Observations oi fine scale structure in the mesosphere and lower thermosphere

E. V. T&mm

and B. G-a

Norwegian &fence: Research Establishment1 P.O. Box 25, 2007 KjeKler,Norway

Below 95 km the power spectra had a slope of about --5/s, as expected for isotropic ttnbulence Tke relation between the observed fluctuations in ion density and the corresponding fluctuations in neutral gasdensity k discussed. Above 95 km the fluctuations were stronger and showed a “white noise” power spectrum. These flmtuations

are most likely due to plasma instabilities.

The fine sde sm=ctuI-e of the wem ionized plasma in the lower ionosphere has been studied both by in sifu rocket techniques ~MECHTLYet aE., 1967; ZI MMERMANN et al., 1972) and by ground based radar observations (see for example Bm* PROSEet al., 1972; HA~JG et al., 1977; RAs~ocx and Bow&m&, 1976; M&N%%’ et al.. 1969; ~fkR%R and WUOP~, 1976). The nature and cause of the observed irregularities have II& Beea fumly established., fn the region below 100 km where the degree of ionization is very small (104 s-l), one should expect a very close coupling between the ionized component of the gas and the neutral air. The air in this part of the atmosphere is believed to be in a state of turbulent mixing, and it seems reasQnable to assum that irregularities in iomzation density are caused by such turbuIence. Above about 1oOkm eiectrodynamic forces wiB probably determine the behaviour of the plasma. On the 1st of March 1978 at 0113 UT two rockets, code named F-47 and F-48 were launched I second apart from And@ya Rocket Range (69”18’N, 16”0f”E) &rough a moderate& disturbed nighttime ionosphere, The rockets carried a &ml of nine different ~n$~~~~~ au measure ~o~~he~~ and neutral gas parameters. Experimenters from Max-Planck Insti#ut fiir Kernphysik, Bonn Wniversit%t, Technische UniversitHt Graz, University of Bergen and the Norwegian Defence Research Establishment participated in the campaign. During the launch periQd the i0riosphere was

ah munitored from the ground by means of riometers, and by a partial r&e&m HF-facility, operated by the University of Trams@ at Ramfjord, near Tromsa (HAIJG er al., 1977). A study of the combined results from all the rocket borne and ground based experiments will be published jointly by all experimenters, in this paper we only present and discuss results from an electrostatic probe mounted on F-47. The probe was designed to measure fine Scale -RuctuatiQns in positive ion density in the lower ionosphere. Section 2 describes the experiment, In Section 3 and 4 the relation between fluctuations in the ion and neutral gas number densities is derived. Section 5 presents the experimental results and in Section 6 possible interpretations are discussed,

The F-47 pay&ad was carried aloft by a NXEAPACHE rocket and reached an appogee of 127.5 km. The electrostatic probe was spherical and mounted at the top of the payload under a split cone that was released at an altitude of 61 km, It consisted of an outer grid with a diameter of 12 cm, an inrier grid collectslr with 11.2 cm diameter and a central spherical copper housing for an eleotrometer. Ike grids QQnSiSted of tW.3 h& §pheTeS held together by a metal belt mounted in the plane of the rocket axis. The probe was designed to measure positive ion current with high time resolution and accuracy. The outer grid and copper housing were kept at rocket body potential, whereas the collector had a bias voltage of -5 V. The electrometer had a dynamical range of fQur deca&S, from 2 - IQ-” A

180

E. V. THRANEand B. GRANDAL

to 2 . lo-’ A. Linear amplification was used and the current range was divided into four subranges each covering one decade. Automatic range switching was provided with a hysteresis of about 10%. The current was sampled at a rate of 1136 Hz and converted to 8 bit words, and in addition 2 bits were used for subrange indication. This format provides a resolution of 0.4% of the saturation current in each subrange.

3. ‘IWE PBINCIPLE OF ION CUBBENT MEASuBEMENT

Theories describing the behaviour of gridded electrostatic probes moving through the ionospheric plasma have been outlined by SAGAL~N et al. (1963), SMIDDY and STUART (1969) and FOLKESTAD (1970). For high Mach numbers, M> 3, the expected current should to a first approximation be the amount of charge swept out by the projection of the outer grid surface in the flow direction, per unit time: I = eNicrUR

(I)

where e is the ionic charge, N, the positive ion number density, u the effective cross section of the probe and vR the rocket velocity. The cross section (+ is determined by the mechanical construction of the grid, and by flow conditions. The metal belt holding the grids must be expected to cause a small spin modulation in the ion current with twice the rocket spin frequency. Probe theory in the lower ionosphere is complicated by the change in flow conditions near a supersonic vehicle, from continuum flow below about 7.5 km to essentially free molecular flow above 100 km. The effective cross section u will therefore change with height, and a commonly used analytical procedure has been to normalize the ion current profile measured by the probe with absolute measurements of electron density, for example by means of Faraday rotation measurements (MECHTLY et al., 1967; BENNETT. et al., 1972). This procedure should be valid at heights where the negative ion density is small. The effective cross section will vary slowly with height, so that the ion current may be assumed to be proportional to ion density over small height intervals. Thus a probe with high time resolution may be used to study tie structure in the medium. The main aim of the present experiment is to study the relative fluctuations ANJN; of the ion number density, and derive the corresponding fluctuations in the neutral gas.

4. RELATION BJTIWEEN FLUCCUATIONS IN THE POSIllVE ION AND NEGAS DENSITIES IN THE MFSOSPHERE

Our arguments in this section are based upon the assumption that the electrons and ions can be regarded as conservative passive tracers in the process of turbulent mixing of the neutral air. This assumption implies that the electron and ion concentrations do not change through ion production, recombination or chemical reactions within a characteristic lifetime of a turbulent eddy. The problem has been considered by several authors (see for example CUNNOLD, 1975, and the very detailed treatment by HILL and BO~HILL, 1978) who have concluded that the assumption is reasonable in the D-region, that is at heights below about 9.5 km. The lifetime of a turbulent eddy is of the order of 10-100 s in this region (CUNNOLD, 1975), whereas the lifetime of an ion against recombination is 7 = ~/I,QN~ where 4 is the effective recombination rate. Typical values of T range from about 200 s at 90 km to 1000 s near 70 km. HILL and BO~HIU (1976) have considered effects accompanying the displacement of air parcels, such as changes in the ionizing radiation, and the advection of minor constituents affecting the photo-chemical equilibrium in the air parcels. They find that in general the relaxation time for positive ions is of the order of 100-1000 s. The use of positive ions as passive tracers of turbulent motion in the height range 60-95 km should therefore be permissible.

4.1.

The effects of the shockfront

The rocketborne probe passes through the medium at about three times the speed of sound, a, and should record an instantaneous, “frozen” picture of the irregularities in ion density along its path. We have already mentioned that the complex flow through the shockfront makes it difficult to calculate the effective cross section of the probe, so that estimates of absolute ion density N, are uncertain. Behind the shockfront, in the vicinity of the probe, there will be a region with high density and temperature. In continuum flow the ratio of pressure, density and temperature behind the shock to ambient atmospheric parameters are given by the Rankine-Hugoniot relations (JOHANNESSEN, 1974). For the neutral number density, the ratio depends only upon the Mach number In ambient nshock M = v,/a where vR is the rocket velocity. Since M changes slowly with height it follows that a relative fluctuation 6nln does change appreciably across the shockfront at a given height.

Observations of fine scale structure in the mesosphere and lower thermosphere The high density and temperature will in principle change the ionization balance through an increase in the ion production and a decrease in the recombination rate. However, the air will flow past the probe in about one tenth of a millisecond, and during this time the changes due to ion production and loss are very small compared to the ambient density. Typical values in the D-region are for the ion production, q = 10 crne3 s-l and the ion density, N, = lo3 cmm3. Thus in 0.1 ms the change in ion production is of the order of only lo-’ times the total ion density. We therefore conclude that, although supersonic how conditions will influence the effective cross section of the probe, the fluctuations in ion density will not change, that is

4.2. The effects of turbulence upon D-region

ion

density ~ucfu~tions

Turbulence in a horizont~ly stratified atmosphere and its effects upon the concentration of conservative passive tracers, such as the ionospheric ions and electrons, have been treated in the textbooks on atmospheric turbulence (TATARSKII, 1971; LUMLEY and PANOFSKY, 1964). It seems clear that, in the presence of vertical pressure and density gradients, vertical displacements of air elements will create fluctuations in gas density, whereas density fluctuations due to horizontal displacements will be of second order. Furthermore, the characteristic velocity of the turbulent motion is of the order of l-10 ms-‘, which is much smaller than the speed of sound. The lifetime of a turbulent eddy (l-100 s) is much shorter than the period corresponding to the acoustic cut-off frequency (T = 250 s). Therefore, any local pressure variation caused by the turbulence will be removed by rearrangements in the gas, which will occur at the speed of sound. It is thus reasonable to assume that a gas element vertically displaced by turbulent motion, will at all times keep an internal pressure equal to the pressure of the undisturbed ambient gas surrounding the element. It will fu~hermo~e be assumed that the time scales of the motions are too short for heat exchange, so that all processes are adiabatic. The validity of this assumption may be questioned in the D-region, since the rate of heat exchange between an air parcel displaced by turbulent motion and the surrounding air will depend upon the temperature gradient, as well as the size and shape of the air parcel Adiabatic processes must therefore be re-

181

garded as an extreme possibility, and one should keep in mind that thermal conduction and molecular diffusion will tend to smooth out the irregularities and may determine their fifetimes. We now turn to the problem of finding the explicit form of the relation between fluctuations in the ion and neutral gas. The turbulence will create irregularities in ion and electron density through the process of vertical displacement discussed above, but the intensity of these irregularities will depend upon the vertical gradient of both the neutral gas and ion number density, and therefore upon the mixing ratio x = N$n, as pointed out by GALLET (1955) and CUNNOLD (1975). We shall now derive a simple relation between a fluctuation Snln in the neutral air and the corresponding fluctuation SNJN, in the ion number density in the presence of a vertical gradient in x. By differentiating the equation of state, p = nkT, with respect to the height z, we obtain 1 dp ldn --_=-_+--_ pdz ndz

1 dT Tdz

(3)

We may rewrite (3) in the form --= 1 %

_$+$E n

(4)

where the scale heights are defined by 1 1 dp --=_-_ I-& pdz 1 --=__ H,,

1 dn ndz’

(5) (6)

These scale heights represent height variations in the unperturbed atmosphere. They are obtained by averaging the atmospheric parameters over height intervats large compared with the scales of the fluctuations we study here. Over height intervals where the scale heights may be considered constant, p(z) = p(O)e+“~

n(z) = n(0)e--“‘Hn

(7)

where p(0) and n(0) indicate values at a reference height z = 0. Consider an air element with pressure pE and number density nE, initially in equilibrium with the ambient air at a position 2 = O[n, (0) = n(O), Let the element tance z.

pE (0) = p(O)].

be displaced a small vertical dis[z <
182

E. V. T~RANJZand B. GRANDAL

Assuming that the element moves with a velocity much smaller than the speed of sound, its internal pressure will adapt to the ambient pressure at all positions so that l&(z) = P(z)*

(8)

Its number density will, however, be given by the adiabatic law Pi%(z)%(z)-’

=PE(o)IIEto)-y

(9)

and using (7) and (8), we have t&(Z)= n,(O)

I$$1l” =

n(0)eC'TH*.

(10)

At the new position z, the number density perturbation 6n relative to the ambient number density is given by

Sn k(z) - 4%) = ntO)e-“‘YH~_ 1

-z.z

n

n(z)

=

e~l,Hn_l,rY~z

_

1

n(0)e-“‘H~

(11) For small z we may write

$- (.$-+-)*.

(12)

Note that &r/n = 0 when H,, = yH,. In this case the atmosphere has a temperature gradient (see Equation S), equal to the superadiabatic lapse rate, and a vertical adiabatic displacement of an air element causes no density perturbation. The ion number density has a height gradient which may also be characterized by a scale height, obtained by averaging over height intervals larger than the scale of the fluctuations, 1 1 dN, ---..-=:-__~ Hi Ni dz

(13)

For a height interval in which I& does not change appreciably, we have (14)

During the displacement of the air element we now assume that its ion number density NE is proportional to the neutral number density. The perturbation in ion number density relative to the ambient medium at the height z must be SN

hri~(~)-N~(z)=N~(O)e-"~~~_~ Ni (0)e-"H* N,(z)

’

(15)

In analogy with (12) we obtain

$L (-J&-&J.

(17) where

(18) Thus a knowledge of the ion density height gradient expressed by Hi, and of the height variation of the neutral atmosphere expressed by HP and H,, should enable us to derive fluctuations in neutral air number density from probe observations of SNJNi. A perturbation is assumed to be caused by a vertical displacement .z of an air element, and (17) is, of course, only valid when F is constant over this distance. In general we must expect a spectrum of irregularities of different scales at any height, and only if F is constant over a height interval larger than the scale of the largest fluctuation, wili the spectra in ion and neutral number density have the same shape. In practice, as will be discussed later, we use data from 1 km height intervals to derive power spectra of the fluctuations, and our requirement for the conversion (17) is therefore that F does not change appreciably over these intervals. 5. EXPERIMENTAL

RESULTS

5.1. Launch conditions and large scale structures

Ni = N&“~.

x=

We also note that SNJN, = 0 when Hi = $?l,. Thus the ion density may have a (negative) height gradient that exactly matches the density change in the air element during an adiabatic displacement. In this case the turbulent density fluctuations in the neutral air becomes invisible to the ion probe, and there are no electron density irregularities present to scatter a radio wave passing through the region. From (12) and (16) we may now derive the relation between irregularities in ion and neutral number density

(16)

The rocket was launched during moderately disturbed night time conditions with negligible magnetic disturbance, and a stable riometer absorption of about 1 dB at 30 MHZ. As mentioned in the introduction the ionosphere was monitored during count-down and launch by the partial reflection radar near Tromso, 120 km from rocket range. The radar works at 2.75 MHz, and the amplitude of the partial reflections is a sensitive indicator of the state of the lower ionosphere. The radar data, that is the amplitude height scan for ordinary and extraordinary waves, was transferred in near real time to the rocket range via a datalink. The launch conditions

Observations of fine scale structure in the mesosphere and lower thermosphere

183

5.2. The observed fine scale structure in ion density

PDS. KIN NUMBER DENSITY

m-3

Fig. 1. Ion density versus height measured during the flight. Absolute values were obtained by normalizing to electron densities derived from Faraday rotation measurements above about 90 km. (FRIEDRICH,private communication).

were judged to be right when partial reflections observed in the height range 65-95 km indicated the presence of irregularities and appreciable ionization densities in the D-region. An additional requirement was that the riometers at both sites showed stable, moderate absorption. The clamshell opened at 61 km on the upleg, and the electrostatic probe worked from this time throughout the flight until about 50 km on the downleg. Figure 1 shows the ion density versus height derived from the measurements. These curves have been normalized to the electron densities above about 90 km as measured with the Faraday technique (FRIEDRICH, private communication). The curves represent ion densities averaged over about 200 m intervals, and thus the small scale structure is not visible. We note, however, that there is structure present on scales of a few km, and that ion densities on the downleg are significantly smaller than the upleg values. The particle counters in the payload showed that the source of ionization is precipitating electrons with energies above 10 keV, and that the particle flux was less intense on the downleg.

The rocket velocity changes from about 1100 ms-’ at 60 km to about 200 ms-’ at apogee (127.5 km). With sampling rate of 1136Hz, this means that the spatial distance between sampling points changes from 1.1 m to 0.2 m in this height region. We should, therefore, expect to resolve apparent spatial structure in ion density of a few meters in the D-region and at about 1 meter in the E-region. The data show fine scale structure throughout the whole flight, but the intensity and the scale of the fluctuations vary significantly. Figures 2a and b show two examples of the raw data for 70 km and 105 km respectively. The first example shows structure of a few per cent of the background and scales of tens of meters, the second show noiselike fluctuations with apparent scales down to about 1 m and with amplitudes of lo15%. A detailed analysis of the fluctuations was made as follows: we treat the measurements of ion density Ni as a time series and define a fluctuation, relative to a background density, as

Slv,(t) N(t)-(N) f(t)===

(19)

(N>

where (Ni) is the running average over a suitable time interval. The root mean square @MS) fluctuations are given by SN,s

=

&‘4(t) -@Ji))*).

Thus the relative FCh4.Sfluctuations

(20)

are

SNRMS

EI,=Jmm

(21)

By defining the Fourier transform of f(t) as CC F(o) = _m f( t)e’” d t I the power spectrum of the fluctuations P(o) = IF(w)l’.

(22)

is given by (23)

It follows that

(24 We analyse the data in blocks of points, corresponding to time series of than one second, or to height intervals 1 km at 70 km to 200 m at apogee. The

1024 data a little less from about data blocks

E. V. THRONE and B. GRANDAL

184

b)

E

0

“‘,‘,,,‘,,,,~,,,,,,,,,,,,,,,,,‘,”””l””,””r 105.0 105.2

lOS.4 HEffiHT

106.6

105.8

01,,,,,,,,,,‘,,‘,,“‘,‘,“““‘(“““.”I”””””””””” 69.2 69.4 696 69.8 HEIGHT Fig. 2. The observed

detailed

structure

70.2

704

KM

in ion current for two height near 105 km.

are centered at heights given by integral numbers of kilometers. The running mean (NJ is computed for each datapoint using 200 observations. In this way the running mean should not show effects of rocket spin (spin period -0.2s). The spin effects will, of course, be visible in the fluctuations, which are defined as deviations from the running mean. The length of the data “window” of 1024 data points, will give a spectral resolution of about 1 Hz. Figure 3 shows a series of power spectra derived for separate data blocks as described above, using a fast Fourier transform algorithm (SINGLETON, 1969). The spectral intensity of a frequency f is averaged over the interval f to l.lf. We note the presence of spectral components at the spin frequency fs and at 2f,. The latter component is expected since the probe has a 180” symmetry in a plane through the rocket axis. The sampling rate will limit the frequencies that can be resolved at the high frequency end, the length of the data block and the contamination in the spectrum from the rocket spin will set a limit at the low frequencies. We believe that useful information may be derived in the frequency range lo-300 Hz. These limits are indicated in Fig. 3. The frequency scale may be converted into a scale in length, using the relation A = v,/f where v, is the rocket velocity. This scale is indicated for each spectrum. We note that the two D-region spectra have characteristic slopes, very different from the slopes

1061)

KM

intervals.

(a) Near

70 km; (b)

of the E-region spectra, and that the intensities are also different. An attempt has been made to estimate the spectral index n, using the relation P(w) a mn. Figure 4 shows the derived index n versus height together with the mean square fluctuation

where z=lOHz

and

2=300Hz.

The figure shows several interesting features: (a) Below 95 km, in the D-region, the root mean square fluctuation SMRMs/(N) varies strongly with height but is in general of the order of 0.5%. The spectral index n is fairly easy to determine from the spectra and does not change appreciably with height. Averaging over values below 95 km we obtain ti = -1.58, with a standard deviation a,, = 0.23. The vertical solid line in Fig. 4 indicates the mean, the shaded area the standard deviation. In the height region 77-78 km, the intensity of the fluctuations was very small. Apart from the spin frequency, only “white noise” was observed. No spectral index was derived for these heights. (b) Above 95 km the rocket seems to have entered a different regime with strong, very small scale fluctuations. cYN~~J(N~) is of the order of 3% in

Observations of fine scale structure in the mesosphere and lower thermosphere

i

the height region 105-115 km. In this range the spectral index n is close to zero, indicating a “white noise” spectrum. There are no indications that noise could have been produced in the payload. The rocket leaves the strongly disturbed region at about 120 km, but enters it again on the downleg. In this part of the flight the disturbance seems to have moved down in height by 5-10 km. (c) Above 120 km the intensity of the fluctuations is small, and the spin frequency dominates the spectrum in the lower frequency range, that is below about 30 Hz. The spectrum above 30 Hz has a noiselike character, and about the same intensity as observed near 78 km. When the payload enters the D-region on the downleg, strong harmonic components of the spin frequency appear in the spectrum. The rocket motor was separated from the payload on the upleg at 68 km, and the magnetometer on board indicates that the payload maintains its orientation until 55 km on the downleg. The probe is therefore in the wake of the payload in the downleg continuum flow regime, and antennas and other asymmetries in the payload may create fluctuations in the flow near the probe. The strong spin harmonics makes interpretation of the downleg D-region data impossible in terms of ion density fluctuations, both as far as spectral slope and intensity are concerned.

b

6

lo-'

1/

lo-$

g lo-'

1

6. INTERPRETATION 8

185

lo’ loa lag

10.’ 1

69km 0’

UP / ’

1

j 902 /

lo’

10'

!

1

A(m)

I

101

dV

f(Hz)

Fig. 3. Power spectra P(f) of the ion density fluctuations aNi/ for four different height intervals centered at 69, 90, 105 and 109 km. The broken lines indicate the estimated limits of useful observations. The upper abcissa scale indicates possible length scales of the fluctuations.

OF THE OBSERVATIONS

In the preceding section we have presented power spectra P(o) of the ion number density fluctuations, derived from measured time series Ni(t). These time series represent both spatial and temporal variations of the ion density. However, at heights where the rocket moves much faster than the thermal velocity of ions and neutral molecules, the time series may be interpreted as spatial variations in ion density. At these heights the frequency f = 42a may be converted into a length scale A = v,/f where vR is the rocket velocity. This conversion should be reasonable where v, is supersonic, that is below about 115 km. Above this level we can no longer expect to distinguish between spatial and temporal variations. Below 115 km we may therefore interpret the spectra P(o) as one-dimensional power spectra P(k) of the spatial fluctuations of ion number density, where the wave number k = 2rrlA. We determined the slope n of the spectra assuming P(w) 0~ c0”. Thus P(w) = P(kun) 0~(ku,)“.

(26)

I L

-2

..,

. . . . . .,

-1 SPECTRAL

.,

6 INDEX

,

1 n

Fig. 4. (a) Spectral index n versus height. The solid straight line indicates the mean index for the region 6.5-95 km, and the shaded area shows the standard deviation. The broken line indicates the “Kohnogorov”

slope of -5/3. (b) The mean square reIative fluctuation in ion density versus height. [See equation (2597.

Since uR may be considered as constant 1 km height interval, we obtain P(k) 0: k”.

over a (23)

We may therefore conclude that the same spectral index will describe both P(w) and P(k). Let us now consider the spatial scales of irregularities which we may expect to observe with our experiment. As discussed in Section 5 we have a low frequency cut ofI due to spin contamination at 1OHz. The approximate high frequency cut off due to the sampling rate of 1136 Hz, is 300 Hz. Using the known rocket velocity as a function of height, we may now estimate the limits of spatial scales that we can observe, These limits are indicated in Fig. 5. We shall now relate these limits to the characteristic scales of atmospheric turbulence. In turbulent flows the energy is fed into the turbulence at large scales and transmitted without energy dissipation through hierarchy of scales in the inertial subrange to final dissipation in the viscous range. In an atmosphere with a vertical pressure gradient, the inertial subrange is limited at large scales by the influence of buoyancy forces. GELLER (1972) estimates the largest eddy size for isotropic turbulence to be I=200 m in the mesosphere. On the other hand, the smallest possible scales for turbulent eddies is determined by viscous

forces. The Kolmogorov microscale rl is often used as an estimate of the velocity scale of the smallest eddies: (TENNEKES and LU~EY, 1972)

where E = molecular

mean free path

R = z = Reynolds

number

u = turbulent velocity 6 = kinematic viscosity I= length scale of largest eddies M=uja a = speed of sound. It may be shown (TYKES and LUCY, 1972) that for air, where the kinematic viscosity and thermal difIusivity are about equal, ?I may also be used to indicate the smallest irregularity of a scalar such as the density. Figure 5 shows an estimate of rl as a function of height. The parameters 5, 6 and a were taken from the U.S. STANDARD ATMOSPHERE (1962). We chose I= 200 m and u as one tenth of typical horizontal wind speeds in the region of interest. (U.S. STANDATMOSPHERE SWP-m, 1966). The numbers were u = 2 ms-r in the region

Observations of fine scale structure in the mesosphere and lower thermosphere

601 0’

L ““‘,:

. 1

““‘:

x

’

,M*,

“a”’

r62

’

’ ‘“3

Fig. 5. The Kolmogorov microscale q versus height. The shaded area indicate extreme limits of q. The broken line shows the estimated largest scale of atmospheric turbulindicate the estimated sensitivity ence I. Amin and A,, range of experiment.

60-100 km increasing to 6ms-’ at 130 km. The limit marked nhish was obtained by multiplying u and 1 by 10, whereas nLowrepresents division of u and 1 by 10. Figure 5 also shows the upper limit I = 200 m of the inertial subrange. Finally the figure indicates the limits to the resolution of the probe, based upon the discussion above. We note that below about 95 km the probe should indeed observe the smaller scales in the inertial subrange, but that in the E-region the subrange scales are outside the sensitive range of the experiment. 6.1. Fluctuations

in the D-region

In Section 4.2 we discussed the relation between the observed fluctuations in ion and neutral number density. We concluded that the observed fluctuations can be converted into neutral number density fluctuations by multiplication with a factor F, provided F was constant over the sampling height intervals of about 1 km. This condition implies that pressure, neutral density and ion density vary exponentially with height over 1 km. The scale heights for pressure HP and density H,, were taken from CIRA (1972) for March 70”N, and the gradient in ion density -l/H, was computed from a running mean of the observed ion density Ni(h). In this manner a correction factor F was derived for all heights between 65 and 95 km, and applied to the observed ion density fluctuation. It is important to realize the limitations of the simple model on which the correction term is based. The model assumes that small scale fluctuations are superimposed on stable large scale background gradients in neutral gas and ion density. These gradients must be stable over periods longer than the lifetime of the largest

187

eddies, that is several tens of seconds. We have no direct evidence that this assumption holds for our observations. Figure 1 shows changes in the gradient of ionization density over height intervals of a few kilometers, and there is no close similarity between structures observed on the upleg and downleg parts of the flight. In the D-region, however, this is not surprising since upleg and downleg observations are separated in time by more than 150 seconds and in distance by more than 30 km. Close inspection of the data shows that it is normally easy to find a representative ionization density gradient over a height interval of 1 km for the upleg data. Estimates of the average, as well as the extreme gradients were made for each interval. Figure 6 shows the mean square fluctuation in ion number density, the factor F2 and finally the derived mean square fluctuation in neutral density (&r,,/(n))‘. We note that there is a marked height structure in the intensity of the fluctuations. The error bars indicate the extreme errors in F’ due to uncertainties in determining the ion density gradient. From Fig. 4 we note that, in the D-region, the spectral index n is nearly constant, n65_95Lm = 1.58*0.23. This slope is very close to the value n = -513, which is the expected value for a one dimensional spectrum of density fluctuations in the inertial subrange of homogeneous, isotropic turbulence (KOLMOGOROV, 1941; TATARSKII, 1972). From the previous discussion it seems clear that the scales in the inertial subrange should indeed be visible to our experiment below 95 km. We therefore conclude that the data indicate the presence of neutral air turbulence in the D-region, and that, in spite of the uncertainties, the derivation of the intensity of this turbulence yields reasonable estimates. The relative root mean square density fluctuations &n&(n) are in the range 0.1 to l%, that is nearly an order of magnitude smaller than the observed ion density perturbations. The neutral air turbulence varies strongly in intensity throughout the height region 65-95 km. Furthermore, the most intense turbulence seems to occur in narrow height intervals with a thickness of a few kilometers. Such layers of turbulence are observed at 66, 81, 85, 89 and 93 km. There is no corresponding change in spectral slope. 6.2. FIuctwations in the E-region In the height region 95 to 115 km the intensity of the observed ion number density fluctuations is large, and the spectral index n = 0. Above 95 km, according to Fig. 5, the turbulent fluctuations in the

E. V. ?kRnrsE and B. GRANDAL

Fig. 6. (a) Mean square relative fluctuationin ion density versus height. (b) Correction factor F2 versus height. (c) Mean square relative fluctuation in neutral density. inertia1 subrange are too large to be observed with our experiment. The probe might be expected to measure fluctuations in the viscous range, however, these should be very weak and have a steep spectral stope (n = -71. We conclude that the Auctuations observed in the E-region are not caused by neutral air turbulence, but are most likely related to electrodynamic processes involving the ionized species. @.JETA (1977) and SMITH and KLAUS (1978) have observed “flat” spectra at these heights

BFUKSE J, S., BURKE M. J., COYNET. N. R. and REED J. E. BENNE~F. IX G., HALLJ. E. and R~CZSNSON P. H. G.

CIRA

near the equator and attribute these to a twostream instability. ~n~ortunatei~ we have no data to confirm or reject this hypothesis for our experimental conditions, but the presence of an amoral electrojet at these heights is not unlikely, even though the ma~etomete~ indicated quiet condiCons at the rocket range. A~k~wl~~ge~~~ts-~e

built by

~RRVAR

HAGEN

instrwnent was designed ROAR CHRISENSEH.

and

and

1972

.l. geophys. Res. ?7,4829.

1972

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