsteady-state conditions for limited time scales. The averaged E profile from PIP for z > 90 km (broadened line) agrees with the values compiled by Hocking. The energy dissipation rates as derived from the BUGATTI measurements (see dashed line in Fig. 5) are in general smaller than Hocking’s values, but it should be noted that the latter exhibit only 67% of all available data and are perhaps biased towards higher E values, because of some unusually high E values included in this summary (Hocking, private communication). The variability of the measured energy dissipation rates is large, up to two orders of magnitude. This is not unexpected, in the light of the atmosphere at these heights exhibiting a great variability both in space and time. In Fig. 6 profiles of the eddy diffusions coefficient

Turbulent

energy dissipation

773

and eddy diffusion

0 :M-T2

1 :M-T6

0 :M-T2

x :M-T6

0 :M-T3

+ :M-T7

0 :M-T3

+ :M-T7

o :M-T4

* :M-T8

o :M-T4

* :M-T8

A :M-T5

:

BUGATTI

.

:M-T5

601“““” 100

:

““‘l” K

Fig. 6. Eddy diffusion coefficient of all M-T flights as derived with the ‘u, method’ (see Section 4). The hatched area represents measurements summarized by HOCKING(1985). The dotted-dashed line shows the molecular diffusion coefficient for argon from a model atmosphere (USSA 1976). The broader line for z > 90 km represents a K value from PIP averaged over all M-T flights and calculated at all altitudes, regardless of whether the obtained spectral index is compatible with - 5/3 or not (see text).

(K) for all M-T flights derived by the ‘u, method’ are shown, together with the K profile from the U.S. Standard Atmosphere 1976 (dotted line). A summary of K measurements as presented by HOCKING (1985b) is also shown, as a hatched area. In addition, the molecular diffusion coefficient for argon (data from USSA 1976) is shown. Since the MAP/WINE K profiles presented in this paper were obtained from the E profiles, the general behavior of the K profiles is similar to the E profiles, although new important features appear. The K values, as derived with the ‘uZ method’, are typically one order of magnitude smaller than the values summarized by Hocking. This is not surprising, due to the lower limit character of the former quantities. This is especially obvious for altitudes above approximately 100 km, where the shown K profiles are not meaningful, since they are up to two orders of magnitudes

10'

from

I

BUGATTI

111111” / ‘LuJ! / ‘iLd

102

Cn

103

10"

[m2/sl

Fig. 7. As Fig. 6, except that the ‘C, method’ is applied (see Section 4). smaller than the molecular diffusion coefficients. This means that the time scale for diffusive transport is considerably shorter than that of turbulent mixing and, subsequently, turbulence cannot exist for noticeable time scales. The comparison between these K values and the molecular diffusion coefficients again indicates that the outer scale L, is larger than 600m (see Section 4.1). Figure 7 is similar to Fig. 6, except that K values obtained by the ‘C, method’ are presented. Here the K profiles of the MAP/WINE campaign agree with Hocking’s collective, except for the flights M-T5, M-T6 and M-T7. The averaged values for heights above 90 km (thick line) in general remain above the molecular diffusion coefficient. At some height intervals in the lower thermosphere the eddy diffusion coefficients derived from the mass spectrometer are slightly smaller than the molecular diffusion coefficient, which may either be due to the uncertainty of the utilized method (see below) or probably could have been present in the atmosphere for limited temporal scales. It is interesting to note that the E and K profiles as shown in Figs. 4-7 show a tendency for a local mini-

F.-J.

774

LOBKEN

et al.

VOLGOGRAD

SW1 .

1

DFC

g23

31

SW2 .

IO Jan

Figure

8b

HEISS

I

(48ON/46OE)

20

31

84

ISLAND

SW2

SW1

SW3 t

10

Feb

FW .

20

29

84

10

Mar

84

(81°N/580E1

SW3

FW

I

-._ 1

10

Dee

20

83

31

10

Jan

20

84

31

10

Feb

20

29

84

10

War

84

Fig. 8a. Turbulent energy dissipation rates at Volgograd (48”N/46”E). Triangles show local stratospheric warmings (SW) and final warmings (FW). The altitude of all measurements is approximately 75 km. Fig. 8b. As Fig. 8a, but measured at Heiss Island (Sl”N58”E).

around 80 km. A similar minimum has been observed by THRANEet al. (1985) and is in qualitative agreement with predictions of LINDZEN(1981) who studied turbulence originating from gravity wave and tidal breakdown. It should be noted (1) that this local minimum is obtained with both the ‘u, method’ and the ‘C,, method’ and (2) that it is not a feature of the utilized o, profiles. ALLENet al. (198 1) presented eddy diffusion profiles

mum

derived from photochemical studies which show a trend of decreasing values with increasing altitude for heights around and below the mesopause, similar to *After careful inspection E values were corrected with respect to values published earlier in the CA0 MAP/ WINE Data Catalogue.

our results, although details are perceptibly different. The experimental errors of the profiles of e and K which have been presented are estimated to be a factor of S-10 (even more at the lower and higher ends of the probed altitude range). This error is mainly caused by the uncertainties of the obtained background atmosphere (e.g. temperature profile). Possible error sources of the principle theoretical approach as discussed in Section 4 are not included in this estimation.

Figures 8a and 8b present ad~tional results* obtained concerning a possible seasonal variation of e. The Volgograd data (Fig. 8a) show a decrease in mean E from midwinter towards equinox ; there are also significant short time variations. The altitude of

Turbulent

energy dissipation

all measurements is approximately 75 km. Figure 8b shows E values measured at Heiss Island (81”N, 58”E). On average they are higher than at Volgograd (48”N, 46”E). An unexpected feature is the similarity of E variations at polar and mid latitudes. At both stations E values tend to decrease in periods of stratwarms, marked by triangles in the upper part of Fig. 8a. This may indicate that the intensity of turbulence depends on global scale meteorological processes.

7. CONCLUSIONS

Two different theoretical approaches (referred to as ‘uZ’ and ‘C, method’) were applied to the analysis of new experimental data on turbulent parameters in the mesosphere. Systematic differences between the results of the two methods were obtained. Although

and eddy diffusion

175

some indications of possible reasons for this difference are given, this subject needs further theoretical and experimental investigations. The E and K profiles as derived with the ‘C,, method’ in general agree with data obtained by totally different experimental methods. The results from the mass spectrometer show, on average, smaller values than those summarized by HOCKING (1985b). Noticeable differences appear amongst the flights, demonstrating the great variability of the amosphere in the probed altitude regime and during the time of the campaign. Our measurements show in general an increase of K with decreasing altitude for heights below - 80 km. The intercomparison of the BUGATTI and PIP power spectra shows for the first time that the assumption of positive ions being passive tracers for neutral gas fluctuations is permissible.

REFERENCES

ALLENM., YUNG Y. L. and WATERSJ. W. BATCHELOR G. K. FRITTSD. C. and DUNKERTON T. J. GAGE K. S. and BALSLEYB. B. GALALXNI. F., NEELOVI. 0. and PACHOMOV S. V. GELLERM. A. Hill R. J. and CLIFFORDS. F. HOCKINGW. K. HOCKINGW. K. JUSTUSC. G. JOHNSON F. S. LILLY D. K., WACO D. E. and ADELFANG S. I. LINUZENR. S. LOBKENF.-J. and VONZAHN U.

1981 1950 1985 1980 1981 1912 1978 1985a 1985b 1967 1975 1974 1981 1983

LOBKENF.-J., P~~TzCH. and VONZAHN U.

1985

TATARSKIIV. I

1961

TATARSKIIV. I.

1971

THRANEE. V. and GRANDALB. THRANEE. V., ANDREABEN0., BLIX T., BREKKEA., PHILBRICKC. R., SCHMIDLIN F. J., WIDDELH.-U., VONZAHN U. and L~~BKEN F.-J. WEINSTOCK J. WEINSTOCK J. WEINSTOCK J. VANZANDTT. E., GREENJ. L., GAGE K. S. and CLARK W. L. VONZAHN U.

1981 1985

J. geophys. Res. 86, 3617. J. R. met. Sot. 76, 133. J. atmos. Sci. 42, 549. Radio Sci. 15, 243. Trudy tsent. aerol. Obs. 144, 22. Aeronomy Report no. 48, p. 88, University of Illinois. J. opt. Sot. Am. 68,892. Radio Sci. 20, 1403. Handbook for MAP 16,290. J. geophys. Res. 72, 1035. J. atmos. Sci. 32, 1658. J. appl. Met. 13,488. J. geophys. Res. 86,9707. ESA SP-183, p. 31. ESA Scientific and Technical Publishing Branch, Noordwijk, the Netherlands. ESA SP-229, p. 259. ESA Scientific and Technical Publishing Branch, Noordwijk, the Netherlands. Wave Propagation in a Turbulent Medium. McGrawHill, New York (translated from the Russian). The Effects of the Turbulent Atmosphere on Wave Propagation. Israel Program for Scientitific Translations Ltd, U.S. Department of Commerce, NTIS, Springfield, VA 22 15 1 (translated from the Russian). J. atmos. terr. Phys. 43, 179. J. atmos. terr. Phys. 47, 243.

1978a 1978b 1981 1978

J. atmos. Sci. 35, 1022. J. atmos. Sci. 35,634. J. atmos. Sci. 38, 880. Radio Sci. 13, 819.

1983

ESA SP-183, p. 147. ESA Scientific and Technical Publishing Branch, Noordwijk, the Netherlands. J. atmos. terr. Phys. 49, 607. ESA SP-229, p. 267. ESA Scientifical and Technical Publishing Branch, Noordwijk, the Netherlands. J. geophys. Res. (submitted). AFGL-TR-80-0020, Environmental Research Papers no. 691, Hanscom AFB, MA, U.S.A.

u.

VONZAHN. U. and PijTZ CH

1987 1985

VONZAHN U., I?JTZ CH. and LOBKENF.-J. ZIMMERMAN S. P. and MURPHYE. A.

1987 1980

VON ZAHN