Vertical Perturbations Research Articles

Height and critical frequency variations of the sporadic-E layer at midlatitudes

The present study concerns variations in height and critical frequency of sporadic E layer over a wide period range of hours to several days, covering tidal and planetary oscillation domain. Besides periodicities in the tidal and planetary range that are known to occur within time series of critical frequencies ( foEs) of sporadic-E layer [Pancheva, D., Haldoupis, C., Meek, C.E., Manson, A.H., Mitchell, N.J., 2003. Evidence of a role for modulated atmospheric tides in the dependence of sporadic E layers on planetary waves. Journal of Geophysical Research 108, Art. No. 1176; Haldoupis, C., Pancheva, D., Michell, N.J., 2004. A study of tidal and planetary wave periodicities present in midlatitude sporadic E layers. Journal of Geophysical Research 109, Art. No. A02302] among others, we evidence the existence of the 4-day planetary wave well developed in the height of sporadic E time serie ( hEs). Moreover it is shown that the central-period of the diurnal tidal component of hEs is not exactly 24 h but it varies between 22 and 26 h at the planetary wave period. At a first glance, this is surprising since the origin of the diurnal tide is a forced oscillation with a 24 h period due to the Earth rotation and the periodic heating of the atmosphere by the Sun. Our interpretation is based on the perturbation of the height of the Es layer imposed by the planetary wave. In this mechanism the Es layer is moved up and down by the planetary wave producing a Doppler effect and resulting in a shift of the central-period around 24 h. With this interpretation, the excursion of the central-period is related to the vertical velocity perturbation of the Es layer due to the planetary wave. For a central period varying between 22 and 26 h the peturbation velocities are 0.026 and - 0.022 m / s , respectively.

Chaotic and regular motion around generalized Kalnajs discs

The motion of test particles in the gravitational fields generated by the first four members of the infinite family of generalized Kalnajs discs is studied. In first instance, we analyse the stability of circular orbits under radial and vertical perturbations and describe the behaviour of general equatorial orbits and so we find that radial stability and vertical instability dominate such disc models. Then we study bounded axially symmetric orbits by using the Poincaré surfaces of section and Lyapunov characteristic numbers and find chaos in the case of disc-crossing orbits and completely regular motion in other cases.

Formation of large (≃100 μm) ice crystals near the tropical tropopause

Abstract. Recent high-altitude aircraft measurements with in situ imaging instruments indicated the presence of relatively large (≃100 μm length), thin (aspect ratios of ≃6:1 or larger) hexagonal plate ice crystals near the tropical tropopause in very low concentrations (<0.01 L−1). These crystals were not produced by deep convection or aggregation. We use simple growth-sedimentation calculations as well as detailed cloud simulations to evaluate the conditions required to grow the large crystals. Uncertainties in crystal aspect ratio leave a range of possibilities, which could be constrained by knowledge of the water vapor concentration in the air where the crystal growth occurred. Unfortunately, water vapor measurements made in the cloud formation region near the tropopause with different instruments ranged from <2 ppmv to ≃3.5 ppmv. The higher water vapor concentrations correspond to very large ice supersaturations (relative humidities with respect to ice of about 200%). If the aspect ratios of the hexagonal plate crystals are as small as the image analysis suggests (6:1, see companion paper (Lawson et al., 2008)) then growth of the large crystals before they sediment out of the supersaturated layer would only be possible if the water vapor concentration were on the high end of the range indicated by the different measurements (>3 ppmv). On the other hand, if the crystal aspect ratios are quite a bit larger (≃10:1), then H2O concentrations toward the low end of the measurement range (≃2–2.5 ppmv) would suffice to grow the large crystals. Gravity-wave driven temperature and vertical wind perturbations only slightly modify the H2O concentrations needed to grow the crystals. We find that it would not be possible to grow the large crystals with water concentrations less than 2 ppmv, even with assumptions of a very high aspect ratio of 15 and steady upward motion of 2 cm s−1 to loft the crystals in the tropopause region. These calculations would seem to imply that the measurements indicating water vapor concentrations less than 2 ppmv are implausible, but we cannot rule out the possibility that higher humidity prevailed upstream of the aircraft measurements and the air was dehydrated by the cloud formation. Simulations of the cloud formation with a detailed model indicate that homogeneous freezing should generate ice concentrations larger than the observed concencentrations (20 L−1), and even concentrations as low as 20 L−1 should have depleted the vapor in excess of saturation and prevented growth of large crystals. It seems likely that the large crystals resulted from ice nucleation on effective heterogeneous nuclei at low ice supersaturations. Improvements in our understanding of detailed cloud microphysical processes require resolution of the water vapor measurement discrepancies in these very cold, dry regions of the atmosphere.

Satellite‐based measurements of gravity wave‐induced midlatitude plasma density perturbations

Large amplitude anticorrelated wave structures appear at midlatitudes in the nighttime ionospheric plasma and neutral density measurements made at altitudes between 250 and 300 km by the Dynamics Explorer‐2 satellite. The wavelengths along the satellite orbit track are generally longer than a hundred kilometers, and the vertical perturbation velocities are about 20 m/s. These characteristics are consistent with plasma motions driven by gravity waves in the neutral atmosphere as they propagate upward from lower atmospheric source regions. The altitude and the horizontal wavelengths observed provide in situ empirical validation of a recently developed gravity wave propagation model that includes the effects of both kinematic viscosity and thermal diffusivity at high altitudes.

Nonlinear Numerical Simulations of Magneto-Acoustic Wave Propagation in Small-Scale Flux Tubes

We present results of nonlinear, two-dimensional, numerical simulations of magneto-acoustic wave propagation in the photosphere and chromosphere of small-scale flux tubes with internal structure. Waves with realistic periods of three to five minutes are studied, after horizontal and vertical oscillatory perturbations are applied to the equilibrium model. Spurious reflections of shock waves from the upper boundary are minimized by a special boundary condition. This has allowed us to increase the duration of the simulations and to make it long enough to perform a statistical analysis of oscillations. The simulations show that deep horizontal motions of the flux tube generate a slow (magnetic) mode and a surface mode. These modes are efficiently transformed into a slow (acoustic) mode in the v A<c S atmosphere. The slow (acoustic) mode propagates vertically along the field lines, forms shocks, and remains always within the flux tube. It might effectively deposit the energy of the driver into the chromosphere. When the driver oscillates with a high frequency, above the cutoff, nonlinear wave propagation occurs with the same dominant driver period at all heights. At low frequencies, below the cutoff, the dominant period of oscillations changes with height from that of the driver in the photosphere to its first harmonic (half period) in the chromosphere. Depending on the period and on the type of the driver, different shock patterns are observed.

The effect of canopy roughness density on the constitutive components of the dispersive stresses

How to represent the effects of variable canopy morphology on turbulence remains a fundamental challenge yet to be confronted. Planar averaging over some minimal area can be applied to average-out this sort of spatial variability in the time-averaged mean momentum balance. Because of the multiply connected air-spaces, spatial averaging gives rise to covariance or dispersive stress terms that are produced by the spatial correlations of the time-averaged quantities. These terms are “unclosed” and require parameterization, which to date remains lacking due to the absence of data. Here, flume experiments were conducted to quantify the magnitude and sign of the dispersive stresses for a cylindric canopy where the rod density was varied but the individual rod dimensions (rod height hc and rod diameter dr) remained the same. Quadrant analysis was used to explore the genesis of their spatial coherency inside the canopy for a wide range of rod densities. When compared to the conventional turbulent stresses, these dispersive stresses can be significant in the lowest layers of sparse canopies. For dense canopies, the dispersive terms remain negligible when compared to the conventional momentum fluxes at all the canopy levels consistent with previous experiments in vegetated and urban canopies. It was also shown that the spatial locations contributing most to the dispersive terms were in the immediate vicinity downstream of the rods. In the deeper layers of sparse canopies, these positions contributed large and negative stresses, but in the upper levels of the canopy, they contributed large but positive stresses. Because the longitudinal velocity spatial perturbation \(({\bar{u}}^{\prime\prime})\) behind the rods is negative, the switch in sign in these stresses was connected with the sign of the vertical velocity spatial perturbation \(({\bar{w}}^{\prime\prime}).\) Simplified scaling arguments, using a reduced mean continuity equation and the vertical mean momentum balance for the flow field near the rods, offer clues as to why \({\bar{w}}^{\prime\prime} > 0\) in much of the lower canopy levels (about 0.75 hc) while \({\bar{w}}^{\prime\prime} < 0\) in the upper canopy levels.

Assessment of the non‐hydrostatic effect on the upper atmosphere using a general circulation model (GCM)

Under hydrostatic equilibrium, a typical assumption used in global thermosphere ionosphere models, the pressure gradient in the vertical direction is exactly balanced by the gravity force. Using the non‐hydrostatic Global Ionosphere Thermosphere Model (GITM), which solves the complete vertical momentum equation, the primary characteristics of non‐hydrostatic effects on the upper atmosphere are investigated. Our results show that after a sudden intense enhancement of high‐latitude Joule heating, the vertical pressure gradient force can locally be 25% larger than the gravity force, resulting in a significant disturbance away from hydrostatic equilibrium. This disturbance is transported from the lower altitude source region to high altitudes through an acoustic wave, which has been simulated in a global circulation model for the first time. Due to the conservation of perturbation energy, the magnitude of the vertical wind perturbation increases with altitude and reaches 150 (250) m/s at 300 (430) km during the disturbance. The upward neutral wind lifts the atmosphere and raises the neutral density at high altitudes by more than 100%. These large vertical winds are not typically reproduced by hydrostatic models of the thermosphere and ionosphere. Our results give an explanation of the cause of such strong vertical winds reported in many observations.

Gravity wave propagation in a nonisothermal atmosphere with height varying background wind

We derive a gravity wave propagation equation for a compressible and non‐isothermal atmosphere with a variable background wind profile. Impact of all the gradient terms on the vertical wavenumber depends only on the intrinsic horizontal phase velocity and the background atmosphere. For the background wind variation, any one of the linear first order derivative, second order derivative and the square of the first order derivative terms can be the dominant term under different conditions. For temperature variation, only the linear first order derivative is important for waves having a slow intrinsic horizontal phase velocity. Our equation indicates that the effect of wind shear on the vertical wavenumber is opposite to that predicted by the Taylor‐Goldstein equation, which assumes an incompressible fluid. We also derive an expression for the amplitude of the vertical wind perturbation.

Vertical perturbations of human gait: organisation and adaptation of leg muscle responses

During the last several years, evidence has arisen that the neuronal control of human locomotion depends on feedback from load receptors. The aim of the present study was to determine the effects and the course of sudden and unexpected changes in body load (vertical perturbations) on leg muscle activity patterns during walking on a treadmill. Twenty-two healthy subjects walking with 25% body weight support (BWS) were repetitively and randomly loaded to 5% or unloaded to 45% BWS during left mid-stance. At the new level of BWS, the subjects performed 3-11 steps before returning to 25% BWS (base level). EMG activity of upper and lower leg muscles was recorded from both sides. The bilateral leg muscle activity pattern changed following perturbations in the lower leg muscles and the net effect of the vertical perturbations showed onset latencies with a range of 90-105 ms. Body loading enhanced while unloading diminished the magnitude of ipsilateral extensor EMG amplitude, compared to walking at base level. Contralateral leg flexor burst activity was shortened following loading and prolonged following unloading perturbation while flexor EMG amplitude was unchanged. A general decrease in EMG amplitudes occurred during the course of the experiment. This is assumed to be due to adaptation. Only the muscles directly activated by the perturbations did not significantly change EMG amplitude. This is assumed to be due to the required compensation of the perturbations by polysynaptic spinal reflexes released following the perturbations. The findings underline the importance of load receptor input for the control of locomotion.

Characterization of the atmospheric electrical environment near a corona ion-emitting source

Presence of high concentrations of corona ions in any air environment cause changes in the earth's natural dc e-field; while their interaction with airborne aerosols produce charged particles. The charged particles and ions are dispersed by wind, and depending on the prevailing meteorology, their presence can be observed several hundreds of metres from the ion source. This paper presents a study characterizing the electrical environment of a strong substantially constant source of corona ions (a high voltage electricity substation). Results of the study showed that corona ion and particle charge concentrations as well as their associated effect on the vertical dc e-field perturbations decreased with distance from the emitting source. Mean particle charge concentration in the air environment of the ion-emitting source (−1750±745 ions cm −3) was three times higher than that of an urban outdoor air and 17 times that of a mechanically ventilated room. Statistical investigation of possible associations between parameters showed strong associations ( R 2=74%, p<0.05) between particle charge and ion concentration; and 54% correlation between particle charge and magnitude of the vertical dc e-field (mean value of −285±51 V m −1). Although a source of ambient electrical charge, the electricity substation was not a significant generator of aerosol particles within the size range (0.02–1 μm) examined in this study.

Robotic Platform for Human Gait Analysis

A hydraulically actuated platform with 4-degrees of freedom (4-DOF) was designed to be able to apply velocity- or acceleration-controlled floor surface perturbations to freely walking human subjects. The apparatus was required to provide velocity-controlled translational perturbations over the floor surface, rotational perturbations about the ankle joint, and acceleration-controlled vertical translational perturbations. The apparatus was physically constructed, and tested by both measurements of dynamics and repeatability. Crossover of movement from one DOF to another was shown to be less than 1 mm or 0.5 degrees for all desired perturbations. Repeated perturbations were nearly identical with a standard deviation of less than 0.2 mm over translational axes. The application of the platform to human gait research was demonstrated with a protocol of midstance phase perturbations (n=8). For this, the platform controller was programmed to randomly select one out of three conditions: (1) no movement (control); (2) upward perturbation of 0.8 g, 50 mm, 300 ms after heel contact; (3) downward perturbation of 0.8 g, 50 mm, 300 ms after heel contact. In total, 90 trials (3 conditions x 30 repetitions) were recorded for each subject. By singling out the SOL EMG and normalizing and averaging over the subject population, it was shown that the upward and downward perturbations elicited at least two distinctive stereotypical reflex responses in the ankle extensors, opposite in sign. All subjects reported comfort with the apparatus and nobody fell.

Effects of Atmospheric Stability on Wave and Energy Propagation in the Troposphere

Abstract The very high frequency (VHF) middle and upper atmosphere radar radio acoustic sounding system (MU-RASS) in Shigaraki, Japan, is able to provide tropospheric virtual temperature data with high temporal resolution on the order of a few minutes. The objective of this paper is to test the usefulness of MU-RASS as a tool for examining high-frequency changes in atmospheric stability and its effects on wave and energy propagation. For this study, temperature and wind data below 8-km altitude during a 2-day campaign period in October 2001 were used. A long-lasting inversion layer at 3.5-km altitude dominated the observation period. Large vertical wind perturbations with periods of less than 30 min were observed inside this inversion layer. Wavelet analysis was used to identify the dominant wave period for calculating the wind and temperature variances. The temperature variance characteristics exhibited a combination of the horizontal and vertical wind variance characteristics. In conclusion, the high temporal resolution of the MU-RASS enabled the study of short time-scale wind and temperature perturbations. These perturbations were related to the atmospheric stability, wave propagation, and energy in the troposphere, demonstrating the usefulness of the MU-RASS for this kind of study.

Mesospheric dynamical changes induced by the solar proton events in October–November 2003

The Thermosphere Ionosphere Mesosphere Electrodynamic General Circulation Model (TIME‐GCM) was used to study the atmospheric dynamical influence of the solar protons that occurred in Oct–Nov 2003, the fourth largest period of solar proton events (SPEs) measured in the past 40 years. The highly energetic solar protons produced odd hydrogen (HOx) and odd nitrogen (NOy). Significant short‐lived ozone decreases (10–70%) followed these enhancements of HOx and NOy and led to a cooling of most of the lower mesosphere. Temperature changes up to ±2.6 K were computed as well as wind (zonal, meridional, vertical) perturbations up to 20–25% of the background winds as a result of the solar protons. The solar proton‐induced mesospheric temperature and wind perturbations diminished over a period of 4–6 weeks after the SPEs. The Joule heating in the mesosphere, induced by the solar protons, was computed to be relatively insignificant for these solar storms.

Hall Instability of Thin Weakly Ionized Stratified Keplerian Disks

The stratification-driven Hall instability in a weakly ionized polytropic plasma is investigated in the local approximation within an equilibrium Keplerian disk of a small aspect ratio. The leading order of the asymptotic expansions in the aspect ratio is applied to both equilibrium as well as the perturbation problems. The equilibrium disk with an embedded purely toroidal magnetic field is found to be stable to radial, and unstable to vertical short-wave perturbations. The marginal stability surface is found in the space of the local Hall and inverse plasma beta parameters, as well as the free parameter of the model which is related to the total current through the disk. To estimate the minimal values of the equilibrium magnetic field that leads to instability, the latter is constructed as a sum of a current free magnetic field and the simplest approximation for magnetic field created by a distributed electric current.

Evolution of Subjective Visual Vertical Perturbation After Stroke

Objective. The perception of visual verticality is often perturbed after stroke and might be an underlying component of imbalance. The aim of this study was to describe the evolution of visual vertical (VV) perturbation and to investigate the factors affecting it. Methods. Thirty patients with hemiplegia after a single hemispheric stroke (17 left lesioned [LL] and 13 right lesioned [RL]) were studied. Visual verticality was tested within 45 days of stroke, and then at 3 and 6 months. Subjects sat in a dark room and adjusted a luminous rod to the vertical position. The differences between patients’ adjustments and vertical were calculated. The effects on VV evolution of the side, size, type, and location of the lesion were tested. Results. Sixty percent of the recent stroke patients had an initial inaccurate perception of verticality, and 39% of these patients recovered during the 1st 3 months after stroke. The evolution of VV tilt depended on the side of the lesion (P = 0.01), with better recovery in LL patients. None of the other factors studied affected VV normalization. Conclusions. The poorer recovery of vertical perception after right-side stroke might be due to the predominant role of the right hemisphere in spatial cognition, and might be involved in the poorer recovery of balance after stroke in RL patients.

Gravity wave parameters and their seasonal variations derived from Na lidar observations at 23°S

The nightly and seasonal variability of gravity wave activity and spectra in the mesopause region are studied with 10 years of sodium lidar observations. From the linear layer density response to gravity wave forcing, the lidar data were analyzed to get the atmospheric density perturbations and their spectra. The atmospheric density perturbation, density variance for fluctuations with vertical scales between 2 and 10 km, and amplitudes of density perturbation spectra at m = 2π/8 km and 2π/4 km all exhibit large nightly variability as well as large seasonal variations, with the semiannual maxima occurring near the equinoxes. The mean RMS atmospheric density perturbation and the mean RMS horizontal wind perturbations over our site are 5.1% and 25 m/s, respectively. The growth lengths of the density perturbations in spring and autumn are lower than those in summer and winter, and the annual mean value is 38 km. The annual mean density shear variance is about 15 (%/km)2, and the maxima occur near the equinoxes. The mean Richardson number is about 1.0. The mean value of the RMS vertical wind perturbation is 0.85 m/s with a maximum occurring at the end of the year. The m spectra show power law shapes, and their range of variation is between −2.06 and −3.81 with an annual mean value of −2.93. The ω spectra also show power law shapes, and their range of variation is between −1.06 and −2.32, with an annual mean of −1.64. The mean amplitudes of density perturbation spectrum, Fa(m) (m = 2π/4 km), and of the horizontal wind fluctuation, Fu(m) (m = 2π/4 km), are 1.35(m/cycles) and 3 × 105(m2 s−2/(cycles/m)), respectively. The value of λz* averaged around autumn equinox is 14.8 km, which is lower than the value of 16.8 km, averaged around spring equinox. The annual mean of T* is 23.5 hours. The fact that the joint (m,ω) spectra are not separable, together with the large variability found in the m spectra slopes, is not compatible with linear instability theory but is compatible with Doppler spreading theories and diffusive filtering theory.

Forward Modeling of Acoustic Wave Propagation in the Quiet Solar Subphotosphere

The results of numerical simulations of acoustic wave propagation and dispersion in the nonmagnetic solar subphotosphere are presented. Initial equilibrium density and pressure stratifications are taken from a standard solar model but modified to suppress convective instabilities in fully compressible two-dimensional ideal hydrodynamical modeling. Acoustic waves are generated by sources located below the height corresponding to the visible solar surface. The dynamic response of the solar interior to two acoustic source types, namely a harmonic source and one representing downward-propagating photospheric plumes, is studied. A large number of randomly distributed localized cooling sources with random amplitudes is also introduced. The methods used to analyze the simulation data are similar to ones used in observational studies in local helioseismology. Time-distance diagrams of the pressure and vertical velocity perturbations at the level corresponding to the solar surface show the appearance of wave packets propagating with different speeds, which are reflected at different depths beneath the subphotosphere. The (ω, kh) power spectra, derived from the vertical velocity data, show the existence of g-, f-, and p-modes; p-mode ridges are identifiable up to high radial orders of n ≈ 11; g-modes appear in the simulations, unlike in the real Sun, where they cannot propagate in the convectively unstable solar subphotosphere. Cross-correlation analysis of vertical velocity perturbations shows a good correspondence with the observed time-distance helioseismic data for quiet Sun. Thus, the ability of the implemented approach of forward modeling to investigate propagation of acoustic, internal, and surface gravity waves in a realistic solar interior model is shown.

Understanding the structure of the turbulent mixing layer in hydrodynamic instabilities

When a heavy fluid is placed above a light fluid, tiny vertical perturbations in the interface create a characteristic structure of rising bubbles and falling spikes known as Rayleigh-Taylor instability. Rayleigh-Taylor instabilities have received much attention over the past half-century because of their importance in understanding many natural and man-made phenomena, ranging from the rate of formation of heavy elements in supernovae to the design of capsules for Inertial Confinement Fusion. We present a new approach to analyze Rayleigh-Taylor instabilities in which we extract a hierarchical segmentation of the mixing envelope surface to identify bubbles and analyze analogous segmentations of fields on the original interface plane. We compute meaningful statistical information that reveals the evolution of topological features and corroborates the observations made by scientists.

Understanding the Structure of the Turbulent Mixing Layer in Hydrodynamic Instabilities

When a heavy fluid is placed above a light fluid, tiny vertical perturbations in the interface create a characteristic structure of rising bubbles and falling spikes known as Rayleigh-Taylor instability. Rayleigh-Taylor instabilities have received much attention over the past half-century because of their importance in understanding many natural and man-made phenomena, ranging from the rate of formation of heavy elements in supernovae to the design of capsules for Inertial Confinement Fusion. We present a new approach to analyze Rayleigh-Taylor instabilities in which we extract a hierarchical segmentation of the mixing envelope surface to identify bubbles and analyze analogous segmentations of fields on the original interface plane. We compute meaningful statistical information that reveals the evolution of topological features and corroborates the observations made by scientists. We also use geometric tracking to follow the evolution of single bubbles and highlight merge/split events leading to the formation of the large and complex structures characteristic of the later stages. In particular we (i) Provide a formal definition of a bubble; (ii) Segment the envelope surface to identify bubbles; (iii) Provide a multi-scale analysis technique to produce statistical measures of bubble growth; (iv) Correlate bubble measurements with analysis of fields on the interface plane; (v) Track the evolution of individual bubbles over time. Our approach is based on the rigorous mathematical foundations of Morse theory and can be applied to a more general class of applications.

Bending and twisting instabilities of columnar elliptical vortices in a rotating strongly stratified fluid

In this paper, we investigate the three-dimensional stability of the Moore–Saffman elliptical vortex in a rotating stratified fluid. By means of an asymptotic analysis for long vertical wavelength perturbations and small Froude number, we study the effects of Rossby number, external strain, and ellipticity of the vortex on the stability of azimuthal modes m = 1 (corresponding to a bending instability) and m = 2 (corresponding to a twisting instability). In the case of a quasi-geostrophic fluid (small Rossby number), the asymptotic results are in striking agreement with previous numerical stability analyses even for vertical wavelengths of order one. For arbitrary Rossby number, the key finding is that the Rossby number has no effect on the domains of long-wavelength instability of these two modes: the two-dimensional or three-dimensional nature of the instabilities is controlled only by the background strain rate γ and by the rotation rate Ω of the principal axes of the elliptical vortex relative to the rotating frame of reference. For the m = 1 mode, it is shown that when Ω< −γ , the vortex is stable to any long-wavelength disturbances, when − γ< Ω 0, two-dimensional perturbations are most unstable, when 0 Ω<γ , long-wavelength three-dimensional disturbances are the most unstable, and finally when γ< Ω, short-wavelength three-dimensional perturbations are the most unstable. Similarly, the m = 2 instability is two-dimensional or three-dimensional depending only on γ and Ω, independent of the Rossby number. This means that if a long-wavelength three-dimensional instability exists for a given elliptical vortex in a quasi-geostrophic fluid, a similar instability should be observed for any other Rossby number, in particular for infinite Rossby number (strongly stratified fluids). This implies that the planetary rotation plays a minor role in the nature of the instabilities observed in rotating strongly stratified fluids. The present results for the azimuthal mode m = 1 suggest that the vortex-bending instabilities observed previously in quasi-geostrophic fluids (tall-column instability) and in strongly stratified fluids (zigzag instability) are fundamentally related.