### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Model
- 3. Results
- 4. Summary
- Acknowledgments
- References

[1] The three-dimensional nonlinear evolution of equatorial ionospheric bubbles, using a realistic lower atmospheric gravity wave source, has been computed. It is found that three-dimensional finite parallel conductivity effects are important and lead to reduced gravity wave-induced electric fields, less depleted bubbles, and longer time scale bubble evolution compared to the two-dimensional case. It is concluded that nearly zonal propagating gravity waves are needed to excite equatorial ionospheric bubbles in the presence of zonal tidal winds. The simulated ionospheric bubble structures are consistent with recent observations in the SpreadFEx campaign.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Model
- 3. Results
- 4. Summary
- Acknowledgments
- References

[2] Spread-F bubbles, plasma plumes, and depletions frequently occur in the ionosphere and are a major problem of thermosphere-ionosphere coupling and space weather forecasting. Recently, several studies both experimental [*Fritts et al.*, 2008; *Rodrigues et al.*, 2008; *Tsunoda*, 2006; *Basu et al.*, 2007; *Hysell et al.*, 2005; *Nicolls and Kelley*, 2005; *Hei et al.*, 2005; *Otsuka et al.*, 2004; *Kil et al.*, 2004; *Straus et al.*, 2003; *Abdu et al.*, 2003; *Kelley et al.*, 2002; *Hocke and Tsuda*, 2001] and theoretical [*Huba et al.*, 2008; *Bernhardt*, 2007; *Keskinen et al.*, 2006; *Hysell and Kudeki*, 2004; *Tsunoda*, 2005; *Bhattacharyya*, 2004; *Keskinen et al.*, 2003; *Alam Kherani et al.*, 2004] have been devoted to the origin, evolution, and general characterization of equatorial ionospheric bubble structures.

[3] Gravity waves (GW) are thought to provide a neutral atmospheric seeding mechanism [*Kelley et al.*, 1981; *Hysell et al.*, 1990; *Huang and Kelley*, 1996] for equatorial ionospheric bubbles. This is approximately analogous to generating a small density hole at the bottom of a vertical column of water which then produces a rising bubble. *Singh et al.* [1997] used Atmospheric Explorer-E (AE-E) satellite data to show that wavelike horizontal winds were closely correlated with ionospheric plasma drift perturbations and wavelike ion density structures. They suggested that equatorial bubbles developed from these gravity wave structures. *McClure et al.* [1998], also using AE-E observations, demonstrated that plasma physics based seeding mechanisms could not fully account for the seasonal and longitudinal occurrence patterns implying that neutral atmospheric dynamics, e.g., gravity wave seeding, may be necessary. *Straus et al.* [2003], using Global Positioning System (GPS) radio occultation observations, showed that GPS scintillations were strongly correlated with thunderstorm activity in the African sector, implying that gravity waves from tropospheric convective activity can seed equatorial ionospheric bubbles. In addition, *Hocke and Tsuda* [2001], also using GPS occultation data, found a correlation between tropospheric convection, stratospheric gravity waves, and ionospheric irregularities in tropical zones. Recently, it has been reported, using observations gathered in the SpreadFEx campaign [*Fritts et al.*, 2008] in Brazil, that tidal winds, in addition to gravity wave structures, play an important role in the seeding and evolution of equatorial ionospheric bubble structures. Furthermore, observations from the recent SpreadFEx campaign have demonstrated [*Fritts et al.*, 2008] that a fully three-dimensional model for ionospheric bubble evolution with GW seeding and tidal winds is needed.

[4] However, previous studies have not considered the three-dimensional nonlinear evolution of equatorial ionospheric bubbles with gravity wave seeding. The three-dimensional bubble evolution must include finite parallel conductivity effects. It is known that the finite parallel conductivity, i.e., *σ*_{∥} ≠ 0, can reduce the growth rate of the Rayleigh-Taylor instability [*Keskinen et al.*, 2003; *Basu*, 2002] and lead to much longer time scale bubble evolution. Here, the parallel sign ∥ refers to the direction along the geomagnetic field. Finite parallel conductivity effects can also reduce the efficiency of gravity wave seeding of ionospheric bubbles.

[5] In this Letter we compute the three-dimensional nonlinear evolution, including finite parallel conductivity, of ionospheric bubbles with gravity wave seeding. The outline of this Letter is as follows. In section 2 we present the model used to compute the three dimensional evolution of ionospheric bubbles from gravity waves due to tropospheric convection. The realistic model of the GW source used to drive the ionospheric bubble model is also discussed. In section 3 we present results from this model and quantify the effects of finite parallel conductivity on formation of ionospheric bubbles by gravity wave seeding. Finally in section 4 we summarize our results.

### 2. Model

- Top of page
- Abstract
- 1. Introduction
- 2. Model
- 3. Results
- 4. Summary
- Acknowledgments
- References

[6] The evolution of equatorial ionospheric bubbles is computed using a 3D nonlinear plasma fluid model [*Keskinen et al.*, 2003]. This model contains the equations for the ionospheric plasma density, velocity, and current continuity

where *α* denotes ion or electron species, *n*_{α} the density, *m*_{α} the mass, *ν*_{in} the neutral collision frequency, **U** is the thermospheric wind, *ν*_{ie}, *ν*_{ei} is the ion-electron and electron-ion Coulomb collision frequency, **E** the electric field with **E**_{⊥} = −∇_{⊥}ϕ and **E**_{∥} = −∇_{∥}ϕ and ϕ the electrostatic potential, **V** is the velocity, **g** is gravity, and *ν*_{R} is the recombination rate. The electron gyrofrequency is taken to be large compared to the electron collision frequency and electron inertial effects have been ignored. Using equations (2) and (3), the total current **J** in equation (4) can be written as a sum of Pedersen, Hall, polarization, and parallel current contributions [*Keskinen et al.*, 2003]. Ion polarization currents are included to accurately treat the high altitude evolution of the bubble dynamics. Equations (1)–(4) are solved using finite-difference numerical techniques with the x,y,z directions corresponding to the zonal (westward), meridional (north–south), and vertical directions, respectively. Magnetic field line curvature effects are not included. Equation (1) is solved using multi-dimensional flux corrected transport [*Zalesak*, 1979] while equation (4) is solved using an conjugate gradient iterative solver [*Kershaw*, 1978]. The boundary conditions on the potential are Dirichlet at the lower boundary and Neumann ∂ϕ/∂*z* = 0 at the upper boundary in the vertical direction and periodic in the longitudinal direction. Since we consider bubble scale sizes greater than a few hundred meters (hundred kilometers) in the perpendicular (parallel) directions, electron and ion pressure effects are not included since the time scales for parallel and perpendicular diffusive effects, for the scale sizes simulated in the model, are much longer than the time scales of interest. The F-peak of the initial ionospheric density profile is taken to be located at z = 350 km in the equatorial plane and is consistent with recent observations in the SpreadFEx campaign [*Fritts et al.*, 2008]. The ionospheric model used is the parameterized ionospheric model [*Daniell et al.*, 1995]. A vertical drift of 15 m/sec is used to simulate the effects of pre-reversal electric field enhanced vertical drifts.

[7] To compute the thermospheric winds needed in equations (1)–(4), we take **U** = **U**_{0} + **u**′ [*Vadas*, 2007; *Vadas and Fritts*, 2005]. Here **U**_{0} is the mean wind component and **u**′ represents the GW component. The mean wind contribution is temporally fixed and taken to be of the form **U**_{0} = U_{0}(z). Recent observations in the SpreadFEx campaign [*Fritts et al.*, 2008] at the approximate local time, i.e., 21:00 LT, for equatorial ionospheric bubble generation have suggested that the mean zonal winds in the lower thermosphere are mainly composed of diurnal and semidiurnal tidal winds. The thermospheric gravity wave component is obtained by ray tracing of gravity waves from a realistic convection source [*Vadas*, 2007; *Vadas and Fritts*, 2005; *Fritts and Vadas*, 2008]. In the recent SpreadFEx campaign, tropospheric convection was determined to be the most likely source for thermospheric GW structures [*Vadas et al.*, 2009].

[8] The GW amplitudes, wavelengths, and frequencies at thermospheric altitudes, computed from the ray-trace model, are then imposed on the bottomside altitude region of the initial ionospheric model profile. The thermospheric wind in equations (1)–(4) is taken to be **U** = U_{0}(z) + **u**′ with:

with *α* = x, y, z. In equation (5), the GW wavenumbers and frequencies are denoted by k_{α} = 2*π*/*λ*_{α} and *ω*_{r} = 2*π*/*τ*_{r}. Here *λ*_{α} and *τ*_{r} is the GW wavelength and period, respectively. For gravity waves with vertical wavelengths *λ*_{z} < 4*π* H, with H the scale height, the GW dispersion relation can be written [*Vadas*, 2007; *Vadas and Fritts*, 2005] (*ω* − i*ν*k_{eq}^{2})(*ω* − iκk_{eq}^{2}) = *ζ*N^{2}. Here N^{2} = −g(dln*ρ*/dz + g/C_{s}^{2}), *ζ* = k_{x}^{2}k_{z}^{2}/(k_{x}^{2} + k_{y}^{2} + k_{z}^{2} + 1/4H^{2}), and k_{eq}^{2} = −(k_{x}^{2} + k_{y}^{2}) + 1/4 H^{2} + ik_{y}/H + k_{z}^{2}. Here N is the buoyancy frequency, C_{s} is the sound speed, g is gravity, and *ρ* is the neutral density. In this model GW spectral filtering is assumed to be due to viscosity and thermal diffusion. Ion drag, wave saturation, eddy viscosity, and wave breaking processes are neglected.

### 3. Results

- Top of page
- Abstract
- 1. Introduction
- 2. Model
- 3. Results
- 4. Summary
- Acknowledgments
- References

[9] Figure 1 shows the momentum flux spectrum from the GW source in the troposphere [*Vadas*, 2007]. The GW source is created from a vertical body force with full duration of 15 minutes, full diameter of 18 km, and full depth of 12 km. This yields a convective plume with a maximum vertical velocity of approximately 6 m/sec. The location of the tropospheric plume is located in Brazil at early evening local time, i.e., 18:00 LT, and is consistent with the recent SpreadFEx campaign.

[10] Then the GW momentum flux propagates upwards into the lower thermosphere. Figure 2 shows the temperature and mean zonal wind model used to compute the GW amplitudes, wavelengths, and frequencies in the lower thermosphere. The thermospheric temperature T = 1000 K and the mean zonal wind in the lower thermosphere is taken to be 100 m/sec. The profiles in Figure 2 are consistent with recent experimental observations from the SpreadFEx campaign [*Fritts et al.*, 2008; *Fritts and Vadas*, 2008].

[11] Figure 3 shows the computed GW horizontal and vertical wavelengths in the lower thermosphere, as generated by the tropospheric source, using the ray-trace model. In the lower thermosphere, the horizontal GW wavelengths are in the range of 90–1000 km with the vertical wavelengths approximately 110–400 km. In addition, Figure 3 also shows the GW periods in the lower thermosphere from the tropospheric plume which are approximately 20 min at the lowest altitudes and approximately 18 min at the higher altitudes. The model yields GW winds u′_{x}, *u*′_{y}, *u*′_{z} with amplitudes of approximately 35 m/sec, 90 m/sec, and 140 m/sec, respectively, in the lower thermosphere.

[12] Figure 4 displays the nonlinear bubble evolution in the equatorial plane at t = 164 min resulting from the tropospheric convective plume-generated GWs. This time corresponds to elapsed time after the GWs have propagated into the lower thermosphere and GW forcing has begun. A broad spectrum of GW wavelengths distributed from the minimum to maximum wavelengths in Figure 3 are used. As can be seen, one of the bubble structures has reached an altitude of approximately 550 km. The maximum depletion levels in the upper quadrant of Figure 4 is approximately 93%.

[13] It is found that the inclusion of three-dimensional finite parallel conductivity has three important effects. First, the gravity wave induced electric field is reduced. The gravity wave driven electric field **E**_{GW} is smaller than **u**′ × **B**, i.e., **E**_{GW} < **u**′ × B. For the two-dimensional case when the parallel conductivity *σ*_{y} = 0 we find that **E**_{GW} ≃ **u**′ × B. Second, the GW induced density perturbation, in the linear regime, in the bottomside F-region with finite parallel conductivity is smaller than in the two-dimensional case without parallel conductivity. For the 2D case we have found that the GW induced ion density perturbation was larger and approximately 99.2%. Third, the three-dimensional growth rate of the bubble structures with parallel conductivity is also smaller than the two-dimensional case with no parallel conductivity. For the initial conditions corresponding to Figure 4, the purely two-dimensional simulation XZ plane was fully developed at approximately t = 54 min after the onset of GW forcing. Several simulations were also made with reduced gravity wave amplitudes with the result that smaller initial ion density perturbations and longer time scale bubble evolution were found. It was found that large GW meridional scale sizes with *λ*_{y} ≥ 900 km are needed to excite ionospheric bubbles in the presence of zonal tidal winds. The physical mechanism for the smaller 3D growth rate (longer time scale) is that the parallel conductivity diverts a fraction of the perpendicular zonal Pedersen current, which is responsible for driving the Rayleigh-Taylor instability, into parallel electron current with a consequent reduction in the growth rate of the Rayleigh-Taylor instability [*Keskinen et al.*, 2003; *Basu*, 2002]. In addition, the overall bubble structure in Figure 4 is in agreement with radar observations conducted in the recent SpreadFEx campaign in Brazil [*Rodrigues et al.*, 2008; *Takahashi et al.*, 2009] under similar conditions.

### 4. Summary

- Top of page
- Abstract
- 1. Introduction
- 2. Model
- 3. Results
- 4. Summary
- Acknowledgments
- References

[14] Using numerical simulation techniques, we present the first study of the three-dimensional nonlinear evolution, including finite parallel conductivity, of equatorial ionospheric bubbles with gravity waves seeding. Gravity waves in the lower thermosphere are computed from a realistic tropospheric source and tidal wind effects are included. It is found that finite parallel conductivity effects are important and lead to reduced gravity wave induced electric fields, less depleted bubbles, and longer time scale bubble evolution. It is concluded that, for the cases studied, that nearly zonally propagating gravity waves, in the presence of zonal tidal winds, are needed for excitation of equatorial ionospheric bubbles. The general bubble structure from the simulation model is consistent with recent observations.

[15] In the future we hope to quantitatively determine the role of gravity wave amplitudes in seeding equatorial ionospheric bubbles including finite parallel conductivity effects.