3.1. Kelvin-Helmholtz Instability
 The convective rolls occur in regions of large shear, suggesting that shear instabilities may be responsible for generating the structures. Overturning or vortex rolls are a common characteristic of Kelvin-Helmholtz instabilities associated with large shears. The features described here are clearly not associated with such instabilities for a number of reasons. Although the shear is large in the part of the atmosphere where the overturning occurs, the region which is unstable in the small Richardson number sense, is localized within a few km in the vertical direction, as discussed in more detail by Bishop et al. , and is localized in time as well. The most unstable horizontal wavelength is expected to be approximately 16 km for a shear instability region with a vertical scale of 2 km [see, e.g., Scorer, 1997]. The largest shear was in the zonal wind component in the altitude range of interest, so the Kelvin-Helmholtz structures would be aligned approximately in the north-south direction, i.e., perpendicular to the mean wind component. Such structure was indeed observed in the chemical release trail, as described in the article by Bishop et al. , but the apparent period produced by such structure advected at a mean velocity of 30 m s−1 is 8–10 min which is much less than the period of several hours that is observed. The secondary instabilities associated with the shear instabilities after they become fully developed are aligned with the wind direction [see, e.g., Palmer et al., 1996] and could produce much longer apparent periods in the earth-fixed frame, but the simulations of Fritts et al.  have shown that the timescale for such an event, from initial instability to restabilization, is of the order of 30 min, i.e., much shorter than the timescale of the features observed here. The secondary instabilities are therefore an unlikely explanation since the timescale is too short and the vertical scale of those instabilities is expected to be considerably smaller than the scale that is observed.
3.2. Gravity Wave Breaking
 Gravity wave breaking is another possible explanation for the features. The simulations of Walterscheid and Schubert  and Prusa et al. , for example, show that wave breaking is expected to produce overturning once per wavelength for waves that exceed criticality. Differences between the simulations and the observations presented here include the fact that the wave breaking effects in the model extend over an altitude range of 20 km or more, whereas our observations show features that are very localized in height and that tend to occur near the transition from the mesopause to the lower thermosphere around 100 km. Another difference is that the breaking wave structures produced by the simulations propagate relatively quickly past an observing point on the ground. For example, the structure shown in Figure 1 of the paper by Walterscheid and Schubert  moves 10–20 km in approximately 20 min, which is a significant fraction of the wavelength. The details of the solutions will undoubtedly depend on the choice of the incident wave spectrum, and it may well be that the spectrum can be tuned to produce solutions that match the observations more closely, but that is not clear at this point.
3.3. Convective Rolls
 An alternative explanation for the observed characteristics of the features described here stems from similarities between conditions in the mesosphere/lower thermosphere transition region and conditions in the planetary boundary layer. Specifically we are interested in possible similarities between the vortex rolls that are commonly observed in the atmospheric boundary layer within the lowest 1–2 km of the atmosphere and the convective rolls that are present in the lidar data. Studies of the convective roll features in the boundary layer have a long history, and the features have been given a number of different names. The earliest observations were of the cloud streets that develop as a consequence of the vortex rolls when sufficient moisture is present. The features themselves have been referred to as boundary layer rolls, vortex rolls, longitudinal instabilities, and organized large eddies. The critical features required to generate them are a region of low stability, i.e., temperature decreasing with altitude, capped by a region of high stability, i.e., temperature increasing with altitude, which is a condition that is also characteristic of the mesosphere/lower thermosphere transition region.
 A further requirement is a shear in the background winds. Brown  and Etling and Brown  have written excellent reviews of the theoretical understanding and the observational data pertaining to the boundary layer vortex rolls. The theoretical papers have focused on longitudinal instabilities. The latter are ultimately inflection point instabilities or generalized shear instabilities, as described in more detail by Brown  and Stensrud and Shirer , for example, which can exist in both viscid and inviscid flow [see also Balmforth and Morrison, 1999]. When an inflection point is present in the flow, the rolls can develop and draw on the energy of the mean flow. The eddy viscosity is clearly an important component of the boundary layer dynamics with a significant influence on the characteristics of the convective roll modes. The angle between the roll axes and the geostrophic wind, for example, is an effect of the eddy viscosity. The eddy diffusion in the altitude range of interest to us is also frequently enhanced below the height of the turbopause, as discussed in the article by Bishop et al.  and in a number of the papers cited therein. Breaking gravity waves are the likely to be the drivers for the dynamical processes that lead to the enhanced diffusion, as well as being the drivers of some of the large shears that are observed in the mesosphere/lower thermosphere region.
 The paper by Lilly  was one of the first to discuss the instability of the Ekman boundary layer wind profile due to the inflection point in the wind profile associated with the rotation of the wind vector with height. His linear analytic treatment clearly indicated that the flow was unstable, but such linear analytic theories have not been particularly successful in predicting the characteristics of the unstable structures, as discussed by Etling and Brown . Stability analysis is complicated because of the dependence on the Reynolds number Re, the Rayleigh number Ra, the Prandtl number Pr, the bulk Richardson number Ri and the Rossby number Ro. In addition the instability depends on the angle between the mean flow and the roll orientation and on the horizontal wavelength. Numerical modeling studies have been more successful. The results show that aspect ratios of 5–6 are expected, although boundary layer observations have shown aspect ratios as large as 15. The theoretical analyses also show that the vortex rolls are aligned nearly parallel to the mean wind, but with small angles of approximately 10–20° between the wind direction and the axis of the rolls.
 In the boundary layer models, the most natural lower boundary condition is a no-slip condition, and the upper boundary condition is often taken as a rigid lid, although the latter may not be realistic. The formulation of the boundary layer problem is therefore treated as a Dirichlet problem. The region of interest for us in the mesopause/lower thermosphere is the altitude range where the winds and wind shears are large (approximately 90–110 km) since the overturning features observed in the sodium density data occur in the region of large winds and shears [Larsen, 2002], which are presumed to be the drivers for the observed instabilities. There are no rigid surfaces in the altitude range, but it is clear that the gradients become small outside the region. In fact, the wind speeds also decrease significantly at altitudes below the heights of interest. A reasonable choice of boundary conditions would be to specify the vertical derivatives at the upper and lower boundaries, i.e., to formulate the equations as a Neumann problem. Using the Neumann versus Dirichlet constraints will not change the stability characteristics, although the solution for a specific set of boundary conditions will effectively determine the phasing.
 The instabilities can exist in purely turning shear since the requirement is that an inflection point must exist in the profile of one component of the wind. Brown  pointed out that, although the initial study by Lilly  focused on the instability of the Ekman wind profile, the instability can be produced by other types of forcing that produce turning shear, such as the thermal wind or, perhaps more appropriately for the mesosphere and lower thermosphere region, the turning shear associated with the tidal motions. As pointed out by Brown , instabilities will occur at very moderate velocities if there is an inflection point in the velocity profile. If there are nearly constant flow velocities in two adjacent regions, the transition from one to the other will almost certainly require the presence of an inflection point. The typical background winds in the region of interest for our study are characterized by a rotation of the wind vector with height and an increase in the wind speed with a maximum that usually occurs between 100 and 110-km altitude [Larsen, 2002]. The occurrence of an inflection point is therefore highly likely.
 For the TOMEX case, the vertical scale of the overturning is approximately 6 km which gives a horizontal scale of 36 to 90 km for the aspect ratios cited above. The differences between the density data from the different beam directions in the TOMEX experiment are small, suggesting that the horizontal scale of the structures is at least many tens of kilometers. For a wind speed of 30 m s−1 and a roll axis aligned at an angle of 20° from the mean wind direction, the apparent period in the earth-fixed frame will be between 1 and 2.5 hours, i.e., consistent with the periods found in the data presented here. The parameters in the other observations presented here are comparable to those observed on the TOMEX night. The data that we have included here shows vortex curls in both the clockwise and counterclockwise sense. Since the instability produces counterrotating helical flow in adjacent vortex rolls, both types of rotation can be expected.