Secondary instability generated on the equatorial plasma bubbles wall due to an interaction with midnight brightness wave

Interaction between Equatorial Plasma Bubbles (EPBs) and midnight Brightness wave (MBW) was observed over Bom Jesus da Lapa (13.3° S, 43.5° W; Quasi-Dipole geomagnetic latitude of 14.1° S), using OI 630 nm all-sky images. On the night of December 22nd, 2019, an EPB was seen propagating eastward in its fossil stage until it interacted with an MBW. After the interaction, the west walls of EPBs generated secondary instabilities that can be associated with gradient drift instability (GDI) and/or Kelvin–Helmholtz instabilities (KHI). We suggest that the MBW contributed to generate a shear in the EPBs walls due to changes in the thermospheric dynamics, such as neutral wind in the F layer height. Furthermore, spectral analysis of the all-sky images suggests that GDI and/or KHI generated turbulence and helped to dissipate the EPBs.


Introduction
In the equatorial ionosphere, several geophysical phenomena occur; the main phenomena are called Equatorial plasma bubbles (EPBs).EPBs are frequently observed from September to April over South America.They typically drift eastward with speeds ranging from 50 to 200 m/s and a latitudinal dimension from hundreds to thousands of kilometers (e.g., Barros et al. 2018).Also, EPBs are plasma depletions generated by Rayleigh-Taylor instability in the equatorial ionosphere's bottom side (Abdu 2001).The gravitational force and density gradient are antiparallel in the F-layer bottom-side, resulting in Rayleigh-Taylor instability (Haerendel 1973;Kelley 2009).In addition, EPB generates scintillations on the electromagnetic signals that can reduce the accuracy of GNSS signals or even disable them in extreme cases resulting in effects on social life highly dependent on technology.Much research has been conducted in recent decades forecasting of EPBs to reduce the impact of these anomalies on society (Takahashi et al. 2016).
In the equatorial thermosphere, the neutral temperature tends to decrease along the night.However, on some days, the neutral temperature increases near midnight.This phenomenon in the neutral temperature is known as midnight temperature maximum (MTM) (e.g., Herrero et al. 1993;Figueiredo et al. 2017;Mesquita et al. 2018 and references therein).The MTM causes a large increase in neutral temperature during the summer solstice (DJF).In addition, it changes the direction of the meridional wind from equatorward to poleward (Herrero et al. 1993;Meriwether et al. 2011).As a result of the poleward wind, the F layer moves downward along the magnetic field lines, consequently, the intensity of the OI 630 nm emission increase (Link and Cogger 1988).Moreover, Akmaev et al. (2010) showed that the MTM typically leads the Midnight neutral Density Maximum (MDM), whereby the MDM occurs above the MTM at the same longitude or lagging eastward of the MTM at the same height.Finally, when the MTM is observed in all-sky images, it is called a midnight brightness wave (MBW), and it propagates poleward in both hemispheres (e.g., Colerico et al. 1996).
Despite EPB and MBW being equatorial phenomena that frequently happen in the ionosphere and thermosphere; however, their interaction is rare.In the literature, we find only a pre-printed (Figueiredo et al. 2020) and peer-reviewed papers (Hickey and Martinis 2020) about EPB and MBW interaction.Hickey and Martinis (2020) observed an event in that MBW modified the EPB depletion, and the EPB structure became brighter than the ambient.Based on numerical simulation by Krall et al. (2009), Hickey and Martinis (2020) suggest that a poleward meridional wind and a converging zonal wind generated by MBW/MTM can turn an EPB into a brightness structure.
This work aims to describe and discuss the interaction between EPBs and an MBW that generated secondary instabilities on the west walls EPBs over Bom Jesus da Lapa observatory, Brazil, using OI 630.0 nm airglow imaging.The following sections will provide details about the interaction and a possible explanation.

Instrumentation and methodology
In December 2019, the National Institute for Space Research (INPE) and the Federal Institute of Education, Science and Technology Baiano (IF Baiano) collaborated to build a new airglow observatory at Bom Jesus da Lapa (BJL) (Wrasse et al. 2021), located at 13.3° S, 43.5° W (Quasi-Dipole geomagnetic latitude of 14.1° S). Figure 1 shows the observatory's location, marked by a black circle in the center.The magnetic equator at 250 km altitude is shown as a black line, while red lines represent magnetic field lines and quasi-dipole latitudes.The all-sky imager at the BJL observatory measures airglow emissions from the mesosphere to the thermosphere.This observatory provides good coverage of the area under the Equatorial Ionization Anomaly (EIA) South crest, making it an ideal location for monitoring the dynamics of the ionosphere and thermosphere.
Fig. 1 The airglow observatory at Bom Jesus da Lapa, Brazil, is represented by a black dot in the center of the black circle.The black circle denotes the field of view of the all-sky imager for the OI 630 nm emission, which has a radius of 9°.The black line shows the magnetic equator at 250 km altitude, while the magnetic field lines and quasi-dipole latitudes are represented by the red lines The all-sky imager at the BJL observatory is a versatile instrument that can be used to measure a variety of airglow emissions.The imager has a 180° field of view fisheye lens, a 3-inch diameter interference filter, a telecentric lens system, and a 1024 × 1024 pixels array CCD camera.The imager measures the following airglow emissions: Hydroxyl (715-930 nm) with 15 s of image integration; OI 557.7 nm, O 2 , and OI 630.0 nm with 90 s of image integration.The imager is a valuable tool for studying the dynamics of the ionosphere and thermosphere.It can be used to track changes in airglow emissions over time, providing insights into the processes that are driving these changes.

Spectral analysis
We characterize the spectral properties of the secondary instability arising at EPB walls by computing the power spectrum of the relative intensity data from the unwarped images.Two different methods are described in this section.Consider a coordinate system in which the X direction corresponds to the West-East direction and the Y direction corresponds to the South-North direction.Let I(x, y, t) denote the intensity at position (x, y), at time t.The one-dimensional spatial Fourier transform of I along the Y direction for a fixed value of x can be written as where k y represents the wavenumber in the Y direction, i = √ −1 , and the (^) denotes a complex quantity.The power spectrum PS along the Y direction is given by Similar expressions for Eqs. ( 1) and (2) can be written for the Fourier transform of I and the power spectrum along the X direction, for fixed y and t.
Since the EPBs are generally not aligned with the Y direction in the unwarped images, Eq. ( 1) can be rewritten for an arbitrary line path s(t) as follows.Let I(s, t) be the intensity data along s at time t.The Fourier transform of I can be written as where N s represents the number of points along s, and k s is the wavenumber along s.Therefore, the power spectrum can be obtained by The development of secondary instabilities at the EPB wall can be analyzed with a spectrogram constructed by plotting PS(k s , t) as a function of both k s and t.Note that the path s(t) must be set to a straight line, parallel to an EPB and intersecting the EPB wall contour.Moreover, the path s(t) must be carefully defined for each image to ensure that s(t) "follows" the drift of the EPB wall at the same position relative to the wall contour.Since EPB walls can be tilted from the geographic meridian as they drift, the path s(t) will deviate from the pixel alignment of the airglow images.To maintain the spatial resolution along s(t) the same at different times, we carefully measure the length of s(t) and keep it constant within all unwarped images.Since each pixel in the unwarped images represent the same spatial scale (3 km), the length of the path s(t) will also represent a constant spatial scale for all images.Then, we divide s(t) into a set of equidistant points, and obtain the intensity I(s, t) at each point along s(t) by applying a bilinear interpolation.This ensures that the set of spatial scales and wavenumbers is the same for all images, even after the EPB wall becomes tilted due to the drift.
The power spectrum of the intensity images at the EPB walls can also be computed by taking the average of PS(x, k y , t) over x, around the wall contour.The x-averaged power spectrum PS x can be defined by where x i and x f represent the initial and final values of x over which the average is computed.The Fourier transforms of Eqs. ( 1) and (3) are computed using the fast Fourier transform (FFT) algorithm.The FFT and the bilinear interpolation algorithms employed in this paper are implemented on the GNU Octave program (Eaton 2012).

Results and discussion
On the night of December 22nd, 2019, Fig. 2 shows the original (panel I) and unwarped (panel II) (2024 × 2024 km 2 ) OI 630.0 nm relative intensity images taken at the BJL observatory.It is important to note that the geomagnetic conditions were quiet (Kp ≤ 3).Between 03:30 UT and 04:09 UT (Local time = UT − 3 h), we observed four EPBs, marked as B1, B2, B3, and B4, moving eastward in Fig. 2. In addition, the zonal drift speed of the EPB was 49 ± 5 m/s.The zonal drift speed was calculated using a 2-D Fourier Transform (Wrasse et al. 2007).Furthermore, EPBs after local midnight are normally called fossil plasmas bubbles.They are frequently used ( 4) (5) as background ionosphere motion tracers because they move with the ambient plasma (e.g., Sobral et al. 2009).
Moreover, secondary structures were generated on the west wall of EPB B3 and B4.At the same time, a bright region was observed propagating southwestward in the top images.Colerico et al. (1996) observed bright structures propagating southward over Arequipa, Peru, using an all-sky imager.They called this phenomenon a midnight brightness wave (MBW).The MBW is an optical phenomenon generated by the downward movement of the F layer due to the midnight temperature maximum.The MTM increases the neutral temperature and changes the neutral wind direction near midnight.This has been observed by other researchers, such as Herrero et al. (1993), Meriwether et al. (2011), andFigueiredo et al. (2017).Using the zonal and meridional keograms of the images, we calculated the speed of the meridional movement of the MBW, which is 166 ± 19 m/s.An animation with OI 630.0 nm images of Fig. 2 is presented in Additional file 1: Movie S1.
Hickey and Martinis (2020) observed an interesting interaction between EPB and MBW.The authors observed a bright zone on the EPB walls.They suggested that bright intensification in the EPB walls is due to changes in the neutral wind caused by the MBW.On the other hand, our present observation showed an MBW and an EPB interacting.We do not observe the brightness of the EPBs wall, but secondary instabilities on the west EPB wall.
Figure 2 shows the development of billows associated with secondary instability on the west wall of EPB B3 during the interaction between EPBs and an MBW.The first billow grows at 03:30 UT with 28 km wide and 324 km latitudinal length.At 03:48 UT, the second billow appears.At 04:09 UT, the EPB B3 starts to dissipate, but the billows still grow with 60 km wide and 412 km latitudinal length, i.e., increase the distance themselves.On the other hand, EPB B4 shows oscillatory characteristics on the west wall, but it does not develop to billows as EPB B3.We calculated the fluctuations distance on EPB B4 at 03:48 UT and found an oscillation with a length of ~ 139 km.
Regarding the secondary instability that appears on the west wall of EPB B3 and B4, Tsunoda (1983) suggested that the western wall is more favorable for the onset of wind-driven secondary instabilities because the nighttime thermospheric zonal neutral wind blows eastward in the opposite direction as the zonal plasma density gradient.However, Yokoyama et al. (2015) showed via a high-resolution plasma bubble model that a vertical shear of zonal plasma drift velocity at the bottom side of the F layer plays a key role in speeding instability growth at the west wall and causing EPBs east-west asymmetry.Also, it has been discussed that a shear instability mechanism plays a crucial role in seeding the EPBs (Hysell and Kudeki 2004;Hysell et al. 2005;Aveiro and Hysell 2010).Behnke and Harper (1973) and Harper (1973) observed that the MTM reversal the thermospheric meridional wind component, consequently, causes the drop in the F layer.Herrero et al. (1993) showed that a simple meridional wind abatement is all that is required for the F layer collapse to occur (e.g., see results of Figueiredo et al. (2017)).Based on our observations, we suggest that the plasma density descending along the magnetic field lines and EPB B3/B4 receding along the same lines interact and may generate secondary instabilities on the west wall of EPB.
Based on the secondary instabilities observed in the plasma bubbles, we can suggest two possibilities: gradient drift instability and/or Kelvin Helmholtz instabilities.Rathod et al. (2021) and references therein state that the F region is a transition region where the collision frequency is weak enough to allow GDI and KHI to grow.To grow the GDI, it is necessary for the E × B drift to have a component moving in the same direction as the plasma density gradient.On the other hand, KHI is hydrodynamics instability that is generated by the velocity shear interface.In the ionosphere, these plasma irregularities are important to produce turbulence.
We compute the power spectrum of the relative intensity along a line path (Eq.4) located on the west wall of EPBs B3 and B4, over the interval from 02:40:49 UT to 04:20:25 UT, which gives a sequence of 21 images.Figure 3a, b show the spectrograms of EPB B4 and B3 as a function of the wavenumber k and time t (a sequential number).Also, the energy is represented by a color scale.Figure 3a shows that most of the energy is contained in low-k modes.From 03:27:04 UT to 04:13:18 UT (corresponding to the interval [14,28] in the x-axis of Fig. 3a), a red patch marked by an arrow can be observed going from k ~ 0.008 to k ~ 0.005.This means that energy is transferring from high-k to low-k, which is related to the growth of structures on the west wall of EPB B4.
The spectrogram of Fig. 3b also shows that most of the energy is contained in low-k modes.However, the dark red area clearly spreads toward higher-k as the time increases, which suggests that energy is being transferred to higher wavenumbers.This might be related to the instability breaking observed in the west wall of EPB B3.Whereby, we suggest that the MTM/MBW passage increases the collisional frequency in low altitudes and low geomagnetic latitudes in the F region due to the increases in the neutral density.Furthermore, the MBW reversed the neutral wind from its original direction (equatorward) to poleward, causing, the F layer abatement from high to low altitude along the magnetic field lines.This result enhances the local vertical electron density gradient, generating a vertical gradient polarization electric field.So, this environment might be enough to trigger the GDI on the west wall of EPB B4.Conversely, it might be possible that EPB B3 developed the KHI due to the higher background velocity shear between MBW and EPB B3 along the magnetic field lines.Huba et al. (1988) performed a numerical simulation to investigate the KHI both with and without magnetic-ionospheric coupling in high latitudes.The authors observed that ionospheric coupling (collisional effects) influences the KHI such as slowing its expansion and suppressing vortex formation.Keskinen et al. (1988) performed (3) lead to nonlinear structures; (4) generate small scale turbulence.Therefore, in summary, the KHI can develop vortices that can break and spread energy towards smaller scales, leading to an energy cascade and turbulence (Huba et al. 1988;Keskinen et al. 1988).
Next, we analyze the ionospheric turbulence caused by the breakdown of KHI vortices on the west wall of EPB B3.We compute the x-averaged power spectrum PS x (Eq.5) of the intensity data within the black rectangles displayed in Fig. 4a, b, for the unwarped images at 03:51:58 UT and 04:13:18 UT, respectively.The rectangles cover the billows structures seen at the west walls of B3. Figure 4c displays PS x of the selected intensity data in Fig. 4a.The black arrow points to the characteristic scale of the KHI vortices in the north-south direction.The power spectrum follows a power-law PS x (k y ) ~ k y −n with a spectral index of n = 2.68 ± 0.22, computed within the interval [0.005, 0.02].This spectral index is close to values from observational (e.g., Chian et al. 2018) and numerical (e.g., Huba et al. 1988) studies.Figure 4d shows the PS x of the selected region in Fig. 4b.In this figure, the spectral index is equal to − 1.76, indicating that the spectral index has decreased over time, which can result in more energy transfer from the KHI scale toward smaller scales, due to KHI wave breaking.Rino et al. (2018Rino et al. ( , 2023) ) studied how the spectral density of EPBs varies over time.They reported that the spectral density rises in the growth phase of EPBs and falls in the decay phase, changing the power-law exponent from ~ 3 to ~ 2. They also suggested that the background plasma turbulence may influence the spectral density of EPBs.Our observations support their findings, as shown in Fig. 4c, d.The spectral density of EPB B3 follows a powerlaw distribution with an exponent decreasing from 2.68 to 1.76, which agrees with the simulation results of Rino et al. (2023, Fig. 6).
Regarding Fig. 4d, we find that PS(k y ) ~ k −n y with n = 1.76 ± 0.7 at 04:13 UT.Huba et al. (1988) applied the power spectrum to their numerical simulations results of the KHI with a collisional regime and found that PS(k x ) = k −n x with n = 1.9 ± 0.5 and PS(k y ) = k −n y with n = 1.6 ± 0.5 at a late time (t = 56 s.).In addition, according to Basu et al. (1988), the PS(k y ) = k −n y with n within the interval [1.7, 2] in the direction of velocity shear.Our present results agree with Huba et al. (1988) and Basu et al. (1988).Huba et al. (1988) explained that the suppression of large-scale vortices in the ionosphere (i.e., in the collisional regime) is thought to be the cause of the "shallowing" of the spectrum.Also, the authors point out that in the long-wavelength regime, i.e., at small wavenumber k, the large-scale vortices contain significant power.If these vortices do not emerge (as they do in the collisional regime), the power at small k decreases, resulting in a reduced power spectrum.Therefore, our observational results agree with the numerical simulation of KHI made by Huba et al. (1988).In addition, as observed in Figs. 3 and 4, EPB B3 and B4 dissipate faster than EPB B1 and B2.Therefore, the KHI generated on the west EPB B3 can lead to the development of vortices that can break and spread energy towards smaller scales, leading to an energy cascade and turbulence.
A limitation of our study is the lack of in situ plasma density gradient and neutral wind data.These data could provide further insights into the interaction between EPB and MBW, triggering KHI and GDI to advance the discussions.Therefore, we recommend further observations with multi-instruments and numerical simulations to investigate this kind of interaction and its effect on generating secondary instabilities on the EPB wall.

Summary
On the night of December 22nd, 2019, at the Bom Jesus da Lapa airglow observatory in Brazil, we observed an interesting interaction between the Equatorial Plasma Bubbles (EPBs) and a Midnight Brightness Wave (MBW).The EPBs were moving eastward in an apparent fossil stage until they interacted with an MBW.This interaction triggered Kelvin Helmholtz Instability (KHI) and/or Gradient Drift Instability (GDI) on the west walls of the EPBs.Contrary to previous literature, we found that the MBW did not enrich the EPB wall with plasma.Instead, it generated vortices that broke and dispersed energy to smaller scales.The process of KHI and GDI leads to an energy cascade and turbulence generating an environment to the EPBs dissipate.
In this paper, the spectral properties of the turbulence induced by the breakdown of KHI vortices were characterized.The power spectra computed from intensity images displayed power laws with spectral slopes varying from − 2.68 to − 1.76.The latter value is similar to the − 5/3 spectral index obtained in fluid experiments and the Kolmogorov 1941 theory of hydrodynamic turbulence (Frisch 1995).The − 5/3 slope of power spectra has been also widely reported from observational data in turbulent plasmas, for example, the solar wind (Matthaeus et al. 1982;Leamon et al. 1998;Bruno and Carbone 2005;Narita et al. 2006;Chian and Miranda 2009;Miranda et al. 2021).In magnetohydrodynamic (MHD) turbulence, the slope − 3/2 has been reported in agreement with the Iroshnikov-Kraichnan theory of MHD turbulence (Biskamp and Schwarz 2001).However, the mechanisms leading to these spectral slopes can be very different in the ionosphere.For example, Chian et al. (2018) showed that the spectral slope of ionospheric turbulence in the presence of EPBs can be close to − 2.3 in the bottomside F-region, and close to − 5/3 in the peak F-region.A careful analysis of the spectral slopes obtained in this paper will be the topic of a future work.

Fig. 2
Fig. 2 OI 630 nm original (I) and unwarped (II) images taken from Bom Jesus da Lapa observatory on the night of December 22nd, 2019, between 03:30 and 04:09 UT (LT = UT − 3 h) show the interaction between EPB and MBW.The interaction generated GDI and/or KHI on the west wall of the EPB B3 and oscillation structures on EPB B4.The letters and numbers, B1, B2, B3, and B4 are the EPB's identification

Fig. 3 a
Fig. 3 a Spectrogram obtained from the sequence of 29 "slices" at EPB B4.A white arrow indicates the spectral signature of the oscillations due to the growth of the GDI.b Spectrogram obtained from the sequence of "slices" at EPB B3.The white arrow indicates the spectral signature of the energy cascade due to turbulence generation

Fig. 4 a
Fig. 4 a Unwarped image taken at 03:51:58 UT.The black rectangle indicates the selected region of the EPB B3 for spectrum analysis.b Unwarped image taken at 04:13:18 UT, and selected region for spectrum analysis.c Power spectrum PS x (k y ) for the selected region of the EPB B3 at 03:51:58 UT. d Power spectrum PS x (k y ) for the selected region of the EPB B3 at 04:13:18 UT.Black arrows indicate the north-south characteristic scale of the KHI vortices.Black continuous lines indicate the spectral slope The airglow images data used in this study were provided by Embrace/INPE (http:// www2.inpe.br/ clima espac ial/ portal/ linea rimag evideo/).Thanks to the Brazilian Ministry of Science, Technology and Innovation (MCTI) and the Brazilian Space Agency (AEB) who supported the present work under the grants PO 20VB.0009.The authors would like to thank the IF Baiano for supporting and maintaining the Bom Jesus da Lapa airglow observatory.C.A.O.B. Figueiredo thanks to the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) under the process 2018/09066-8 and 2019/22548-4, and Fundação de Apoio à Pesquisa do Estado da Paraíba.R. A. Miranda acknowledges financial support from FAP DF (Brazil) under award number 180/2020, DPI/DPG/UnB, and CNPq (Brazil) under award numbers 407493/2022-0 and 407341/2022-6.The present work was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), under the processes 314972/2020-0, 301670/2023-4, 303871/2023-7.