Observations of electric fields associated with internal gravity waves

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114,, doi: /2008ja013733, 2009 Observations of electric fields associated with internal gravity waves Roger H. Varney, 1 Michael C. Kelley, 1 and Erhan Kudeki 2 Received 9 September 2008; revised 19 November 2008; accepted 1 December 2008; published 7 February [1] At the Jicamarca Radio Observatory, the vertical drift component yields a very accurate measure of the eastward electric field. Occasionally, this drift component displays a downward phase progression, evidence for a relationship to a gravity wave. We examined the Jicamarca database for events of this type and made an attempt to determine the properties of the associated waves. The only measurables we have are the amplitudes, the frequency in the Earth-fixed frame, and the vertical wavelength. In order to avoid shorting by the current along magnetic field lines, we argue that the propagation must be close to pure zonal. We then use measurements or models of the zonal plasma drift and argue that the zonal wind should be in the same direction and about 15% higher. Using this estimate, we then determine the frequency in the wind frame by solving the dispersion relation for gravity waves and the Doppler-shift equation simultaneously. Typical values for the horizontal wavelength, vertical wavelength, and period in the wind frame are 600 km, 350 km, and 25 min, respectively. The typical gravity wave-induced vertical drift perpendicular to B in these events is a few meters per second. This is marginal at best for seeding the Rayleigh-Taylor instability. However, larger-amplitude events may be masked by the development of the plumes themselves. All but two events found thus far occurred at night but the daytime cases are fascinating since the E region is expected to short out such fields. Citation: Varney, R. H., M. C. Kelley, and E. Kudeki (2009), Observations of electric fields associated with internal gravity waves, J. Geophys. Res., 114,, doi: /2008ja Introduction [2] Evidence for the existence of internal waves in the atmosphere first came from studying the distortion of longlived visible meteor trails [Liller and Whipple, 1954] and from observations of traveling ionospheric disturbances (TIDs) using radio wave techniques. The theory for these waves was worked out by Hines [1960, 1963] and a large literature base detailing his work has been published in a monograph [Hines, 1974]. Interest in these waves remains high in the upper atmospheric and ionospheric communities due to the fact that such waves grow with height, creating large amplitudes. [3] The idea that such waves may become electrified was put forward by Klostermeyer [1978], who conjectured that such waves might be responsible for convective equatorial ionospheric storms, also known as equatorial spread F due to the appearance of ionosonde traces during such disturbances. He argued that perturbation winds can drive currents across the magnetic field via the expression J = s p (U B), where s p is the Pedersen conductivity and U is the neutral wind. If 1 School of Electrical and Computer Engineering, Cornell University, Ithaca, New York, USA. 2 School of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA. Copyright 2009 by the American Geophysical Union /09/2008JA these currents are not divergence-free, polarization electric fields will result. In turn, such fields would put the plasma in motion via the E B drift. The mechanism is illustrated in Figure 1, where the lines are parallel to the wave fronts and the magnetic field is into the paper. Because of the alternating directions of the winds, the currents they drive are not divergence-free, even in a spatially uniform plasma [Kelley, 1989]. The result is alternating sheets of charge with electric fields between that mirror the wavelength of the neutral disturbance. In the presence of a vertical plasma density gradient, the vertical component of the plasma drift will create rising and falling regions of plasma, creating a plasma structure that would display a horizontal wavelength identical to the gravity wave. [4] Kelley et al. [1981] explored this idea further, noting that the Klostermeyer mechanism can only yield vertical E B drifts less than or equal to the vertical wind component, whereas drifts in excess of 1000 m/s have been observed. They argued, however, that if a small initial disturbance was created on the bottomside of the equatorial F layer by the gravity wave wind field, it would be amplified by the Raleigh-Taylor plasma instability. This conjecture was verified by a two-dimensional numerical simulation of the effect of a gravity wave wind field on an initially undisturbed plasma [Huang and Kelley, 1996] and, to this day, such waves remain a candidate for the seeding of convective equatorial ionospheric storms. 1of6

2 field lines that dip toward lower altitudes with distance from the equator. [6] Although these ideas have been articulated for some time now, only two measurements of gravity wave-induced electric fields have been published. Gelinas et al. [2002] reported electric field measurements on a rocket that were made in conjunction with wind measurements using a trimethyl aluminum chemi-luminescent trail. The other example is that of Kudeki et al. [1999], who mentioned the indications of such fields in the Jicamarca data set we discuss next. Here we take a more detailed look at a body of Jicamarca data to study this important problem. Figure 1. Phase fronts for an upward propagating (group velocity) gravity wave with associated currents and polarization electric fields. [5] If the charges in Figure 1 are shorted out along the magnetic field lines, the electric fields are weakened and may even vanish. There are three ways in which this shorting can occur. The field lines in the equatorial F region eventually bend and enter the off-equatorial E region where a finite conductivity exists. During the day, the E region conductivity is large and we expect the gravity wave-driven electric fields to be small, but at night they may be supported. Second, if the k vector of the wave is somewhat out of the plane shown above, magnetic field lines can connect regions of positive and negative charge, which also shorts out the electric fields [Prakash and Pandy, 1980]. Finally, if the vertical wavelength is too short, the fields can be shorted out by currents on 2. Data Presentation [7] In Figure 2 we reproduce the Jicamarca data set first published by Kudeki et al. [1999]. The upper two plots are color-coded representations of the two components of the plasma ion drift perpendicular to the magnetic field, which is what the radar measures when oriented in this plane. [8] The perpendicular drift of the ions is given by the expression, V i? ¼ E B B 2 þ Mg B eb 2 þ k BT i rn B; neb2 where E and B are the electric and magnetic fields; n is the plasma density; T i is the ion temperature, which we take to be spatially uniform; g is the gravitational acceleration; and the other terms have their usual meanings. The second two terms on the right-hand side are orders of magnitude smaller than the first. Thus, measurement of the ion drift perpendicular to B is an unambiguous measure of the electric field. Figure 2. Color-coded ion drift velocities measured in the vertical (w) and horizontal (u) directions. Blue colors correspond to blue-shifted Doppler echoes associated with downward (westward) drifts, and red colors correspond to upward (eastward) drifts. 2of6

3 Figure 3. Stack plot of the vertical drift velocities at individual heights. The lowest height is 225 km, and each subsequent line is 15 km higher and has been shifted by 2 m/s upward. The red portions of the plots are points inferred by interpolation. The slanted black lines are identical and have been aligned with peaks in the data to illustrate the downward phase velocity. Line-of-sight drifts made at other incoherent scatter radar sites (ISR) are complicated by the component of the drift parallel to the magnetic field. In addition, since the spectrum of the ISR signal is extremely narrow in the plane perpendicular to B, the drift measurements at Jicamarca are very accurate, with error bars less than 1 m/s. [9] The fascinating aspect of Figure 2 is the parallel streaks in the color plots, which slant downward with time. These streaks are visible on both the vertical and zonal drift plots at around 23 LT. As is well known, a characteristic of gravity waves is that, for a source in the lower atmosphere, the phase velocity is downward when the group or energy velocity is upward [Hines, 1960; Kelley, 1989]. This behavior is further verified in Figure 3 in which the perturbation velocity is plotted at several heights and a straight line is drawn through several sets of maxima. [10] The fact that the perturbation velocities in this representation have this characteristic is very solid evidence that the electric fields are gravity wave induced. We have examined 151 plots of the vertical drift made at Jicamarca over a span of eleven years and have found and analyzed 22 examples similar to Figures 2 and 3. Other examples of striated lots were found but with vertical wavelengths too small to measure and may or may not be related to gravity waves. [11] We now use data to seek solutions to the dispersion relation for gravity waves as given by the relation, w 2 ¼ k 2 N 2 k 2 þ m 2 þ 1 4H 2 ; where N is the Brunt-Vaisala frequency, k is the horizontal wave number, m is the vertical wave number, and H is the scale height. In this equation, w is the wave frequency in the wind s frame of reference. This is related to the frequency w 0 in the Earth frame, which we can measure by the Doppler effect, as w ¼ w 0 þ k U: ð1þ ð2þ To determine w 0 and the wave amplitude, we performed a Fourier analysis of the vertical drift data at each height and averaged the results. The vertical drift at each height was Fourier-transformed using a Hamming window. The frequency estimate at each height was generated by interpolating over this transform and finding a local maximum. Missing vertical drift data points were estimated using interpolation with cubic splines. As an example, for the data in Figures 2 and 3, we found that w 0 = rad/s with a standard deviation of rad/s, and a vertical amplitude of w = m/s with a standard deviation of m/s. [12] To determine m, we constructed the cross-spectral density of pairs of adjacent heights, using Welch s averaged periodogram method. For each pair of heights, an estimated frequency range was constructed. Let the standard error in our frequency estimate be Err = t* p w ffiffiffi where w is the mean M frequency, M is the number of pairs of heights used, and t*is the t-statistic of the 97.5th percentile of the t distribution with M 1 degrees of freedom. The estimated frequency range for each pair of heights was the lower of the two frequency estimates minus the standard error to the higher of the frequency estimates plus the standard error. The argument of the peak value of the cross-spectral density in this frequency range was used as an estimate of the phase difference between the two heights. This phase difference can be translated into a wave number using m = f Here, f is the phase difference and the meters is the distance between adjacent range gates. The wave number estimates for each pair of heights were averaged together using a weighted average by error. The error estimates were the standard deviation of the argument of the cross-spectral density over the estimated frequency range. The average was computed using the following formula: m ¼ P M m i i¼1 s i PM : i¼1 1 s i The s parameters are the error estimates for each pair of heights. In this calculation, any negative (upward) values of m were excluded because we do not expect the gravity wave to have any negative values. For 29 September 1994 this process estimated the vertical wave number to be m = rad/m, which corresponds to a vertical wavelength of km. [13] The Brunt-Vaisala frequency and scale height were determined from MSIS to be rad/s and km, respectively. It is generally accepted that the zonal plasma drift is due to the F region dynamo which, in turn, corresponds to a zonal neutral wind that is 10 20% higher than the plasma velocity. We thus take the zonal component of the mean neutral wind, U = m/s, and set w, the vertical component of the mean neutral wind, equal to zero, which is the usual case for the neutral atmosphere. The mean meridional wind does not enter the calculation since we are restricting our study to waves that propagate near the magnetic east-west direction. For days that have zonal drift data, U was taken to be 15% higher than the average zonal drift over the time window. For days without zonal drift data, a model of the zonal drift from Fejer et al. [2005] was used instead. Equations (1) and (2) are thus two equations in two unknowns 3of6

4 Table 1. Properties of Observed Linear Gravity Waves a Date Period (min) w (m/s) l z (km) l x (km) Period (min) l x + (km) Period+ (min) 29 Sep ± ± Oct ± ± Apr ± ± May ± ± May ± ± Oct ± ± Oct ± ± * 10 Jul ± ± Jul ± ± Sep ± ± Sep ± ± Dec ± ± Jun ± ± * 3 Jun ± ± * 4 Jun ± ± * 11 Oct ± ± Nov ± ± Dec ± ± Apr ± ± Jun ± ± * 16 Jun ± ± Nov ± ± * a Summary of the properties of the 22 gravity waves we analyzed. The neutral wind estimates, derived using the model from Fejer et al. [2005], are denoted with an asterisk. Entries for horizontal wavelength and period that are blank correspond to events for which the second root was nonreal. U (m/s) that can be solved for k and w. The properties found for the waves studied are listed in Table 1. [14] In Figure 4 we plot the vertical component of the wave amplitude versus height for all 22 examples. Gravity waves are expected to grow exponentially with height to conserve energy, whereas these waves do not appear to grow as they rise. We argue that, by the time these waves reach the thermosphere, the viscosity limits their growth. [15] In Figure 5, each point indicates the horizontal (x axis) and the absolute value of the vertical (z axis) phase velocity for each event. The points seem to group around the following two sets of values: (V phasex, V phasez ) = (520 m/s, 160 m/s) and (V phasex, V phasez ) = (250 m/s, 100 m/s). For reference, at the average period of 41 min in the Earth-fixed frame, these correspond respectively to vertical wavelengths of 394 km and 246 km. [16] In Figures 6 and 7 we show the two examples on days 16 December 2003 and 1 June 2002 in which a clear downward phase velocity is apparent during the daytime. These events are especially remarkable because we expect the E region to short out these fields. The color plots for these two days are presented, along with line plots of the portion containing the gravity wave. Slanted lines have been superimposed on the line plots to highlight the downward phase progression. For both of these events, a meaningful measurement of the vertical wavelength was possible using the crossspectral density technique described above. This implies that the data show some correlation between altitudes with a downward phase progression. 3. Conclusions [17] In 15% of the days studied, detectable electric fields were created by gravity waves. At the equator, this can occur Figure 4. Peak amplitude of the vertical fluctuation (dw) as a function of height for the examples studied. Figure 5. Phase velocities plot. The red dots correspond to negative solutions (westward propagation) of the dispersion relation, and the blue dots correspond to positive (eastward propagation). 4of6

5 Figure 6. Vertical velocity measurements for 16 December (top) Parallel slants are seen near 17 LT. (bottom) A stack plot of the velocities with slanted black lines drawn through peaks to highlight the downward phase progression with time. In this plot, the lowest height is 225 km, and each subsequent height has been shifted 2 m/s upward. when the wave vector is nearly perpendicular to the magnetic meridian and the vertical wavelength is large. In these conditions, the fields are not shorted out by conduction along the magnetic field lines. [18] The wavelengths we determine in the course of the analysis are quite large, although the periods are quite reasonable for gravity waves observed at ionospheric heights as TIDs. On the other hand, large wavelengths are consistent with the notion that viscosity will damp waves with short scales. As a rule of thumb, the criterion that waves not be damped is [Gossard and Hook, 1975]: nk 2 N 2 w 3 < 1; where n is the kinematic viscosity. With the smallest wavelength waves we find in the grouped solutions of Figure 5 and with n = 106 m 2 /s, the ratio above is 0.6, suggesting that the waves are very close to being damped. This result is also consistent with the fact that the amplitudes we find as a function of height do not increase exponentially but only very slowly. [19] It is thought that gravity waves launched by weather sources have wavelengths less than a few hundred kms [Gossard and Hooke, 1975; S. L. Vadas, personal communication, 2006]. However, it has recently been shown that gravity waves with such wavelengths can be created in situ (S. L. Vadas and D. C. Fritts, personal communication, 2006). This is a promising development that we hope to explore soon. In addition, a new dispersion relation including viscosity in a more consistent manner has been published and will also be investigated [Vadas and Fritts, 2005]. In addition, the assumption of incompressible flow, which led to the relationship ku = mw, does not seem to hold for these data, suggesting that the linear approach may not be valid. [20] The daytime data were unexpected. Using an ionospheric conductivity model from the World Data Center for Geomagnetism, Kyoto ( ionocond/index.html), the F region-integrated conductivity during the event at noon on 1 June 2003 was calculated to be 59.8 S, and the E region conductivity integrated for both hemispheres was S. The corresponding attenuation for these conductivities is thus only 29.6%, which shows that the shorting effect may not be as important as thought. This finding may also shed light on observations of daytime equatorial spread F [e.g., Woodman et al., 1985]. [21] Huang and Kelley [1996] have shown that a wind field of 4.5 m/s is sufficient to induce vertical plasma drifts, which then form undulations susceptible to the generalized Rayleigh- Taylor instability, causing Convective Equatorial Ionospheric Storms/Equatorial Spread F. Our average vertical drift perturbations are 60% smaller than those simulated but could still result in bubble generation in two hours. More likely, we simply may not be able to detect larger-amplitude structures 5of6

6 Figure 7. Vertical velocity measurements for 1 June (top) Parallel slants are visible near noon. (bottom) A stack plot of the velocities with slanted black lines drawn through peaks to highlight the downward phase progression with time. In this plot, the lowest height is 300 km, and each subsequent height has been shifted 4 m/s upward. due to the generation of plumes. Periodic structures generated in this manner may contribute to seeding the longest wavelength component of bubble separations seen by satellite. Kudeki et al. [2007] have shown that seeding by the collisional shear instability near sunset is probably the most important source of seeding but gravity waves most likely play a secondary but not insignificant role in seeding. [22] Acknowledgments. Work at Cornell was sponsored by the Atmospheric Science Division of the National Science Foundation under grant ATM [23] Amitava Bhattacharjee thanks T. Ramkumar and another reviewer for their assistance in evaluating this paper. References Fejer, B. G., J. R. Souza, A. S. Santos, and A. E. Costa Pereira (2005), Climatology of F region zonal plasma drifts over Jicamarca, J. Geophys. Res., 110, A12310, doi: /2005ja Gelinas, L. J., M. C. Kelley, and M. F. Larsen (2002), Large-scale E region electric field structure due to gravity wave winds, J. Atmos. Sol. Terr. Phys., 64(12 14), Gossard, W. H., and E. E. Hook (1975), Waves in the Atmosphere, p. 223, Elsevier, Amsterdam. Hines, C. O. (1960), Internal gravity waves at ionospheric height, Can. J. Phys., 38, Hines, C. O. (1963), The upper atmosphere in motion, Q. J. R. Meterol. Soc., 89, Hines, C. O. (Ed.) (1974), The Upper Atmosphere in Motion, Geophys. Monogr. Ser., vol. 18, AGU, Washington, D. C. Huang, C.-S., and M. C. Kelley (1996), Nonlinear evolution of equatorial spread F: 1. On the role of plasma instabilities and spatial resonance associated with gravity wave seeding, J. Geophys. Res., 101, 283. Kelley, M. C. (1989), The Earth s Ionosphere: Plasma Physics and Electrodynamics, Int. Geophys. Ser., vol. 43, Academic, San Diego, Calif. Kelley, M. C., M. F. Larsen, C. A. LaHoz, and J. P. McClure (1981), Gravity wave initiation of equatorial spread F: A case study, J. Geophys. Res., 86, Klostermeyer, J. (1978), Nonlinear investigation of the spatial resonance effect in the nighttime equatorial F region, J. Geophys. Res., 83, Kudeki, E., S. Bhattacharyya, and R. F. Woodman (1999), A new approach in incoherent scatter F region E B drift measurements at Jicamarca, J. Geophys. Res., 104(A12), 28,145 28,162. Kudeki, E., A. Akgiray, M. Milla, J. L. Chau, and D. L. Hysell (2007), Equatorial spread-f initiation: Post-sunset vortex, thermospheric winds, gravity waves, J. Atmos. Sol. Terr. Phys., 69(17 18), Liller, W., and F. L. Whipple (1954), Upper atmospheric wind variations with altitude, special supplement, J. Atmos. Terr. Phys., 1, 112. Prakash, S., and R. Pandy (1980), On the production of large scale irregularities in the equatorial F region, Int. Symp. Equatorial Aeron., 6th, 3 7. Vadas, S. L., and D. C. Fritts (2005), Thermospheric responses to gravity waves: Influences of increasing viscosity and thermal diffusivity, J. Geophys. Res., 110, D15103, doi: /2004jd Woodman, R. F., J. E. Pingree, and W. E. Swartz (1985), Spread-F-like irregularities observed by the Jicamarca radar during the daytime, J. Atmos. Terr. Phys., 47, 867. M. C. Kelley, School of Electrical and Computer Engineering, Cornell University, 320 Rhodes Hall, Ithaca, NY 14853, USA. (mikek@ece.cornell. edu) E. Kudeki, School of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, 302 CSL Coordinated Science Laboratory, MC-228, 1308 West Main Street, Urbana, IL 61801, USA. (erhan@uiuc.edu) R. H. Varney, School of Electrical and Computer Engineering, Cornell University, 351 Rhodes Hall, Ithaca, NY 14853, USA. (rhv5@cornell.edu) 6of6