Submitted to Annales Geophysicae, 2005

Possible ionospheric preconditioning by shear flow leading toequatorial spread F

D. L. Hysell

Earth and Atmospheric Science, Cornell University, Ithaca, New York

E. Kudeki

Electrical and Computer Engineering, University of Illinois, Urbana, Illinois

J. L. Chau

Radio Observatorio de Jicamarca, Instituto Geofısico del Peru, Lima

Abstract. Vertical shear in the zonal plasma drift speed is apparent in incoherentand coherent scatter radar observations of the bottomside F region ionospheremade at Jicamarca from about 1600–2200 LT. The relative importance of thefactors controlling the shear, which include competition between the E and Fregion dynamos as well as vertical currents driven in the E and F regions at the dipequator, is presently unknown. Bottom-type scattering layers arise in strata wherethe neutral and plasma drifts differ widely, and periodic structuring of irregularitieswithin the layers is telltale of intermediate-scale waves in the bottomside. Theseprecursor waves appear to be able to seed ionospheric interchange instabilitiesand initiate full-blown equatorial spread F. The seed or precursor waves maybe generated by a collisional shear instability. However, assessing the viabilityof shear instability requires measurements of the same parameters needed tounderstand shear flow quantitatively — thermospheric neutral wind and off-equatorial conductivity profiles.

Introduction

A new perspective on the stability of the postsunset equa-torial F region ionosphere is emerging from experimentsconducted at the Jicamarca Radio Observatory near Lima,Peru. The Jicamarca incoherent scatter radar has special-ized capabilities for observing both the ionospheric condi-tions that lead to equatorial spread F and for monitoring theplasma irregularities appearing subsequently. Being able toobserve incoherent scatter looking perpendicular to the geo-magnetic field, the 50 MHz radar can exploit the long corre-lation time of the signal to make very accurate measurementsof the line-of-sight plasma drift speed [Woodman, 1970].Using a dual beam configuration, unambiguous profiles ofthe plasma vector drift velocity in the plane perpendicularto B can also be obtained. The modularity of the Jicamarcaphased array antenna permits the application of aperture syn-

thesis imaging, which yields unambiguous two- or three-dimensional images of the spatial configuration of plasma ir-regularities producing field-aligned backscatter [Kudeki andSurucu, 1991; Woodman, 1997].

A striking characteristic of the bottomside F region iono-sphere extending from late afternoon to a few hours beforemidnight is shear flow, as first noted by Kudeki et al. [1981]and Tsunoda et al. [1981]. Plasma drifts westward in thebottomside F region while drifting eastward near and abovethe F peak, with the shear being strongest just after sun-set. Shear flow was studied theoretically by Haerendel et al.[1992] and Haerendel and Eccles [1992] and is a componentof the postsunset vortex described recently by Kudeki andBhattacharyya [1999]. Constraints imposed by low latitudecurrent closure in the vicinity of the solar terminator ulti-mately control shear flow, but the phenomenon is not well

1

: SHEAR FLOW 2

accounted for quantitatively.

In this manuscript, we review recent findings suggestingthat shear flow may destabilize the equatorial F region, pos-sibly preconditioning it for interchange instabilities respon-sible for spread F. If so, then monitoring plasma flows andanticipating shear instability may provide a means of fore-casting some instances of spread F. Since the thermosphericneutral wind speed both drives the plasma flow and influ-ences shear instability, monitoring neutral circulation willbe necessary. The C/NOFS satellite therefore has a crucialrole to play in this analysis. However, additional ground-based instrumentation will be required for measuring off-equatorial conductivity, which both influences shear flowand inhibits instability.

Examples of shear flow

Figure 1 shows examples of ionospheric structure and cir-culation from paired events observed in November or De-cember 2001, 2002, and 2003. The data were acquired us-ing refined experimental techniques introduced recently byKudeki et al. [1999]. The top panel shown for each eventrepresents relative backscatter power in grayscale logarith-mic format. Although the backscatter power has been scaledby the square of the range, it is not calibrated, is distorted tosome degree by magnetoionic effects, and is meant to servehere only as a rough estimate of the relative electron densityin undisturbed regions of the ionosphere. Regions of intensebackscatter signify coherent scatter from plasma irregulari-ties and are plotted using different amplitude scaling.

The middle panel of each event in Figure 1 shows ver-tical velocity derived from the average Doppler shift of Ji-camarca’s dual beams, which are directed approximately 3

east and west of magnetic zenith for this experiment. Thebottom panel shows zonal velocity derived from the differ-ence of the dual beam Doppler shifts. Both coherent andincoherent scatter data were utilized in generating the pan-els. All the data were derived from geomagnetically quietperiods.

The three examples on the left side of Figure 1 repre-sent events when ionospheric irregularities were confined tonarrow layers in the bottomside. These “bottom-type” lay-ers are nearly ubiquitous immediately after sunset duringequinox and December solstice in the Peruvian sector butdo not represent significant ionospheric disruptions and arenot associated with strong radio scintillations. In contrast,the three examples on the right portray occurrences of “full-blown” equatorial spread F. Forecasting topside spread Fevents like these on the basis of available data is a goal of thespace weather community. Forecast strategies have often in-volved applying a threshold condition to the intensity of the

Figure 2. Range time intensity (RTI) image of a topsidespread F event. Only a bottom-type layer was present priorto about 2100 LT.

prereversal enhancement of the vertical drift. Ascent drivesthe F layer to altitudes with reduced ion-neutral collision fre-quencies more susceptible to gravitational interchange insta-bility. Cursory examination of the data here alone suggestthat such a strategy should have merit but would be fallibleand could not be applied before about 1830 LT or only aboutan hour before the onset of instability. Discriminating be-tween plasma ascent leading to instability and ascent causedby instability would also be problematic.

Shear flow is evident in all of the events in Figure 1 andis most obvious after about 1930 LT when backscatter frombottom-type layers points to rapid westward motion imme-diately below regions of rapid eastward motion. It mightseem fortuitous that the bottom-type layers exist to providea radar target, since the valley region plasma is insufficientlydense to be monitored using incoherent scatter. However,Kudeki and Bhattacharyya [1999] pointed out that, assum-ing the thermospheric winds are eastward throughout theF region, the bottom-type layers occupy strata where theplasma drifts are strongly retrograde. Given that significanthorizontal density gradients are also present in these strataaround sunset due to photochemical and dynamical effects,the strata would be prone to horizontal wind-driven inter-change instabilities. They hypothesized that such instabil-ities are responsible for the bottom-type scattering layers,which are byproducts of retrograde drifts in the bottomsideand therefore not merely fortuitous.

The Kudeki and Bhattacharyya [1999] theory explainswhy the bottom-type layers exhibit no vertical development,as exemplified by the RTI map in Figure 2. Since the primaryplasma waves grow by advection, they always remain con-fined to the strata where the drifts are retrograde. In contrast,

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Figure 1. Six examples of ionospheric conditions around twilight. Each example shows the backscatter power (top panel),vertical plasma drift (middle panel), and zonal plasma drift (lower panel), plotted against the scales shown. Symbols plottedin the middle panel represent the vertical drift velocity at 450 km altitude for reference. The left and right columns portrayevents when topside spread F did not and did occur, respectively. Note that UT = LT + 5h.

: SHEAR FLOW 4

Figure 3. Radar image of plasma irregularities within thebottom-type layer seen in the previous figure. The irregu-larities are shown at the moment they first drifted westwardinto the radar illuminated volume.

interchange instabilities driven by gravity or a zonal electricfield must grow by convection, as did the two radar plumespassing over Jicamarca later in the same event. Another uni-versal characteristic of the layers is that they vanish at thefirst appearance of topside spread F irregularities and sel-dom reappear. This feature is at least partially explained bytheory, since retrograde plasma drifts arise ultimately fromthe demands of the current system near the solar terminatorand should cease by some local time. Topside plumes likelydisrupt the local circulation and break up any bottom-typelayers nearby.

Further evidence that wind-driven instability is at workin the bottomside was provided by Hysell et al. [2004], whoused aperture synthesis imaging techniques to analyze thestructure of the primary waves in bottom-type scattering lay-ers. They found that the primary waves were kilometricin scale and generally horizontally oriented and elongatedrather than vertically. The primary waves they observed ap-peared to grow by advection rather than convection, consis-tent with the wind driven interchange instability theory.

Moreover, Hysell et al. [2004] found that the primaryplasma waves in bottom-type layers sometimes cluster to-gether in regular, wavelike patches separated horizontallyby about 30 km. Clustering took place only in those eventswhen topside spread F occurred later. They associated the

clustering with a horizontal wave in the background plasmadensity that would present alternately stable and unstablehorizontal gradients for wind-driven interchange instability.Figure 3 shows a radar image derived from the bottom-typelayer in Figure 2 illustrating such clustering.

Finally, Hysell et al. [2004] concluded that the clusteredor patchy bottom-type layers were telltale of decakilometricwaves in the bottomside F region that could serve to precon-dition or seed the ionosphere for gravitational interchangeinstabilities (Rayleigh Taylor) to follow. This hypothesiswas supported by the fact that the intermediate-scale plasmairregularities that formed later in the spread F events sharedthe same decakilometric wavelength. This suggests a fore-cast strategy for spread F based on detecting clustering inbottom-type layers immediately after sunset. The strategy isbeing evaluated for its merits but in no event would be appli-cable before about 1930 LT when the layers first appear.

The ∼30 km wavelength of the undulations in the bottom-side F region inferred from the patchy bottom-type scatter-ers does not correspond to a characteristic scale length of theionospheric interchange instability. This is why it is seen aspreconditioning rather than just the early stages of instabil-ity. Preconditioning or seeding of the postsunset ionosphereis often attributed to gravity waves [Kelley et al., 1981]. Thishypothesis is difficult to test experimentally, however, sinceonly the effects of gravity waves and not the gravity wavesthemselves can be detected in the thermosphere using ISRs.Recently, Vadas and Fritts [2004] examined the issue theo-retically, showing that a spectrum of gravity waves launchedby mesoscale convection cells could survive wind shears andviscous and conductive damping and penetrate into the lowerthermosphere. However, the 30 km wavelength is at the ex-treme short wavelength edge of allowed wavelengths, andnothing in their theory would tend to favor it.

Meanwhile, the 30 km wavelength is roughly compara-ble to the vertical scale length of the plasma shear flow.Recently, Hysell and Kudeki [2004] examined the possibil-ity that shear flow may cause the bottomside F region tobecome unstable and produce the precursor waves inferredfrom radar imaging. If so, then shear flow itself could pre-condition the ionosphere for full-blown spread F. A quanti-tative understanding of the shear instability might thereforelead to a forecast strategy for spread F with the potentialfor advanced warning, given that shear develops early in theevening. Below, we review the causes of shear flow in theequatorial ionosphere, formulate the shear instability prob-lem, and compose an approximate but closed-form expres-sion for the instability growth rate.

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Origins of shear flow

That shear flow should exist in the bottomside equatorialF region was evident in the numerical modeling results ofHeelis et al. [1974], argued on theoretical grounds by Fejer[1981], and observed by Kudeki et al. [1981] and Tsunodaet al. [1981]. This shear can be understood, at least partly, interms of dynamo theory.

A model of the ionospheric dynamo was described byRichmond [1973] who assumed a dipole, equipotential modelfor the geomagnetic field and considered an individual fluxtube. Quasineutrality in a plasma imposes the constraint thatthe total current density be solenoidal (∇ · J = 0), where

J = σP (E⊥ + u × B)

+ σH b × (E⊥ + u × B) + σE‖ (1)

is the current density and σP , σH , and σ are the Pedersen,Hall, and direct conductivities, respectively. Also, E is theelectric field, u is the neutral wind velocity, and b is a unitvector parallel to the geomagnetic field B.

Application of the quasineutrality condition to the cur-rent density within a magnetic flux tube, neglect of horizon-tal variations in the fields and conductivities, and integrationof the result over the coordinate parallel to B while takingthe magnetic field lines to be equipotentials leads directlyto the following equation governing the vertical ionosphericelectric field:

Ep =

(

Eφhφ

∫

σHhqdq (2)

−

∫

(σP uφ + σHup) Bhφhqdq

+dI

dφ

)

/

(

hp

∫

σP

hφhq

hp

dq

)

written here using the orthogonal coordinate system (p, q, φ),where p is normal to the dipole magnetic field and in theplane containing the dipole moment, q is parallel to the fieldline, and φ is the magnetic longitude. The h factors arethe coordinate scale factors (see for example Hysell et al.[2004]. Also, dI/dφ represents the differential current den-sity passing through the flux tube in the p direction.

Equation (2) succinctly summarized the factors that influ-ence the vertical electric field in the equatorial ionosphere.These factors have been discussed individually in theoreti-cal and experimental contexts by a number of investigatorsincluding Anandarao et al. [1978]; Fejer [1981]; Stenning[1981]; Takeda and Maeda [1983]; Farley et al. [1986] andby Haerendel et al. [1992], Haerendel and Eccles [1992],and recently by Eccles [1998] in a more complete theo-retical treatment. They include 1) zonal electric fields on

flux tubes with significant Hall conductivity, as are respon-sible for driving the equatorial electrojet, 2) zonal winds onflux tubes with significant Pedersen conductivity, as drivethe E and F region dynamos, 3) vertical winds, a largelyunknown quantity, and 4) vertical boundary currents forcedfrom above or below the flux tube in question. In the bottom-side and valley regions around twilight, this last factor couldresult from the closure of the equatorial electrojet, whichmust turn partly vertical at the boundary of the evening ter-minator. It could also result from the F region dynamo op-erating in flux tubes near the F peak. The finite efficiency ofthe dynamo implies the existence of an upward vertical cur-rent there. The demands imposed by this current can onlybe supported at lower altitudes, where the conductivity issmaller, by a potentially large vertical electric field [Haeren-del et al., 1992; Haerendel and Eccles, 1992].

Which of these effects dominates in the postsunset bot-tomside? Haerendel et al. [1992] attribute most of the shearthere to the boundary current effect. They also consideredthe effect of zonal electric fields, which generate verticalpolarization electric fields on flux tubes with significant in-tegrated Hall conductivities in accordance with (2). Thismechanism was deemed to be effective mainly in the troughregion of the F1 layer and below. While Haerendel et al.[1992] did not discount the importance of the E region dy-namo in producing shears and westward F region drifts alto-gether, they restricted the domain of importance to the valleyregion. However, this appraisal was based on E region neu-tral wind estimates of only 25 m/s which we now recognizeto be a drastic underestimate, by a factor of five or more,in light of recent chemical release experiments [Larsen andOdom, 1997].

To summarize, although the various factors that can in-fluence shear flow in the ionosphere are individually under-stood, their relative importance is not. Resolution of theproblem evidently requires specification of both the neutralwind profile in the mesosphere, lower thermosphere, andthermosphere as well as the off-equatorial conductivity pro-files.

Shear-induced instability

Hysell and Kudeki [2004] recently addressed the stabilityof the F region ionosphere in a sheared flow with an eigen-value analysis. Keskinen et al. [1988] had already shown thatelectrostatic Kelvin Helmholtz instabilities are stabilized byion-neutral collisions in the auroral ionosphere, but that anal-ysis did not explore the collisional branch of the instabilityin the limit of steep plasma density gradients as are foundin the bottomside equatorial F region. Following Keskinenet al. [1988], Hysell and Kudeki [2004] neglected Hall and

: SHEAR FLOW 6

parallel currents but allowed for polarization currents in theirtwo-dimensional analysis:

J =ne

ΩiB

[

νin (E + u × B) +

(

∂

∂t+ v · ∇

)

E

]

(3)

The quasineutrality condition, together with the ion continu-ity equation, formed the basis of their model. Linearizationof the model was performed according to

n(x, z) = n(z) + n1(z)ei(kxx−ωt) (4)

φ(x, z) = φ(z) + φ1(z)ei(kxx−ωt) (5)

where terms with subscripts 0 and 1 represent zero- and first-order quantities, respectively, and where the Cartesian coor-dinates x, y, and z represented the eastward, northward, andupward directions at the magnetic equator. The linearizedmodel equations took the form:

(ω − kxv)n1 = −kx

B

dn

dzφ1 (6)

(ω + iνin − kxv)

[

d

dz

(

ndφ1

dz

)

− nk2xφ1

]

= −indνin

dz

dφ1

dz− kx

d

dz

(

ndvdz

)

φ1

+id

dz(Bνin(u − v)n1) (7)

where ω is the complex frequency and serves as the eigen-value, kx is the assumed horizontal wavenumber, v is thebackground horizontal plasma flow speed arising from gra-dients in the zero-order electrostatic potential, and νin is theion-neutral collision frequency.

Combined, the model equations constitute an eigenvalueproblem describing the perturbed potential φ1(z) in an inho-mogeneous, magnetized, two-dimensional plasma undergo-ing shear flow. This problem was solved computationally forequilibrium velocity, collision frequency, and density pro-files specified by:

v(z) = VTanh(z/L)

νin(z) = ν − ν1Tanh(z/L)

n(z) = Nuν/νin(z)

u − v(z)

and shown to yield rapidly growing solutions even in thecollisional regime (νin À |ω|). Those results are reproducedhere in Figure 4, which shows how the instability growth rateincreases with increments in ν1 and the increasingly steepnumber density profile that accompanies them.

An approximate, closed-form expression for the growthrate highlighting its dependence on background ionospheric

0.2 0.4 0.6 0.8kL

0.05

0.1

0.15

0.2

0.25Γ

1.0

1.25

0.75

Figure 4. Normalized growth rate γ (scaled to V/L) versusnormalized wavenumber kL given u = 2 and ν = 2 for threedifferent values of ν1. The points represent (9) evaluated atthe value of kx indicated and with kz = 1.25 (see text).

parameters is derived below. In our analysis, we focus onthe collisional branch of the instability thought to operate inthe bottomside equatorial F region by applying the limit νin

→ ∞ in (6) and (7), leading to:

d

dz

(

νinndφ1

dz

)

− νinnk2xφ1

= −kx

d

dz

(

νinu − v

ω − kxv

dn

dzφ1

)

We next multiply the equation by φ∗1 and integrate over alti-

tudes where the perturbed potential exists:

−

∫

dz νinn

(

|φ′1|

2 + k2x|φ1|

2)

= kx

∫

dz νinu − v

ω − kxvn

′φ1φ∗1′ (8)

where the prime notation refers to differentiation with re-spect to z and where integration by parts has been employed.Since the left side of (8) is real, the frequency ω = ωr +iγ can only be complex valued if the eigenfunction φ1 isalso somewhere complex. This is a necessary conditionfor wave growth and affirms the conjecture of Hysell andKudeki [2004] that the asymmetric flow pattern arising fromthe complex eigenfunction is a crucial feature of the colli-sional shear instability. Complex eigenfunctions guaranteethat the wavefronts (surfaces of constant phase) that formand the convection that follows them are neither strictly ver-tical nor horizontal, either one of these geometries tendingto be stable.

The real and imaginary parts of (8) yield integral equa-tions for the wave frequency and growth rate that depend

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on the shape of the eigenfunction that are no easier to eval-uate than was the original eigenvalue problem. The insta-bility in question is inherently nonlocal and is sensitive tothe ionospheric velocity, number density, and collision fre-quency profiles. However, the numerical calculations of Hy-sell and Kudeki [2004] suggested that in the vicinity of theshear node, where v′′

vanishes and about which φ is local-ized, the complex potential can be approximated by φ(z) ≈φ exp(ikzz). Utilizing this approximation and neglectingωr − kxv by comparison to γ in this region, an expressionfor the growth rate γ can be derived from the real part of (8):

γ ≈kxkz

∫

dz νin(u − v)n′|φ1|

2

k2∫

dz νinn|φ1|2

=kxkz〈νin(u − v)n

′〉

k2〈νinn〉(9)

where the averaging is weighted by the norm of the poten-tial, a function that generally peaks about one scale heightbelow the shear node and extends for several scale heightsabove and below it. Note that the choice of kx affects themode shape and the associated value of kz so that the de-pendence of the growth rate on the horizontal wavenumberis not apparent from this analysis.

Given mode shapes and values for kz derived from a com-plete boundary value analysis, (9) gives growth rate esti-mates that are roughly consistent with the eigenvalues ofthe full model expressed by (6) and (7) (see points plottedin Figure 4). Furthermore, (9) accounts for the results ofa numerical shear instability simulation reported on by Hy-sell and Kudeki [2004], which produced growing waves withrelatively long e-folding times (∼50 min.) despite the pres-ence of a steep vertical density gradient and widely differingplasma and neutral drift speeds in the simulation. In thattwo-dimensional simulation, shear flow was induced withthe introduction of an ad hoc constant conductivity termmeant to represent electrical loading by an off-equatorial Eregion plasma. The effective E region conductivity shortedout the F region dynamo in the valley region but not in thevicinity of the F peak, the net result being vertical shear. Theadd hoc term would contribute significantly to the denomi-nator of (9), which represents the factors that dissipate po-larization charge, but not to the numerator, which representsfactors that accumulate polarization charge. The E regionloading both caused essential relative plasma-neutral driftsand shorted out the polarization electric fields driven by theinstability.

In view of the evident impact of off-equatorial effects onionospheric stability, we have generalized (9), rewriting it interms of a dipole magnetic coordinate system and flux-tube

integrated variables:

γ ≈κφκp〈

hφhq

hpνin(u − v)n

′〉

κ2φ〈

hphq

hφνinn〉 + κ2

p〈hφhq

hpνinn〉

(10)

where the horizontal lines represent averages over a mag-netic flux tube, the prime represents a derivative with re-spect to the p coordinate, and where the κ terms are constant,nondimensional wavenumbers related to the wavenumberthrough the appropriate scale factor, e.g. kφ = κφ/hφ.

In the absence of information regarding the mode shapeof the perturbed potential, we postulate that one may still use(9) or (10) to assess the stability of the ionosphere, assumingthat the two wavenumber components are comparable andreplacing the weighted average with a straight average overthe bottomside F region.

Discussion

New experimental capabilities at Jicamarca have focusedattention on shear flow in the postsunset bottomside F re-gion ionosphere and the possible role it plays in the vari-ability of equatorial spread F. While the existence of shearflow has been recognized for more than two decades, com-bined coherent and incoherent scatter observations presentlyallow us to locate the shear node and to assess the shearstrength quantitatively. Shear flow exists for a period ofseveral hours surrounding sunset and is most intense aftersunset at low bottomside altitudes approaching the valley re-gion. The scale length for the shear is measured in tens ofkilometers there.

Shear flow arises mainly from the competition betweenthe E and F region dynamos and from demands on the verti-cal boundary currents in the bottomside imposed from aboveby the imperfectly efficient F region dynamo and from be-low by interruptions in the equatorial electrojet around theevening terminator [Haerendel et al., 1992; Haerendel andEccles, 1992]. Assessing the relative importance of thesefactors quantitatively is impeded by a lack of neutral windprofile measurements in the equatorial thermosphere as wellas of off-equatorial E and valley region conductivities.

One consequence of vertical shear is the existence of re-gions where the zonal plasma flow is strongly retrograde,i.e., in the direction opposite the local neutral wind. Whenhorizontal conductivity gradients are also present in such aregion, wind-driven interchange instabilities and plasma ir-regularities results. This now appears to be the explanationfor bottom-type scattering layers, which occupy retrogradestrata and appear when the tilted postsunset F region sup-plies the necessary zonal conductivity gradient [Kudeki andBhattacharyya, 1999]. It should be noted that the existence

: SHEAR FLOW 8

of vigorous wind-driven interchange instabilities in the bot-tomside does not by itself imply that E region conductivityloading on the associated magnetic flux tubes is insignifi-cant. Hysell et al. [2004] recently showed that the relativelysmall wavelengths of the bottom-type plasma irregularities,combined with finite parallel conductivity, would allow theirregularities to grow even on flux tubes where the E regiondynamo is dominant.

On occasions when topside spread F occurs, the bottom-type layers seem to be organized in clusters separated byabout 30 km. We interpret this modulation as evidence ofdecakilometric undulations or waves in the bottomside F re-gion. The wind-driven instabilities would be stable and un-stable in the different phases of such waves. In several in-stances, the topside irregularities that followed also exhib-ited structuring with this characteristic scale size. The de-cakilometric waves therefore appear to serve as seed wavesfor full-blown spread F. The existence of seed waves is oftenpostulated to explain the rapid appearance and developmentof radar plumes and intense plasma irregularities shortly af-ter sunset in the equatorial ionosphere. Gravity waves prop-agating into the thermosphere may seed the ionosphere aswell but are not expected to preferentially excite waves atthe observed wavelength. The ∼30 km wavelengths is itselfunrelated to interchange instability, posing further questionsabout its origin. That the shear scale length is also measuredin tens of kilometers suggests a connection.

Beyond creating conditions for wind-driven instabilities,shear flow may itself affect the stability of the bottomside Fregion. Boundary value analyses by Guzdar et al. [1983],Huba and Lee [1983], and Satyanarayana et al. [1984] in-dicated that shear flow generally stabilizes ionospheric in-terchange instabilities. However, Fu et al. [1986], Ronchiet al. [1989], and Flaherty et al. [1999] challenged this ideaby pointing out the limitations of boundary value analysis,which is incomplete when applied to non-normal modelslike those describing sheared flows. The issue of shear flowstabilization remains contentious, and a number of recenttheoretical and computational studies continue to support theidea [Hassam, 1992; Sekar and Kelley, 1998; Chakrabartiand Lakhina, 2003].

However, by extending the work of Keskinen et al. [1988]to the equatorial zone, Hysell and Kudeki [2004] showedthat a collisional shear instability may exist in the postsun-set ionosphere and be responsible for the precursor waves.In the collisional limit, retrograde plasma motion rather thanshear per se drives the instability. However, it is not justa variant of the standard wind-driven interchange instabil-ity, since instability occurs when the neutral wind and thebackground density gradient are normal to one another. Theinstability is the collisional branch of electrostatic Kelvin

Helmholtz and is therefore aptly termed a collisional shearinstability. The instability is not damped by collisions anddoes not require a prereversal enhancement and the eleva-tion of the F layer to function. This may allow it to operateprior to the onset of gravitational interchange instabilities,which are stabilized by collisions, and thereby to serve as asource of seed waves.

An approximate linear growth rate expression for the col-lisional shear instability has been derived. The inherentlynonlocal nature of the instability prevents the derivation ofan exact expression, but the approximation reveals at leasthow the growth rate scales with background parameters.Retrograde plasma motion and a steep vertical plasma den-sity gradient in the retrograde stratum are conducive to wavegrowth. Large flux-tube integrated plasma conductivity sup-presses growth. Whether the former overcomes the latterdepends on the strength of the neutral wind, the cause ofretrograde drifts, and the off-equatorial conductivity distri-bution.

For example, if the boundary current condition is mainlyresponsible for retrograde drifts in the bottomside, then thebottomside flux tubes need not be heavily loaded by conduc-tivity in the off-equatorial E and valley regions, and shear in-stability could be robust. If shear flow is mainly induced bya strong E region dynamo controlling flux tubes in the bot-tomside, however, then the shear instability would likely bedamped. The existence of irregularities in the bottom-typelayers gives no clue about which scenario is operating, sincethey can exist in either case.

Thermospheric wind measurements made by the C/NOFSsatellite will be critical for quantifying the shear instabil-ity theory. In order to evaluate (10), information about theoff-equatorial conductivity distribution will also be required.This could be provided by a meridional chain of sounders, abistatic HF sounder link, or by satellite occultation experi-ments. The same information is required both to quantifythe causes of shear flow in the equatorial ionosphere and toevaluate the growth rate of the gravitational interchange in-stabilities responsible for spread F.

Acknowledgments. This work was supported by the NationalScience Foundation through cooperative agreement ATM-0432565to Cornell University and by NSF grant ATM-0225686 to CornellUniversity. Additional support was received from the Air Force Re-search Laboratory through award 03C0067. The Jicamarca RadioObservatory is operated by the Instituto Geofısico del Peru, Min-istry of Education, with support from the NSF cooperative agree-ments just mentioned. The help of the staff was much appreciated.

: SHEAR FLOW 9

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D. L. Hysell, Department of Earth and Atmo-spheric Sciences, Cornell University, Ithaca, NY 14853(daveh@geology.cornell.edu)

E. Kudeki, Department of Electrical and Computer En-gineering, University of Illinois, Urbana, Il 61801 (er-han@uiuc.edu)

J. L. Chau, Radio Observatorio de Jicamarca, InstitutoGeofısico del Peru, Lima 13, Peru

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