Single-spacecraft detection of rolled-up Kelvin-Helmholtz vortices at the flank magnetopause

Authors


Abstract

[1] Recent numerical simulations suggest that as soon as the Kelvin-Helmholtz instability (KHI) has grown nonlinearly to form a highly rolled-up vortex, plasma mixing is inevitably achieved within the vortex. Identification of rolled-up vortices by in situ measurements is therefore an important task as a step to establish the mechanism by which solar wind plasmas enter the magnetosphere and to understand conditions under which the vortices form. In the present study we show that the rolled-up vortices are detectable even from single-spacecraft measurements. Numerical simulations of the KHI indicate that in the rolled-up vortex the tailward speed of a fraction of low-density, magnetospheric plasmas exceeds that of the magnetosheath flow. This feature appears only after a vortex is rolled up and thus can be used as a marker of roll-up. This signature was indeed found in the Cluster multispacecraft measurements of the rolled-up vortices at the flank magnetopause. By use of this marker, we have searched for events consistent with the roll-up from Geotail observations showing quasi-periodic plasma and field fluctuations in the flank low-latitude boundary layer (LLBL) under northward interplanetary magnetic field (IMF), presumably associated with KH waves. The survey shows that such rolled-up events do occur on both dawn and dusk flanks and are not rare for northward IMF conditions. In addition, in all the rolled-up cases, magnetosheath-like ions are detected on the magnetospheric side of the boundary. These findings indicate that the KHI plays a nonnegligible role in the formation of the flank LLBL under northward IMF.

1. Introduction

[2] It is now well established that the low-latitude boundary layer (LLBL), characterized by a mixture of magnetosheath and magnetospheric plasmas [Sckopke et al., 1981], becomes denser and thicker during northward interplanetary magnetic field (IMF) periods [e.g., Mitchell et al., 1987; Hasegawa et al., 2004a]. Magnetosheath-like plasma, similar to what is usually seen in the LLBL, occasionally extends to the midnight sector of the plasma sheet [Terasawa et al., 1997; Fujimoto et al., 1998] so that such a region is called the cold-dense plasma sheet. However, magnetic reconnection at the low-latitude magnetopause occurs much less efficiently under northward IMF conditions. It thus remains an outstanding problem to determine for such unfavorable conditions how and from which part of the boundary, solar wind plasmas enter the magnetosphere efficiently.

[3] While double poleward-of-the-cusp reconnection is a candidate mechanism by which the solar wind plasma can be captured onto closed portions of the magnetosphere under northward IMF [Song and Russell, 1992; Onsager et al., 2001; Lavraud et al., 2005], the Kelvin-Helmholtz instability (KHI) that can grow along the flank magnetopause, across which a significant velocity shear exists, has often been suggested as an alternative [e.g., Fujimoto and Terasawa, 1994]. For example, Nakamura et al. [2004] and Matsumoto and Hoshino [2004, 2006] have shown, on the basis of numerical simulations, that secondary instabilities induced in a rolled-up vortex that appears in the nonlinear stage of the KHI facilitate transport of plasma. Other simulation studies, conversely, show that reconnection can be triggered rather efficiently as a consequence of the KHI development [e.g., Nykyri and Otto, 2001; Nakamura and Fujimoto, 2005a; Nakamura et al., 2006], leading to the creation of reconnected field lines through which solar wind plasmas can be transferred to the magnetosphere.

[4] The key to these KHI-associated transport mechanisms is the creation of a rolled-up vortex through the vigorous growth of the KHI. Most of the theoretical works cited above suggest that significant transport of plasma is established only when the KHI has grown to the nonlinear stage, forming a fully rolled-up vortex. Recently, Hasegawa et al. [2004b] demonstrated that such rolled-up vortices do form at the dusk-flank magnetopause, on the basis of coordinated multipoint measurements by the Cluster spacecraft during a long period of northward IMF. They also reported the coexistence of cool magnetosheath and hot magnetospheric ions in the vicinity of the vortices, that is, evidence of plasma transport across the magnetopause, although its direct connection with the vortices is not fully understood yet. Their study undoubtedly suggests the importance of the KHI in the formation of the flank LLBL under northward IMF, but since it is not known whether or not the roll-up of vortices is a common aspect of the flank magnetosphere, it has yet to be concluded whether the KHI is sufficient for producing the observed LLBL or it is operating only as a secondary transport mechanism. Cluster has a polar orbit so it encounters the equatorial portion of the flank magnetosphere only for limited time intervals. Furthermore, its apogee is about 20 RE so that Cluster does not cover sufficiently large downtail (x < −10 RE) distances at the flanks, whereas signatures associated with the KHI have often been found at x ∼−15 RE or beyond [e.g., Kivelson and Chen, 1995; Fujimoto et al., 1998; Fairfield et al., 2000]. Therefore the Cluster orbit is not optimal for surveying the occurrence frequency of the roll-up of KH vortices, although its multispacecraft capability allows for unambiguous identification of this phenomenon.

[5] Interestingly, Takagi et al. [2006] have found, on the basis of three-dimensional (3-D) MHD simulations of the KHI in which the mode can grow only at the low-latitude interface, that the tailward speed of a fraction of low-density, magnetospheric plasmas significantly exceeds that of the dense magnetosheath flow within a highly rolled-up KH vortex. This tailward acceleration of low-density plasmas occurs in 2-D situations as well, and its mechanism was described by Nakamura et al. [2004]: at a certain radial distance from the center of a rolled-up vortex, a tenuous plasma must rotate faster than a denser plasma for the force balance in the radial direction to be maintained, i.e., for the two plasmas to exert an equal centrifugal force. This feature is what should appear when a rolled-up vortex forms in a layer across which a significant density gradient is present, as is the case at the magnetopause, and simulations performed under various conditions indeed show that it often (but not always) appears in a fully rolled-up vortex. Figure 1a shows some of simulation results by Takagi et al. [2006], showing the relationship between the structure of the KH vortex and a scatter plot of the sunward component of the flow velocity, Vx, versus density, constructed using data obtained from a simulation domain surrounding the KH vortex, on the assumption that a spacecraft can equally observe that domain. The simulations were run for various magnetosheath field orientations (θ), with other parameters kept constant: the magnetosheath to plasma sheet density ratio of 4, total velocity jump across the shear layer of 2.4 times the magnetosheath Alfvèn speed, magnetosheath β of 3.6, plasma sheet β of infinity (no magnetic field in the plasma sheet), and plasma sheet thickness of 1.3 times the fastest-growing KH wavelength. The results shown in Figure 1a are obtained immediately after saturation. It is seen that in the rolled-up case (top panels), a considerable fraction of low-density (n < 0.6) plasmas has a tailward speed significantly higher than the magnetosheath plasma, represented by Vx = −1 and n = 1 in the figure. On the other hand, the bottom two panels show that no such high-speed feature is found when the KH vortex is not, or only weakly, rolled up. As seen in Figure 1b, the high-speed flows occur in the magnetosheath-side part of the rolled-up vortex and mainly in the most-unstable, low-latitude part. Their study has also shown that when the magnetosheath magnetic field is dominantly northward, the roll-up of the vortices can be achieved as long as the thickness of the plasma sheet is comparable to or larger than the wavelength of the fastest-growing mode; in addition they show that field-line bending induced under the 3-D geometry of the tail flank can lead to a magnetic configuration favorable for magnetic reconnection to occur near the vortices.

Figure 1.

(a) Relationship between the KH vortex structure and a scatter plot of Vx versus density, produced from simulated data (see Takagi et al. [2006] for details). The left panels show the density in color. Vx at the start of simulation runs is −1 (+1) in y > (<) 0. θ represents the angle between the initial direction of the magnetosheath magnetic field and the z axis oriented due north. Note that in the rolled-up case (top panel), a significant fraction of low-density plasmas flows in the −x direction at a speed higher than the magnetosheath plasma which is represented by Vx = −1 and n = 1. (b) The yellow isosurface represents a three-dimensional view of the region where Vx < −1.2 for the rolled-up case.

[6] Since the typical magnetospheric plasma is nearly stagnant or has only a weak streaming speed, the low-density and higher-speed feature discussed above, seen in the rolled-up vortex, is striking. We thought that this peculiar signature, along with other signatures of the KHI, may be used as evidence for the roll-up of KH vortices in single-spacecraft observations. In the present paper, we show that this signature is in fact found in the Cluster observation of rolled-up KH vortices at the dusk flank magnetopause [Hasegawa et al., 2004b] and hence can be used as an indicator of the roll-up of vortices. This low-density and faster-than-sheath signature is then used to search for rolled-up vortices from data obtained by the Geotail spacecraft, which has surveyed, with apogee of 30 RE, the equatorial magnetosphere over years since its insertion into the near-Earth tail orbits in 1995. We present the relationship between the roll-up of KH vortices and the plasma mixing status in the boundary layer and discuss whether the occurrence frequency of the rolled-up vortices, suggested by the detection probability, is significant for the LLBL formation.

2. Verification by Cluster

[7] We first present Cluster data obtained during and around the interval of its encounter with rolled-up KH vortices at the flank magnetopause [Hasegawa et al., 2004b], to see if the signature predicted by the simulation, shown in Figure 1, can in fact be found in the actual measurement. Figure 2 shows a scatter plot in which the x component of the flow velocity, Vx, is plotted as a function of ion density for the interval, 2015–2045 UT on 20 November 2001, during which the rolled-up vortices were unambiguously identified taking full advantage of the multipoint measurements. The data used here are from the HIA part of the CIS instrument for the Cluster 1 and 3 spacecraft (C1 and C3) and from the CODIF part for C4 [Rème et al., 2001] and have 4-s resolution. The negative direction of the x axis represents the orientation of the flow velocity averaged over the above interval. By defining x in this way, x becomes approximately tangential to the average magnetopause surface and becomes oriented sunward because the plasma in the boundary region on average flows antisunward along the boundary (this way of definition is taken in the following scatter plots as well). The data points from the magnetosheath are characterized by Vx ∼ −250 km/s and density of ∼8/cc. The figure clearly shows that a considerable number of data points are characterized by a tailward speed significantly higher than the magnetosheath flow, in the low-density domain (n < 6/cc). Furthermore, the distribution of the data points in the Vx versus density space is quite similar to that seen in the top right panel of Figure 1. Since a scatter plot as shown in Figure 2 can be produced even from single-spacecraft data, our result indicates that single-spacecraft detection of rolled-up vortices is possible by identifying the low-density and faster-than-sheath signature in a suspected KH event.

Figure 2.

Vx versus ion density seen in the rolled-up vortices identified from the multipoint measurements by the Cluster spacecraft [Hasegawa et al., 2004a] (see text for definition of Vx). The low-density and faster-than-sheath feature is evident as in the simulated rolled-up vortex (top panel in Figure 1a).

[8] From close inspection of the time plot shown in Figure 3, we see that the high-speed (Vx < −290 km/s) flows last for 10 to 20 seconds (a few data points because of 4 s resolution) for some of the observed wave periods. They mostly occur when the density increases to, or decreases from, its magnetosheath value, i.e., when the spacecraft traverses the interface between the magnetosheath and the magnetosphere. These features are consistent with expectations from Figure 1b: the former is consistent with that a spacecraft off the most-unstable latitude, as is the case for the Cluster observation, would see the high-speed flows only for a small fraction of time during one wave period, whereas the latter is consistent with that the high-speed flows occur near the magnetosheath-side edge of the vortex where the dense and tenuous plasmas come into contact. Importantly, Figure 2 shows that the accelerated flows are detected most frequently by C3 among the three spacecraft for which ion measurements are available. Taking into account the fact that C3 was the one that skimmed the most magnetosheath-side portion of the vortices (see Figure 2 of Hasegawa et al. [2004b] showing that C3 was ∼1800 km outward from C1 and ∼600 km outward from C4 in the average boundary normal direction), the above feature is also what is predicted from the simulation and thus supports that the observed high-speed flows are caused by the roll-up of vortex.

Figure 3.

Cluster ion data for the interval 2015–2045 UT on 20 November 2001, from which the scatter plot shown in Figure 2 is created. The panels show, from top to bottom, ion number density, ion temperature, and Vx. Red points represent the data characterized by Vx < −290 km/s.

3. Geotail Observations

3.1. Event-Based Check

[9] We now examine whether or not KH waves were fully rolled up in a suspected single-spacecraft event studied before. For this purpose, we picked up the Geotail event on 24 March 1995, which occurred at x ∼ −15 RE on the dusk flank during a stable and strong northward IMF period. This event has been studied extensively by Fujimoto et al. [1998] and Fairfield et al. [2000], who concluded that signatures observed in the event, such as fluctuations with ∼3 min periodicity and a mixture of magnetosheath and magnetospheric ions, are closely associated with the excitation of the KHI at the magnetopause. Figure 4 shows a scatter plot of Vx versus ion density for the interval 0600–0800 UT, during which Geotail was moving from the duskside magnetosheath into the plasma sheet. It is seen that the tailward speed of a fraction of less dense (<6/cc) plasmas is higher than 300 km/s, while that of the magnetosheath plasma, here characterized by the density of ∼10/cc, is less than 250 km/s. Consequently, we can now conclude that in this event, the KHI was growing vigorously to form highly rolled-up vortices.

Figure 4.

Vx versus ion density seen in a dusk-flank boundary crossing event studied by Fujimoto et al. [1998] and Fairfield et al. [2000].

3.2. Result of Survey

[10] We have searched for rolled-up vortices in the flank LLBL, on the basis of the Geotail observations made over 9 years from 1995 to 2003. For these intervals, 3-D ion bulk parameters but only 2-D ion velocity distributions are fully available. To unambiguously identify events consistent with the roll-up, we have used the following criteria: (1) Quasi-periodic fluctuations with the period of 1 to 5 min are seen in energy-versus-time spectrograms of ions observed in the transition region between the magnetosheath and plasma sheet. We also check whether perturbations having a similar period are found in the measurements of the bulk plasma parameters and of the magnetic field. Consequently, events presumably associated with surface waves excited on the magnetopause can be identified. In the present study, we have restricted the events to cases in which at least five wave periods are clearly identifiable. (2) The orientation of the magnetic field sampled on the magnetosheath side of the magnetopause traversal and/or that in the upstream solar wind, seen by the Wind or ACE spacecraft, is northward throughout a relevant interval. The reason for the use of this additional condition is that for other (southward or equatorial) orientations of the magnetosheath field, the magnetic shear across the magnetopause becomes so high that high-speed tailward flows could easily be generated through magnetopause reconnection occurring somewhere on the sunward side of the spacecraft; that is, it is made difficult to judge whether an identified low-density and high-speed feature is in fact due to the roll-up of vortices or to reconnection-associated acceleration. (3) A sufficient number of data points, characterized by the density of less than half of that measured on the magnetosheath side, exhibit an antisunward speed higher than that of the magnetosheath plasma. This can be checked by producing a scatter plot as shown in Figure 4 and allows for the detection of rolled-up vortices.

[11] We here emphasize that the number of events identified using the above three criteria would be a lower bound on actual rolled-up vortices cases because of the following reasons: (1) According to simulations [Takagi et al., 2006], there exist phases in which a KH vortex is rolled up but the low-density and higher-speed feature is not seen. (2) The time resolution of the Geotail ion moment data used in the survey is 12 s so that the low-density and higher-speed feature may have been missed due to time aliasing effects. Note here that structures formed within rolled-up vortices becomes smaller in the nonlinear stage [e.g., Nakamura et al., 2004; Matsumoto and Hoshino, 2004] so that a higher time resolution is required to fully resolve such structures. Indeed, for most of the rolled-up cases, only a few or no data points (corresponding to an interval of order 10 s) are characterized by the high-speed flow during each wave period, consistent with the Cluster observation discussed in the previous section. (3) To produce the scatter plot of Vx versus density, we used the data obtained by the LEP-EA instrument in RAM-A mode only [see Mukai et al., 1994 for details]. This is because the ion bulk parameters based on the other ion instrument, LEP-SW, at times deviate from those based on LEP-EA that gives more reliable data in the boundary region. Which (EA or SW) instrument is used for the calculation of the bulk parameters is automatically selected, according to the intensity of ion fluxes into the LEP-SW instrument. Therefore the data obtained in the outer part of the boundary layer are quite often computed from the LEP-SW measurements. Since the marker of the roll-up is usually found in the magnetosheath-side part of the rolled-up vortex (see Figures 1b and 2), it is likely that we have discarded many rolled-up vortices which were in fact encountered by the spacecraft. Furthermore, there is also a possibility that KH waves are rolled up in further downstream regions, even though they are not at the observation site. Taking these effects into account, we have to keep in mind that the detection probability of the rolled-up events, whose significance is discussed in the last section, is a lower limit.

[12] We remind the readers that flows faster than the upstream solar wind have been found in the magnetosheath adjacent to the magnetopause [Petrinec et al., 1997]. They used data from the LEP-SW instrument onboard Geotail, so events as reported in their paper would not be included in our study. However, it is possible that their high-speed flows result from the KHI, as they point out, since their flows are detected in lower-density portions of the magnetosheath close to the magnetopause. Note in Figure 1b that the high-speed flow can also be seen in the magnetosheath region immediately outside the rolled-up vortex, although the highest speed is achieved in the lower-density magnetospheric region (Figure 1a).

[13] The events identified in the way described above are listed in Table 1, in which their observed conditions are also included. The GSM locations of the events are presented in Figure 5, together with that of the Cluster event. A total of 18 events are encountered along the flank magnetopause, most of which are behind the dawn-dusk terminator. It is surprising that one dawnside event was identified substantially sunward (x ∼ 6 RE) of the terminator, taking into account that on the dayside the velocity jump across the magnetopause is not very high and that the KHI develops spatially as KH waves propagate antisunward. Details of this dayside event are presented in the next subsection. It is seen that rolled-up vortices form on both dawnside and duskside, and that an equal number of events were detected for each side. We discuss, in the discussion section, whether this number is significant at all in the flank LLBL formation.

Figure 5.

Locations of rolled-up KH events identified from the Geotail (solid curves) and Cluster (plus) observations. The dashed curves show an average magnetopause position based on the Roelof and Sibeck [1993] model. The rolled-up events are found along the tail-flank magnetopause, mostly behind the dawn-dusk terminator.

Table 1. Event List of Rolled-Up Vortices Detected by Geotail
DateTime IntervalGSM Position(RE)IMF ConditionIon Mixing StatusFluctuation Period
1995–03–24a0600–0800 UT(−15, 20, 4)Extended strong NBZbMixedc2–3 min
1996–12–121200–1330 UT(−21, −21, 2)Weak NBZ after N-turningWeakly mixedc2–3 min
1997–01–10d2050–2400 UT(−7, 16, 4)Nondominant NBZ after N-turningWeakly mixed2–3 min
1997–01–11d0400–0500 UT(−13, 16, 4)Extended strong NBZMixed∼3 min
1997–02–121430–1600 UT(−13, 22, 3)Extended strong NBZMixed∼2 min
1998–04–130315–0430 UT(−18, 20, 4)Extended strong NBZMixed2–3 min
1998–08–010530–0730 UT(0, 14, _3)Extended strong NBZMixed∼3 min
1998–12–271800–2100 UT(−21, −22, −4)Extended strong NBZMixed3–4 min
1999–02–151445–1515 UT(−4, 16, 2)NBZ after N-turningMixed∼2 min
1999–07–200630–0730 UT(−3, 16, −2)Extended strong NBZMixed2–3 min
2000–11–011030–1200 UT(−8, −16, 6)Extended strong NBZMixed2–3 min
2001–01–251330–1630 UT(−22, −21, 0)Extended strong NBZMixed∼5 min
2001–11–161900–2000 UT(−7, −18, 2)Extended NBZ (often not dominant)Weakly mixed2–3 min
2001–12–072000–2130 UT(−11, −19, −1)Strong NBZ after N-turningWeakly mixed∼3 min
2002–03–250530–0900 UT(−12, −17, −2)Extended strong NBZMixed2–3 min
2002–03–251000–1300 UT(−8, −16, −1)Extended strong NBZMixed2_3 min
2002–08–292300–2400 UT(7, −11, 2)Extended strong NBZMixed2–3 min
2002–10–152100–2300 UT(−1, −14, 3)Extended NBZMixed2–3 min
2003–07–170330–0500 UT(−13, 23, −1)Nondominant NBZ after N-turningWeakly mixed∼2 min

[14] Table 2 summarizes, for the dawnside and duskside, the ion mixing status in the boundary layer in the rolled-up vortices events. We have defined the mixing status by visual inspection of energy-versus-time spectrograms of ions and of density measurements in regions earthward of the magnetopause. “Mixed” means that a significant amount of cool magnetosheath-like ions was present on the magnetospheric side of the magnetopause (total number density >1 /cc), while “weakly mixed” means that magnetosheath-like ions were found on the magnetospheric side but the density was lower than 1 /cc. It is seen that in all the rolled-up events, magnetosheath-like ions were detected on the magnetospheric side, although in several cases their density was low. This result indicates that the rolled-up vortices are, at least, to some extent associated with the transport of solar wind plasmas into the magnetosphere under northward IMF. It is also worth noting that all the weakly mixed events occurred during a weakly northward IMF interval, or soon after a northward turning of the IMF, such features being consistent with earlier observations that the dense status is established after an extended period of northward IMF [Terasawa et al., 1997; Hasegawa et al., 2004a]. The former seems to indicate that the transport process, which may or may not be related to the KHI, is less efficient under weakly northward IMF conditions, whereas the latter is consistent with the fact that it takes a while for the transport under northward IMF to be fully accomplished [Wing et al., 2005].

Table 2. Ion Mixing Status in the Rolled-Up Vortices Events
 DawnsideDuskside
Mixed67
Weakly mixed32
No mixing00
Total99

3.3. Dawnside Examples

[15] We here present two examples encountered on the dawnside because, to our knowledge, these dawnside KH events are the first reported based on Geotail observations and because, as Figure 5 shows, one dawnside event surprisingly occurred on the dayside (x ∼ 6 RE). Note that ISEE 1 and 2 observations demonstrated the presence of surface waves on the dawnside [e.g., Kivelson and Chen, 1995] but found no clear signature of dense ions on the magnetospheric side for such cases.

[16] Figure 6 shows the data for the interval, 2200–2400 UT on 29 August 2002 during which Geotail was moving from the dawnside magnetosphere toward the dayside magnetosheath. At the start of the interval, the satellite observed hot (∼4 keV) and tenuous (<1 /cc) ions, as seen in the typical plasma sheet, while around the end, it exited to the magnetosheath where the magnetic field was oriented strongly northward. From ∼2208 UT, cool (<1 keV) ions appeared, as evident in the ion energy-time spectrogram, and the density started to increase (up to >3 /cc). After this moment, the coexistence of the cool magnetosheath-like and hot plasma sheet populations is clearly seen, and quasi-periodic oscillations are found in all the measured plasma and field parameters. The amplitude of the oscillations is largest exactly when the spacecraft is in the magnetopause transition region (∼2300 UT), across which the temperature decreases, and both Vx and Vy increase negatively, to their magnetosheath-like values. This fact suggests that the source of the fluctuations is in the transition layer, consistent with the excitation of KH waves at the magnetopause. For such a highly fluctuating interval, 2305–2345 UT, the period of perturbation is 2 to 3 min. We note that the characteristics of these perturbations are quite similar to those found in the Cluster observations of the rolled-up vortices on the duskside [Hasegawa et al., 2004b]. The perturbations in the flow are interpreted as being due to vortical motions of plasma [e.g., Fujimoto et al., 2003], whereas those in the field are due to deformation of the field lines when those near the magnetopause are brought into rolled-up vortices [Hasegawa et al., 2004b; Takagi et al., 2006]. According to the observed 2–3 min period and to the tailward flow speed of ∼150 km/s, the wavelength is estimated to be 3 to 4 RE, consistent with that reported in literature [e.g., Kivelson and Chen, 1995; Fairfield et al., 2000].

Figure 6.

Overview of a dawnside event that occurred on 29 August 2002 for the interval 2200–2400 UT. The panels show, from top to bottom, number density, ion temperature, energy-versus-time spectrogram for tailward streaming ions, GSM bulk velocity components, GSM magnetic field components, and field magnitude. Note that this event occurred on the dayside (X ∼ 6 RE). The interval between 2230 UT and 2400 UT is used for producing the scatter plot shown in Figure 7.

[17] The top panel of Figure 7 shows the scatter plot of Vx versus density for the interval 2230–2400 UT. It is seen that a fraction of less dense (<3 /cc) ions were flowing at Vx < −250 km/s, faster than the magnetosheath ions characterized by the density >4/cc and Vx = −200 ∼ −250 km/s. From this feature, we infer that the KH waves were rolled up for the interval under discussion, in spite of the fact that Geotail was located on the dayside (x ∼ 6 RE).

Figure 7.

Vx versus ion density seen in the two example events on 29 August 2002 (Figure 6) and on 25 January 2001 (Figure 8). The faster-than-sheath feature is clearly seen for low-density populations.

[18] In Figure 8, we show the data for another example event. The data are from the interval, 1230–1630 UT on 25 January 2001 during which Geotail was at x ∼ −22 RE on the dawnside. The spacecraft appears to have been skimming the boundary layer region, sometimes observing the plasma sheet (1230–1250 UT, 1615–1620 UT) and other times dense magnetosheath-like regions. The magnetic field was northward throughout the interval, although it was fluctuating perhaps owing to the influence of the KHI. The oscillation in density between less dense (<2/cc) and magnetosheath-like (>4/cc) values suggests the existence of large-amplitude waves on the magnetopause surface, presumably excited through the KHI development. Quasi-periodic fluctuations in the plasma and field parameters are found throughout, but what is remarkable here is that they are much less periodic than in the dayside event shown in Figure 6. Such a less periodic feature seems to indicate that the wavelength of the encountered surface waves is not equal for different wave packets. Another interesting feature is that the period of the fluctuations (∼5 min, according to the top panel) is longer than that for the dayside event (note that the total time interval covered in Figure 8 is twice that in Figure 6). This fact likely reflects the wavelength in this event being longer than that in the dayside event. The wavelength for this event is estimated to be 9 RE, with the antisunward propagation speed of the vortices ∼200 km. Such a longer wavelength and the nonequality of the wavelength might have resulted from coalescence of multiple KH vortices and from its irregular occurrence, respectively, when the instability evolves increasingly with downstream distance. According to our survey (Table 1), however, there seems to be only a weak tendency that the period of quasi-periodic fluctuations becomes longer with distance from the subsolar magnetopause. Such a minor dependence is likely due to the fact that the observations were made under various upstream solar wind conditions. It must also be remembered that the wavelength of the fastest-growing KH mode and the growth rate depend on the initial thickness of the velocity shear layer [e.g., Miura and Pritchett, 1982], which might have been different from event to event. Detailed studies on the solar wind dependence of KH wave properties will be a topic of future investigation.

Figure 8.

Overview of a dawnside event that occurred at X ∼ −22 RE on 25 January 2001 for the interval 1230–1630 UT. The format is the same as in Figure 6. Note that the period of fluctuations is much longer than that in the 29 August 2002 dayside event (Figure 6).

[19] The bottom panel of Figure 7 shows the scatter plot for the interval 1400–1600 UT, which is sandwiched by the two vertical lines in Figure 8. As in the previous examples, the low-density and faster-than-sheath feature is clearly seen, consistent with the roll-up of vortices in this event. One may think that the distribution of the data points is not similar to that seen in the simulation result (top right panel in Figure 1a). It must be pointed out, however, that according to the simulations, the characteristic of the distribution varies with time as the KHI grows, and also that the spacecraft does not necessarily observe equally the domain surrounding the magnetopause as a synthetic spacecraft can do in the simulation box.

4. Discussion

[20] We have confirmed that the signature theoretically expected in a highly rolled-up KH vortex, which is the tailward speed of the magnetospheric plasma exceeding that of the magnetosheath plasma [Takagi et al., 2006], is indeed found in the Cluster observations of rolled-up vortices [Hasegawa et al., 2004b]. We therefore suggest that it can be used as an indicator of the roll-up of vortices in single-spacecraft data. On the basis of this finding, we have surveyed the Geotail data to see how often and where cases consistent with the roll-up of vortices are found under northward IMF conditions. As a result, a total of 18 rolled-up events were identified from nine years of observation from 1995 to 2003, nine events on each flank of the magnetosphere.

[21] We now roughly estimate the significance of this occurrence probability in the formation of the flank LLBL under northward IMF. Since the orbital period of Geotail in the present near-tail phase is about 125 hours, it follows that we had a total of ∼630 orbits during the 9 years. However, since we restricted the survey to steadily northward IMF conditions, the number of orbits under such conditions would be roughly 158, assuming that a steadily northward IMF lasts for 25% of time. If we further assume that either dawn or dusk flank is encountered once per orbital period (Geotail has the perigee of 9 RE and apogee of 30 RE), it is found that 18 events were identified from a total of 158 flank traversals, i.e., the rolled-up cases were encountered with the detection probability of roughly 11%. By considering the several effects discussed in section 3.2, which would have lowered the probability, we can conclude that the roll-up of KH vortices along the flank magnetopause is not rare. In addition, magnetosheath ions are detected on the magnetospheric side of the boundary in all the rolled-up vortices events. This fact, together with our finding that the detection probability of rolled-up events is not low, indicates that the KHI plays a nonnegligible role in the transport of solar wind plasmas for northward IMF periods.

[22] The finding that the detection probability is nearly equal for the dawnside and duskside is in contrast with earlier observations that, in the LLBL and plasma sheet, dense magnetosheath-like ions are more frequently observed on the dawnside than on the duskside and that the dawnside dense ions are found for nonnorthward IMF as well [Wing and Newell, 2002; Hasegawa et al., 2004a]. Our result may therefore indicate that some transport mechanism other than the KHI is also important, in particular on the dawnside, although there is another possibility that the rate at which KHI-associated plasma transport/mixing occurs is different for the dawnside and duskside [e.g., Huba, 1996; Nakamura and Fujimoto, 2005b]. Since poleward-of-the-cusp reconnection does not seem to produce easily the dawn-dusk asymmetry as observed, there may be some mechanisms which are related neither to reconnection nor to the KHI and which are more efficient on the dawnside than on the duskside. Such could be transport caused by finite Larmor radius effects, or diffusive transport induced through wave-particle interactions, possibly connected with Kinetic Alfvèn waves [Johnson and Cheng, 1997]. Since low-frequency waves are at times intense in the dawnside magnetosheath, being situated downstream of the quasi-parallel bow shock, wave-coupled transport may be responsible for transport of the LLBL plasma on the dawnside. It is also of importance to note that for the intervals in which the signatures of KH waves were clearly identified, we did not find significant differences in the ion energy spectra between the dawnside and duskside events, while a distinct dawn-dusk asymmetry in the spectra is usually seen in the LLBL and plasma sheet under northward IMF [Hasegawa et al., 2004a; Wing et al., 2005]. It may be that the above-mentioned mechanisms unrelated to the KHI lead to the asymmetric heating/transport of magnetosheath ions.

[23] Another issue is whether or not KH vortices can inject plasmas deep enough into the near-midnight portion of the plasma sheet, where cold-dense ions are often observed for extended northward IMF intervals [e.g., Terasawa et al., 1997]. While such large-scale transport could be achieved via the KHI when multiple KH vortices can coalesce into a very large vortex and/or when turbulent eddies are generated even on the magnetosphere side of the parent MHD-scale KH vortex, it is not entirely clear if such is viable in the three-dimensional geometry of the magnetosphere [Takagi et al., 2006]. On the other hand, recent studies by Øieroset et al. [2005] and Li et al. [2005] show, based on a global MHD simulation, that double poleward-of-the-cusp reconnection and resultant global convection could transport solar wind plasmas into the plasma sheet region far away from the magnetopause boundary, for a long period of purely northward IMF. Such reconnection driven convection may help carry KHI-injected as well as reconnection-injected plasmas into the central portion of the plasma sheet, although their global simulation so far cannot reproduce realistic KH waves and cannot deal with the transport process in the LLBL adequately so that confirmation of this scenario is not possible for the moment.

Acknowledgments

[24] H.H. thanks Benoit Lavraud for fruitful discussions and valuable comments. The Geotail magnetic field (MGF) data were provided by T. Nagai, whereas the IMF information from the Wind and ACE satellites was through CDAweb (http://cdaweb.gsfc.nasa.gov/). The energy-versus-time spectrograms in Figures 6 and 8 were created using a data analysis tool, STARS (http://www.infonet.cite.ehime-u.ac.jp/STARS/). Part of the work was performed under the auspices of a JSPS Research Fellowship for Young Scientists awarded to H.H.

[25] Amitava Bhattacharjee thanks David Sibeck and Donald Fairfield for their assistance in evaluating this paper.

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