Introduction
The polar regions host the most powerful sources of upper atmosphere
perturbations. These sources are caused by the inflow of energy from the
solar wind and the magnetosphere. For this reason, high-amplitude waves are
often observed in the polar thermosphere. Among different types of waves an
important role is being played by acoustic-gravity waves (AGWs), which
transport the energy between different altitude layers and geographic
regions. They generate an ionospheric response known as travelling ionospheric
disturbance (TID), which can be located from the ground , and
which cause problems for the transionospheric radio communications,
especially for the global navigation satellite system (GNSS) signals . This type of
wave was studied experimentally for more than half-a-century mainly with
remote sensing methods and, to a much lesser extent, with in situ
spacecraft measurements. However, the relation between AGWs and TIDs is far
from being straightforward due to the influence of the geomagnetic field and
particle precipitation. In the F region of ionosphere, the amplitude and
phase relations between the AGW and the TID depends on the altitude
distribution of the plasma density. In the polar region, where there are
particle precipitations and field-aligned currents, the height profile of the
plasma becomes unstable. Moreover in the F region, where the frequency of
neutral-ion collisions is small compared to the gyrofrequency, the ion motion
perpendicular to the magnetic field is inhibited. Therefore, along the
geomagnetic field, which is almost vertical at high latitudes, the ions
move together with the neutral particles. Across the field the ion motion
appears due to the electromagnetic drift. These factors complicate the
relationship between the AGW and the TID. In addition, ground-based data are
subject to Doppler shifting due to high wind velocity, which reaches
1 km s-1 in the polar thermosphere . Thus, it is necessary to combine ground-based and space-based
measurements to get a clear picture of waves in the polar thermosphere.
Neutral particle density (left) and relative density variation
(right) along DE2 orbit 8257 (29 January 1983).
Unfortunately, there are only a small number of space missions involving direct
measurements of atmospheric parameters at ionospheric altitudes. The latest of
such missions – NASA's Atmospheric Explorer and Dynamic Explorer
missions – were launched in 1970s. After that, only gravimetric spacecraft
like CHAMP, GRACE, and GOCE have flown at such altitudes.
Unfortunately, their accelerometer data are not suitable for the study of AGWs,
since it is impossible to distinguish between different reasons of spacecraft
acceleration without using models based on prior assumptions (S. Bruinsma, private
communication, 2013). Even a spacecraft with a perfect instrument suite would be
unable to measure all the parameters because its orbital velocity is much
larger than the AGW phase velocity. For this reason, spacecraft actually
observe snapshots of the waveform's projection along the orbit, i.e. spatial
variations. Ground-based observations, on the other hand, capture temporal
variations. This makes the comparison of the same events observed by spacecraft
and ground-based stations very difficult. An ideal solution to this problem
would be brought by a constellation of ionospheric spacecrafts. Nevertheless, it
is possible to estimate many AGW parameters, such as the period, horizontal
phase velocity, direction of propagation etc., using single spacecraft
measurements .
Properties of polar AGWs
It follows from the analysis of Dynamics Explorer 2 (DE2) data that at
heights from 250 to 400km above the polar caps the AGWs with
wavelengths of several hundreds of kilometres are systematically observed at
different geomagnetic activity levels . DE2's orbit with the
perigee 250km, the apogee 1000km, and the inclination
89.9∘ is very suitable for the study of polar waves. DE2's scientific
payload included both neutral and charged components sensors, which allowed
analysing the AGW/TID coupling directly . The typical
distribution of the total density along the orbit is shown in
Fig. on the left.
Over the polar region, there are distinct wave variations registered, which
are superimposed on the large-scale behaviour of parameters related to changes
in the orbital height, large-scale dynamics, diurnal behaviour, etc. The
wave-like processes were identified against large-scale changes in the
parameters using the sliding average procedure. The number of points of the
sliding window was selected to provide the maximum amount of
cross-correlation between variations in the densities of different gases
(Fedorenko, 2010). For the comparison of AGWs in various gases, one should
consider relative variations of the densities normalized to an undisturbed
average value. The relative variation of neutral density along the same orbit
is shown in Fig. on the right. AGW amplitudes in the polar
regions reach 5–10 %, thus exceeding the amplitudes in mid and low latitudes by an order of magnitude. In the day sector the region of increased
wave activity is bounded by the auroral oval, but in the night sector it can
span down to lower geomagnetic latitudes. The dominant horizontal wavelength
in the polar thermosphere is 500–600km .
In the following subsections we briefly summarize the main features of polar
AGWs as deduced primarily from DE2 measurements.
Relative density variation of Ar and He (left) and N, O, N2, and
Ar (right) above the pole.
Observational signatures
To identify the type of the observed wave, its parameters should be compared
to the theoretical predictions. As an example in Fig. we plotted
relative variations of densities of individual gases above the pole. The
increase of the amplitude with the growth of the molecular mass (on the
right) and the quasi-antiphase oscillations of He and heavy gases (on the
left) are the characteristic signatures of AGW .
The AGW variation of the density, observed from a satellite, is the result of
the superposition of several factors: (1) the longitudinal wave compression
due to the pressure gradient; (2) the adiabatic expansion/contraction of the
gas; (3) the change in the background density at the vertical displacement of
the volume under the influence of gravity. The difference between
oscillation profiles in gases is caused by the difference in the vertical
distribution of their density above the turbopause. In the observed
variations of heavy gases N2 (28 amu) and Ar (40 amu), the changes of
the background density dominates. The wave variations of light gas He
(4 amu) are caused mainly by the adiabatic expansion/contraction. During the
maximal vertical displacement of the gas volume upwards, it expands
adiabatically, so there is a minimum of He density. However, this extension
is not enough to compensate the background gradient densities of heavy gases,
and these gases demonstrate a maximum in the density. At the maximal vertical
displacement of the gas downwards, there is a maximum of He density and a
minimum of N2 and Ar densities. For gases O (16 amu) and N
(14 amu) the adiabatic expansion/contraction is almost compensated by the
change in background density and the elastic compression prevails in the
resulting variations of the density. For this reason, the density variations
of O and N are shifted in phase with respect to densities of N2 and Ar,
and their resulting amplitudes are small. The details of these features are
described earlier in Dudis and Reber (1976) and Fedorenko (2009).
To check if the wave propagates in space it is necessary to study the relation
between the vertical velocity vz and the vertical displacement h of an
elementary volume due to the wave. For a propagating monochromatic wave
vz=iωh,
and the variations of vz are ahead of h by π/2 in the direction of
propagation . The vertical velocity vz was measured by the
WATS experiment onboard DE2 . The vertical displacement h can be
calculated by the relative variations of densities of two gases using a formula
hH=mm1-m2δn1n1-δn2n2,
where n1, n2 are the densities of the gases, δn1, δn2
are their absolute variations, H=kTn/mg is the height scale, k is the
Boltzmann constant, Tn is the neutral temperature, m is the mean
molecular mass, m1, m2 are the molecular masses of the gases, g is the
gravitational acceleration.
Figure shows a typical example of the variations of vz and h
above the polar cap. It is easy to see that the wave propagates in reverse
flight direction (leftwards in the plot). Almost all observed polar AGWs were
propagating towards the dayside . Note that the
systematic phase shift between the density variation of different gases in
Fig. also indicates that the wave is propagating in space. A
positive phase shift between the variations of O and N densities and the
densities of heavier gases like N2 and Ar indicates the direction of wave
propagation .
Thus we conclude that the perturbations observed above the polar caps can be
identified as propagating AGWs.
Variations of vertical velocity and displacement on the southern
polar segment of the DE2 orbit 8286. The arrow indicates the direction of
wave propagation.
Amplitudes of variations of vertical velocity and displacement in
different orbits.
Intrinsic frequency
It is necessary to determine the AGW frequency from in situ measurements to
compare them to the ground-based TID observations. The easiest way to do this
is to use the relation (Eq. ) between the amplitudes of the variations
of vz and h. In Fig. they are plotted against each other for
seven different orbits. We chose the orbital segments above the polar caps in
quiet conditions within the 250–280km altitude range. Two of them
are in the northern hemisphere, and five are in the southern one. All these
orbits show approximately the same dependence, which means that the
corresponding frequencies are very close to each other. A linear fit to these
dependencies gives the mean frequency ω≈9.8×10-3 s-1, which corresponds to a period T≈640 s. The
sound velocity in these conditions is about cs≈850 m s-1, and the isothermic Brunt–Väisälä frequency
ωb=gγ-1/cs≈9.1×10-3 s-1,
where γ is the ratio of specific heats. Within the estimation accuracy
ω is close to ωb or slightly exceeds it. Note that ω is
the intrinsic AGW frequency.
Horizontal phase velocity
The horizontal phase velocity ux can be estimated from the measured
horizontal wavelength λxs=2π/kxs, which is a projection of
the actual horizontal wavelength λx onto the orbit, and the AGW
period T. For the dominant values λxs=500–600km and
T≈(650±50) s the estimated horizontal phase velocity equals
uxs=λxs/T≈770-920 m s-1, which is close to the
speed of sound at given conditions. Of course, AGWs can never become
supersonic . In fact, it is always overestimated due to the
projected wavelength being always larger than the actual one,
λxs>λx. The actual coefficient depends on the angle between
the wavefront and the orbit plane.
AGW amplitudes at different altitudes according to DE2
measurements.
No altitude dependence
In the altitude range from 250 to 400km no altitude dependence of
AGW amplitude was observed (see Fig. ). Each point on
Fig. corresponds to a maximum amplitude of a separate wave train.
The classical AGW theory predicts an exponential growth of
the AGW amplitude as it propagates upwards due to the conservation of the
wave energy in the atmosphere with the exponentially decreasing background
density. In the real atmosphere above about 200 km, the wave energy losses
increase sharply due to the viscosity, especially when the mean free path of
the particles becomes comparable with the wavelength. Therefore, in the real
atmosphere, the increase in the amplitude of the AGW with height becomes
slower. It is possible that the energy losses due to the molecular viscosity
compensate the increase in the amplitude of the AGW. Another possible
explanation is that AGWs propagate quasi-horizontally.
Directions of AGW propagation above the northern polar region for
the polar day (left) and polar night (right) conditions.
AGW energy
At altitudes between 250 and 400km polar AGWs create vertical
flows of energy up to 0.1 erg cm-2 s-1 . This value
is comparable to the energy brought by the precipitating particles in quiet
geomagnetic conditions.
In AGW, in addition to the potential energy of acoustic compression, there is
another kind of potential energy – thermobaric or gravitational potential
energy associated with the vertical displacement of the gas volume under the
action of the gravity. Polar AGWs also have a peculiar property: their
acoustic and gravitational energy densities are almost equal when averaged
over a period . Let us write the average potential energy of an
AGW in the form
Ep=14ρ0vx2ωkxcs2+vz2ωbω2,
where vx and vz are the norms of the horizontal and the vertical
components of the particles' velocities. Since the average over a period
kinetic energy of an AGW is equal to
Ek=14ρ0vx2+vz2,
then, assuming Ep≈Ek, it follows from Eqs. () and
() that
vx2+vz2=vx2ωkxcs2+vz2ωbω2.
One can see from Eq. () that the extreme case vx=0 yields
ω=ωb (Brunt–Väisälä oscillations), and the opposite case
vz=0 yields ω=kxcs (Lamb mode).
DE2 data testify that both the horizontal and vertical components of
velocities are non-zero and close to each other. Since
ω≈ωb, ux must tend to cs, according to
Eq. (). The classical AGW theory prohibits the
propagation of AGWs with such parameters in an isothermal atmosphere, since
they fall into a restricted area in the kx vs. ω plot.
Thus, DE2 data analysis tends towards the existence of a dominant AGW
mode in the polar thermosphere with ω≈ωb and ux→cs, which contradicts the classical theory.
Wind control of AGWs
The wind pattern in the polar thermosphere is due to the superposition of
solar heating and the magnetospheric convection projected along the field
lines. The spatial structure of this pattern is quite complex and the wind
velocity can reach 300–1000 m s-1 depending on the geomagnetic
activity .
The AGWs observed from a satellite can occur directly in the upper
atmosphere, but they may also be connected to sources in the lower
atmosphere. Using an extended gravity wave scheme (Yiğit et al., 2008)
that accounts for realistic wave propagation and dissipation showed that
lower atmospheric gravity waves propagate into the thermosphere and affect
the general circulation of the high-latitude thermosphere under various
conditions (Yiğit et al., 2009, 2012, 2014). Also, numerical simulations
suggest that gravity waves propagate from the surface to the thermosphere
(Hickey et al., 2009, 2010). In the polar ionosphere, there are very powerful
sources of AGWs associated with particle precipitation and the dissipation of
currents. Therefore, the AGWs caused by low atmospheric sources in the polar
region are very difficult to distinguish. Phase velocities of observed AGWs
exceed the speed of sound in the lower atmosphere. This probably indicates their upper atmospheric origin.
The directions of AGW propagation follow a systematic behaviour suggesting that
their propagation is controlled by the wind . The most evident
feature is the predominant propagation of AGW from the nightside to the
dayside, i.e. towards the wind. During the polar day or the polar night the
directions of AGW propagation follow the seasonal variation of the wind pattern
in both hemispheres .
To illustrate this point we plotted in Fig. the dominant
directions of AGW propagation in the northern hemisphere for different UT and
KP values. Once can see that the AGW azimuths tend to follow the
direction of Earth's rotation (counter-clockwise in the northern hemisphere).
During the polar night (January–February) AGWs are tightly packed inside the
polar cap and almost can not be detected outside the auroral oval. In this
case the directions of AGW propagation are driven by the local polar wind
pattern. During the polar day (June–July) an additional flow of AGWs towards
the direction 14:00–15:00 LST can be seen. This flow is due to the
wind caused by solar heating. On the nightside this flow escapes past the
auroral oval, forming a tail-like structure. On the dayside the AGW activity
is constrained within the polar cap.
In the southern hemisphere this picture looks similar to the northern one.
The main differences are more widely spread AGW azimuths and systematically
lower AGW amplitudes. Apparently, this can be explained by a greater distance
between the magnetic and the geographical poles in the south as compared to
the north. The wind-driven circulation in the polar thermosphere can be
considered as a superposition of two wind systems . One of them
is the global wind circulation arising due to the absorption of solar UV- and
EUV-radiation (tied to the geographic coordinate system). The second one is
the vortex circulation arising from the convective motion of ionospheric
plasma (tied to the geomagnetic coordinate system). The geomagnetic input
introduces a strong UT-variation in thermospheric dynamics due to the offset
of the geomagnetic poles from the geographic poles. The spatial area,
disturbed by the polar thermospheric circulation, is greater in the southern
hemisphere due to the greater distance between the geographic and geomagnetic
poles. Accordingly, the region of increased wave activity associated with the
wind in the southern hemisphere is also more extended.
Another clear indicator of AGW-wind coupling is the dependence of the AGW
amplitude on the wind velocity . During AGW propagation, the
density, pressure, temperature, and velocity are periodically changed. The
amplitudes of these variables are connected to each other by the wave
polarization relations. They are proportional to each other .
We have analysed the variations of density, primarily because they were
measured with greater precision and higher time resolution than the velocity
and the temperature. Figure shows the dependence of the AGW
amplitude on the wind velocity to be almost linear. For an explanation of the
functional form of this dependence needs further theoretical investigations.
It should be noted that the waves with amplitudes below 1 % are usually
detected in mid-latitudes, and the waves with amplitudes over 2 % are
mostly seen in high latitudes.
The influence of the conductive ionosphere on the propagation of AGWs is
significant at thermospheric altitudes. For further theoretical analysis of
the interaction between AGW and the wind one needs also to consider the
influence of the geomagnetic field on AGW properties (Kaladze et al., 2008;
Khantadze et al., 2010).
Implications for ground-based TID observations
AGW propagation and dissipation are highly dependent on the background wind
distribution. In the polar thermosphere, a large velocities of wind combined
with narrow AGW intrinsic frequency band lead to a significant modification
of the TID frequency spectrum observed from the ground. Due to the Doppler
effect the apparent frequency Ω measured by a stationary observer in
the ground frame equals
Ω=ω+kh⋅W=ω+|kh||W|cosθ,
where ω is the intrinsic frequency in the frame co-moving with the
wind, kh is the horizontal projection of the wave vector, W
is the wind velocity, and θ is the angle between the horizontal wave
vector and the wind velocity.
Since AGWs propagate towards the wind, the scalar product
kh⋅W is always negative and the apparent frequency is
lower than the intrinsic frequency. According to Eq. (), for AGWs
with dominant horizontal wavelengths from 500 to 600 km and average
wind velocities from 300 to 600 m s-1 typical for the polar
thermosphere, the apparent periods measured on the ground should vary within
the range from 30 min to 1 h. The actually measured TID periods between
30 min and 70 min show good correspondence with this estimation.
Since the wind velocity in the polar thermosphere almost never gets below
250 m s-1, the minimum period detected on the ground should be about
20 min. At perturbed geomagnetic conditions when the wind velocity exceeds
600 m s-1, the apparent TID periods can be as large as several hours,
falling in the large-scale TID range.
The dependence of AGW amplitude on the wind velocity.
Conclusions
The extensive statistical analysis of large volumes of DE2 data allowed us
to determine the following properties of AGWs in the polar thermosphere:
AGWs are systematically observed in the thermosphere at
250 to 400 km above the polar caps regardless of the geomagnetic
activity.
The intrinsic polar AGW frequency is close to the Brunt–Väisälä
frequency.
Polar AGWs systematically propagate towards the wind.
Polar AGW amplitudes do not depend on the altitude, but they almost linearly
depend on the wind velocity.
The observed polar AGW properties listed above contradict the generally
accepted hypothesis that AGWs are generated in the auroral regions. According
to this hypothesis, the energy for AGWs is provided by the precipitating
charged particles and the dissipation of polar current systems. This source
is most effective at the altitudes about 100–120 km, and should
generate a broadband spectrum of AGWs. The periods of about several tens of
minutes can be found in variations of the auroral electrojet and particle
precipitation intensity and are regarded as potential sources of polar waves
.
Our results suggest that the polar waves are primarily driven by the
thermospheric wind. One possible explanation for the listed polar AGW
properties is that the primary waves from different sources are filtered by
the non-uniformly moving medium due to the energy exchange between the waves
and the medium . The dominant intrinsic AGW frequency
close to the Brunt–Väisälä frequency can result from the evolution of
the AGW spectrum in the horizontal shear flow . Another
possible explanation is that the inhomogeneous wind itself may generate AGWs,
for example, due to the Kelvin-Helmholtz mechanism.
These dominant polar thermospheric waves are evident in the in situ
measurements, but are very difficult to identify from the ground. This is
caused by a strong spatial variability of the thermospheric wind pattern. The
apparent TID frequency spectrum measured from the ground is substantially
different from the intrinsic spectrum of polar AGWs due to the Doppler
effect. An introduction of a correction for the wind velocity brings
satellite and ground-based measurements to an agreement. The correction
implies accounting the Doppler shift according to Eq. (6) of the
measured frequency TID in comparison with the frequency of AGW, which is
determined from satellite measurements. Typical TID periods of 30 to 70 min
correspond to a Doppler-shifted Brunt–Väisälä frequency assuming
typical thermospheric wind velocities.
Since the pattern of the polar thermospheric winds are mostly tied to the geomagnetic frame, this
should yield interesting observational consequences. The TIDs measured from the
ground should manifest some effects, caused by the diurnal rotation of the
Earth. In particular, both the amplitude and the period of TIDs should be
maximal when the transpolar thermospheric wind current crosses the instrument's
field of view.