Inertial Instability Research Articles

Nonlinear double-diffusive intrusions at the equator

Previous, linear analysis has suggested that observations of interleaving, quasi-horizontal layers in the equatorial oceans may be explained by double-diffusive or inertial instability. Here we describe an idealized, two-dimensional, numerical investigation of the nonlinear development of these instabilities, focusing almost exclusively on the double-diffusive case. We consider the mechanisms for equilibration and maintenance of the interleaving intrusions and perform a thorough sensitivity analysis. Nonlinearity arising from changes in diffusive regime is found to be more important than advective nonlinearity in promoting global equilibration. When variations in effective flux ratio are weak, local constraints prevent equilibration until large amplitudes are reached. When variations in flux ratio with density ratio are allowed, small-scale staircase and mesoscale intrusive instabilities coexist, leading to staircase-like intrusions with sharp, steppy interfaces. Solutions are found to equilibrate at between 3 and 13 times the amplitude where mean salinity gradients overturn. Cross-equatorial diffusivities between 20 and 400 m 2 s -1 are found in realistic cases with intrusion lengths of up to 40 km. A modified estimate of the effective cross-equatorial diffusivity based on a balance of lateral advection and vertical diffusion tends to overestimate the sensitivity to the mean horizontal and vertical gradients of salinity and underestimates the sensitivity to the vertical diffusivity but does give values within an order of magnitude of those derived from numerical experiments. For comparison, we give a single example of inertially driven interleaving layers which reach 190 km in length giving cross-equatorial heat fluxes four times larger than realistic doublediffusively driven cases. Although the inertial case is not considered in detail, we speculate that observed interleaving is more likely to be created by inertial than double-diffusive instability.

The West African Monsoon Dynamics. Part II: The “Preonset” and “Onset” of the Summer Monsoon

The arrival of the summer monsoon over West Africa has been documented by using daily gridded rainfall data and NCEP‐NCAR reanalyses during the period 1968‐90, and OLR data over the period 1979‐90. Two steps have been characterized through a composite approach: the preonset and the onset of the summer monsoon. The preonset stage corresponds to the arrival in the intertropical front (ITF) at 15 8N, that is, the confluence line between moist southwesterly monsoon winds and dry northeasterly Harmattan, bringing sufficient moisture for isolated convective systems to develop in the Sudano‐Sahelian zone while the intertropical convergence zone (ITCZ) is centered at 58N. The mean date for the preonset occurrence is 14 May and its standard deviation is 9.5 days during the period 1968‐90. This leads to a first clear increase of the positive rainfall slope corresponding to the beginning of the rainy season over this Sudano‐Sahelian area. The onset stage of the summer monsoon over West Africa is linked to an abrupt latitudinal shift of the ITCZ from a quasi-stationary location at 58N in May‐June to another quasi-stationary location at 108N in July‐August. The mean date for the onset occurrence is 24 June and its standard deviation is 8 days during the period 1968‐ 90. This leads to a second increase of the positive rainfall slope over the Sudano‐Sahelian zone signing the northernmost location of the ITCZ and the beginning of the monsoon season. This abrupt shift occurs mostly between 108W and 58E, where a meridional land‐sea contrast exists, and it is characterized by a temporary rainfall and convection decrease over West Africa. Preonset dates, onset dates, and summer rainfall amount over the Sahel are uncorrelated during the period 1968‐90. The atmospheric dynamics associated with the abrupt ITCZ shift has been investigated. Between the preonset and the onset stages, the heat low dynamics associated with the ITF controls the circulation in the low and midlevels. Its meridional circulation intensity is the highest at the beginning of the monsoon onset. This can lead to 1) increased convective inhibition in the ITCZ through intrusion of dry and subsiding air from the north, and 2) increased potential instability through a greater inland moisture advection and a higher monsoon depth induced by a stronger cyclonic circulation in the low levels, through higher vertical wind shear due to westerly monsoon wind and midlevel African easterly jet (AEJ) increases, through enhancement of the instability character of the AEJ, and through increased shortwave radiation received at the surface. During the monsoon onset, once the rainfall minimum occurred due to the convective inhibition, the accumulated potential instability breaks the convective inhibition, the inertial instability of the monsoon circulation is released, and the associated regionalscale circulation increases, leading to the abrupt shift of the ITCZ. Then the ITCZ moves north up to 108N, where thermodynamical conditions are favorable. It is suggested by the authors that the abrupt shift of the ITCZ, initiated by the amplification of the heat low dynamics, could be due to an interaction with the northern orography of the Atlas‐Ahaggar Mountains. Subsidence over and north of this orography, due to both the northern branches of the heat low and of the northern Hadleytype cell, contributes to enhance the high geopotentials north of these mountains and the associated northeasterly winds. This leads to the development of a leeward trough that reinforces the heat low dynamics, maintaining an active convective ITCZ through enhanced moist air advection from the ocean, increasing the northern Hadley circulation, which reinforces the high geopotentials and the interaction with the orography through a positive feedback. The fact that an abrupt shift of the ITCZ is only observed on the western part of West Africa may result from the enhancement of moisture advection, which comes from the west and has a stronger impact west of the Greenwich meridian. The northwest‐southeast orientation of the Atlas‐Ahaggar crest can induce the interaction with the heat low, first in the east where the mountains are nearer to the ITF than in the west, and second in the west. Another consequence of the possible orography-induced interaction with the atmospheric circulation is that the induced leeward trough, increasing the cyclonic vorticity in the heat low, may stimulate moisture convergence in the oceanic ITCZ near the western coast of West Africa.

Shear heating of a fluid‐saturated slip‐weakening dilatant fault zone: 2. Quasi‐drained regime

This paper analyzes slip on a fluid‐infiltrated dilatant fault for imposed (tectonic) strain rates much slower than the rate of fluid exchange between the gouge zone and the surroundings and for exchange of heat slower than of fluid, typical of interseismic or most laboratory loading conditions. The limiting solution, corresponding to the infinitely rapid drainage rate, developed in the companion paper by Garagash and Rudnicki [2003], yielded unbounded slip acceleration for sufficiently large slip weakening of the fault. Analysis for rapid but finite drainage rates (quasi‐drained condition) reveals two types of possible instability. The first is inertial instability (a seismic event) characterized by an unbounded slip rate and attributed to the destabilizing effects of shear heating and fault slip weakening. The second corresponds to loss of uniqueness and arises from the small pressure increase caused by shear heating for rapid but finite rates of drainage. This instability emerges for even small amounts of thermomechanical coupling and a large range of dilatancy and slip weakening. Its resolution probably requires a more elaborate frictional description (e.g., rate and state), but within the slip‐weakening framework here, leads to either slip arrest or inertial instability. The response is always unstable (in one of these two ways) for sufficiently large thermal coupling or initial stress regardless of the amount of slip weakening and dilatancy. The counterintuitive stabilizing effect of increased slip weakening or decreased dilatancy, similar to the effect in the companion paper, also occurs for nearly drained slip.

On the nonlinear evolution of columnar vortices in a rotating environment

We examine the three-dimensional, nonlinear evolution of columnar vortices in a rotating environment. As the initial vorticity distribution, a wavetrain of finite amplitude Kelvin-Helmholtz vortices in shear is employed. Through direct numerical simulation of the Navier-Stokes equations we seek to better understand the process of maturation of the various three-dimensional modes of instability to which such vortical flows are subject, especially those which exist as a consequence of the action of the Coriolis force. In the absence of rotational influence, we thereby demonstrate that the nonlinear evolution of columnar vortices is most strongly controlled by one or the other of two mechanisms. One mechanism of instability is identifiable as a so-called elliptical instability, which promotes the initial bending of vortex tubes in a sinusoidal fashion, while the other is a hyperbolic mode, which is responsible for the development of streamwise vortex streaks in the "braids" between adjacent vortex cores. In the rotating case, anticyclonic vortices are strongly destabilized by weak background rotation, while rapid rotation stabilizes both the cyclones and anticyclones. The strong anticyclones are subject to two distinct forms of instability, namely a Coriolis force modified elliptical instability and an inertial (centrifugal) instability. The former instability is very similar to the nonrotating form of the elliptical instability as it promotes bending of vortex tubes, while the latter instability grows on the edge of the vortex core and generates streaks of vorticity, which surround the vortex core itself. These results of direct numerical simulation fully verify the results of previous linear stability analyses. Taken together, they provide a simple explanation for the broken symmetry that is often observed to be characteristic of the von Karman vortex streets that develop in the atmospheric lee of oceanic islands.

Inertial instabilities of fluid flow in precessing spheroidal shells

As a model for the precession-driven motion in the Earth's core, the flow of incompressible fluid inside a spheroidal shell with imposed rotation and precession is investigated by direct numerical simulation. In one set of simulations, free-slip boundary conditions are used in order to isolate inertial instabilities. These occur as triad resonances involving pairs of inertial modes which have the form of columnar vortices. The simulations reproduce the phenomenon of ‘resonant collapses’ in which the excited modes periodically grow and suddenly decay into turbulence. The experiments of Malkus (1968) are simulated using a hyperviscosity. A hysteretic transition towards developed turbulence observed in one of these experiments can be interpreted as a feature of the basic laminar flow rather than the instability itself. A similar transition can be excluded for Earth's parameters.

Lateral mixing in the equatorial Pacific: The importance of inertial instability

Mixing in the ocean plays a key role in the ocean's dynamics and thermodynamics and how the ocean interacts with the atmosphere. Here we focus on lateral mixing in the equatorial ocean, and in particular the part played by inertial instability. We demonstrate the effectiveness of the instability in promoting mixing in the equatorial thermocline, that is sufficient to affect the large scale structure of the equatorial ocean, and which rectifies problems in existing ocean models. The spatial and temporal variability of the process is likely to impinge on interannual variations of the ocean and El Niño.

Baroclinic characteristics of frictionally destabilized abyssal overflows

Observations show that the near-sill dynamics of dense abyssal overflows is variable and is governed, to a significant extent, by a balance between rotation, bottom friction and downslope acceleration due to gravity. Numerical simulations indicate that the near-sill downslope velocities are comparable to the phase/group velocities of long internal gravity waves. This suggests the possibility that overflows can become supercritical and destabilized by bottom friction. A theory is presented for the frictional destabilization of rotating abyssal overflows and the accompanying baroclinic coupling with the overlying ocean. This mode of transition allows for the formation of downslope and alongslope propagating periodic bores or pulses in the overflow and the generation of amplifying long internal gravity waves in the overlying ocean, and may help to explain aspects of the observed variability which seem unrelated to purely inertial baroclinic instability.

Workshop Findings

This report outlines scientific issues whose resolution will help advance and define the field of multiphase flow. It presents the findings of four study groups and of a workshop sponsored by the Program on Engineering Physics of the Department of Energy. The reason why multiphase flows are much more difficult to analyze than single phase flows is that the phases assume a large number of complicated configurations. Therefore, it should not be surprising that the understanding of why the phases configure in a certain way is the principal scientific issue. Research is needed which identifies the microphysics controlling the organization of the phases, which develops physical models for the resultant multiscale interactions and which tests their validity in integrative experiments/theories that look at the behavior of a system. New experimental techniques and recently developed direct numerical simulations will play important roles in this endeavor. In gas–liquid flows a top priority is to develop an understanding of why the liquid phase in quasi-fully-developed pipe flow changes from one configuration to another. Mixing flows offer a more complicated situation in which several patterns can exist at the same time. They introduce new physical challenges. A second priority is to provide a quantitative description of the phase distribution for selected fully developed flows and for simple mixing flows (that could include heat transfer and phase change). Microphysical problems of interest are identified––including the coupling of molecular and macroscopic behavior that can be observed in many situations and the formation/destruction of interfaces in the coalescence/breakup of drops and bubbles. Solid–fluid flows offer a simpler system in that interfaces are not changing. However, a variety of patterns exist, that depend on the properties of the particles, their concentration and the Reynolds number characterizing the relative velocity. A top priority is the development of a physical understanding of inertial instabilities which give rise to structural features that have a large range of scales. Important microphysical problems are the understanding of particle/particle interactions, particle/boundary interactions that include the effect of wall roughness, and the influence of particles on fluid turbulence. These behaviors can differ depending on the characteristics of the particles, their size distribution and their concentration. For large concentrations, such as exist in granular flows, instabilities associated with particle–particle interactions often cause separations in systems which are not homogeneous. These instabilities are not well understood. Appropriate averaged equations could provide a way to use an understanding of the microphysics obtained in simple systems to describe more complicated flows. The formulation of these equations presents physical challenges since the structure of the phase distribution could affect the choice of averaging methods and closure relations. Universal computational approaches appear to be out of reach at present.

Inertial instability flow in the troposphere over Suriname during the South American Monsoon

Weekly sonde observations in Suriname, supported by ECMWF analyses and a linear stability analysis, are used to analyze the recurrence of inertial instability as the ITCZ migrates over land during the South American Monsoon. A layer of cool moist air from the Atlantic Ocean is then advected southward over Suriname in the shape of a cold front, displacing the warmer air over the continent. The return flow northward, by the upper branch of the Hadley cell, is a region where inertial instability pervades due to cross‐equatorial advection of anticyclonic vorticity and the proximity of the subtropical jet as it migrates closer to the Equator. This unstable region evidently leads to the episodical formation of a meridional sub‐cell below the tropopause, where the damping is calculated to be strong enough to stabilize flow at smaller vertical scales, and yet weak enough to allow the observed cell recurrence ‐ at approximately the inertial frequency of the underlying latitudes. This instability should also contribute to the Hadley cell formation through northward acceleration in the upper branch. The moist saturated conditions in the lower troposphere do allow inertial instability here, but the high damping values within the boundary layer suggests that the observed southward acceleration in the lower branch of the Hadley cell has a cause other than inertial instability.

Nonlinear Vertical Scale Selection in Equatorial Inertial Instability

Abstract The zonal flows of the earth's equatorial stratosphere and mesosphere are prone to inertial instability when the horizontal shear Λ ≠ 0 at the equator. However, it is not clear why the vertical wavelength of the observed structures is much greater than that predicted by the simple linear theory, based on a vertical scale selection by molecular diffusion. Here, a nonlinear mechanism is described that can lead to upscaling from structures with short vertical wavelengths to long vertical wavelengths. The mechanism is dependent upon a secondary Kelvin–Helmholtz instability that develops as the inertial instability grows. Numerical simulations on an equatorial β plane, employing a simple parameterization of the vertical transport of horizontal momentum due to the secondary instability, are used to assess the likely degree of upscaling in a zonally symmetric system. For a fluid with buoyancy frequency N, it is shown that upscaling toward the buoyancy cutoff wavenumber 4Nβ/Λ2 can occur, even when diffus...

Potential of inertial instabilities for fuel film separation in port fuel injection engine conditions

Potential of inertial instabilities for fuel film separation in port fuel injection engine conditions

Potential of inertial instabilities for fuel film separation in port fuel injection engine conditions

In port fuel injection engines, the liquid fuel film accumulated in the vicinity of intake valves is torn away and goes into the cylinder during the intake phase. In order to predict the fuel mixture preparation inside the cylinder, a model for the fuel film separation near the sharp edges of the intake valves has been developed. A separation criterion is set up using an analogy with Rayleigh-Taylor instabilities driven by the inertial forces of the film. The critical value for the separation criterion is adjusted using experimental data obtained in a two-dimensional wind tunnel fitted with different steps shaped as the valve seat and reproducing the main characteristics of the intake of a spark ignition engine. Computational fluid dynamics simulations are performed using the KMB code, a modified version of KIVA-2 already including a film model and a stochastic Lagrangian description of the spray. Computation for the intake stroke on a four-cylinder 1.9 litre port fuel injection engine confirms that the fuel droplets are not completely vaporized at the end of the intake stroke.

The nonlinear evolution of zonally symmetric equatorial inertial instability

The inertial instability of equatorial shear flows is studied, with a view to understanding observed phenomena in the Earth's stratosphere and mesosphere. The basic state is a zonal flow of stratified fluid on an equatorial β-plane, with latitudinal shear. The simplest self-consistent model of the instability is used, so that the basic state and the disturbances are zonally symmetric, and a vertical diffusivity provides the scale selection. We study the interaction between the inertial instability, which takes the form of periodically varying disturbances in the vertical, and the mean flow, where ‘mean’ is a vertical mean.The weakly nonlinear regime is investigated analytically, for flows with an arbitrary dependence on latitude. An amplitude equation of the form dA/dt = A−k2A∫[mid ]A[mid ]2dt is derived for the disturbances, and the evolving stability properties of the mean flow are discussed. In the final steady state, the disturbances vanish, but there is a persistent mean flow change that stabilizes the flow. However, the magnitude of the mean flow change depends strongly on the initial conditions, so that the system has a long memory. The analysis is extended to include the effects of Rayleigh friction and Newtonian cooling, destroying the long-memory property.A more strongly nonlinear regime is investigated with the help of numerical simulations, extending the results up to the point where the instability leads to density contour overturning. The instability is shown to lead to a homogenization of fQ¯ around the initially unstable region, where f is the Coriolis parameter, and Q¯ is the vertical mean of the potential vorticity. As the instability evolves, the line of zero Q¯ moves polewards, rather than equatorwards as might be expected from a simple self-neutralization argument.

Inertial Instability of Arbitrarily Meandering Currents Governed by the Eccentrically Cyclogeostrophic Equation

Using natural coordinates, we have derived a criterion for the inertial instability of arbitrarily meandering currents. Such currents, governed by the eccentrically cyclogeostrophic equation, are adopted as the basic current field for the parcel method. We assume that any virtual displacement which is given to a water parcel moving in the basic field has no influence on this field. From the conservation of mechanical energy for a virtual displacement we derive an inertial instability frequency ω m = [(f + 2u/r)Z]0.5 for the eccentrically cyclogeostrophic current, where f is the Coriolis parameter, u the velocity (always positive), r the radius of curvature of a streamline (negative for an anticyclonic meander), and Z the vertical component of absolute vorticity. If ω m 2 is negative, the eccentrically cyclogeostrophic current becomes unstable. Although the conventional, centrifugal instability criterion, derived from the conservation of angular momentum in a circularly symmetric current field, has a certain meaning for a monopolar vortex, it contains a radial shear vorticity that is difficult to use in arbitrarily meandering currents. The new criterion ω m 2 contains a lateral shear vorticity that is applicable to arbitrarily meandering currents. Examining instabilities of concentric rings with radii of 50–100 km, we consider reasons why the anticyclonic supersolid rotation has been very much less frequently observed than the cyclonic supersolid rotation, despite a prediction of some common stability and a rapid change in radial velocity gradient for the former. Classifying eccentric streamlines into the large and small curvature-gradient types, we point out that the large-gradient curvature in anticyclonic rings is apt to be unstable.

Characteristics of interleaving in the western equatorial Pacific

The characteristics of intrusive thermohaline features in the thermocline of the western equatorial Pacific are examined during two different climatic states. The vertical and meridional structure of the features is determined from a total of 12 high‐resolution meridional sections. Although there is considerable variability of the broader structure of the flow and temperature/salinity fields, the spatial scale of the interleaving is found to be persistent over all sections. The Turner angle and correlations between the spice anomaly and density anomaly suggest that double‐diffusive processes may be important in the vertical flux of properties. The characteristics of the interleaving are compared with the results from the theories of double‐diffusive interleaving and inertial instability. It is found that the observations are consistent with both. It is difficult to differentiate between the two theories in explaining the presence of the layers. Indeed, both mechanisms may be playing a role. The magnitude of the cross‐equatorial fluxes of heat and salt due to the features is estimated and shown to be comparable with estimates due to other processes. There is a strong potential for the interleaving to impinge on the large‐scale dynamics of the equatorial Pacific Ocean.

Inertial instability and sea spirals

The ubiquitous occurrence of submesoscale cyclonic spirals in the sea as inferred from space imagery is interpreted in terms of the inertial instability of a horizontally sheared current in the oceanic mixed layer. The instability is shown to weaken anticyclonic current shear while enhancing cyclonic shear, which, in turn, becomes unstable and creates a cyclonic vortex; concurrently, surface tracer particles concentrated along the evolving cyclonic shear are wound up into a spiral, mimicking the spiral slick patterns seen in the imagery. The entire process, investigated with a fully nonlinear nonhydrostatic 3D numerical model, is contrasted with the baroclinic frontal process considered previously. The differences point to a clear need for field observations of this significant phenomenon, which are presently almost totally lacking.

A minimal axisymmetric hurricane model

AbstractSolutions of an axisymmetric version of the minimal three‐dimensional numerical model of a tropical cyclone developed by Zhu et al. (2001) are described and compared with those of the three‐dimensional model. Vortex evolution is similar in the two models during the early stages of intensification, but the period of rapid intensification occurs earlier in the axisymmetric model due to the higher effective resolution obtained using a staggered grid. There are marked differences at later times, when, in the three‐dimensional model, asymmetric structures develop. The findings are compared with those of an earlier study by Anthes (1972).The axisymmetric model is used to investigate certain fundamental aspects of tropical‐cyclone dynamics, including the emergence of a region of supergradient winds in the boundary layer and the evolution of regions satisfying necessary conditions for inertial and barotropic instability. Supergradient winds develop in the boundary layer within a radius of about 100 km of the vortex axis at an early stage of evolution and appear to be a natural feature of the vortex boundary layer. The development of flow regions satisfying necessary conditions for inertial and barotropic instability occur later, and may be attributed inter alia to the upward transfer of air with relatively high angular momentum, from the boundary layer to the middle and upper layers, by the secondary circulation of the vortex, and the downward transfer of air with relatively low angular momentum to the middle layer. A linear analysis of a two‐layer slab‐symmetric flow suggests why inertial instability does not occur in the axisymmetric model. Barotropic instability does not appear to be the mechanism responsible for the growth of asymmetries in the calculations using the three‐dimensional version of the model. Copyright © 2002 Royal Meteorological Society.

Layered Structure Associated with Low Potential Vorticity near the Tropopause Seen in High-Resolution Radiosondes over Japan

Horizontal wind and temperature data obtained from operational radiosondes over Japan have recently been available with high vertical resolution. Analyzing these data over 4 yr has indicated horizontal velocity layers with vertical scales of about 5 km lasting for a week or more. The layers appear frequently in winter at several stations simultaneously and are dominant in the height range of 8‐16 km. An empirical orthogonal function (EOF) analysis for the time series of layered disturbance amplitude in winter indicates that there are two dominant principal components. The first component (EOF1) describes layered disturbances in the middle of Japan (308‐ 378N) and the second one (EOF2) describes disturbances in the south of Japan (238‐308N). Using global analysis data, the background field of the layered disturbances was examined. An interesting result is that the background potential vorticity (PV) is approximately zero or negative for EOF2 disturbances even though located in a relatively high-latitude region. This fact suggests that the EOF2 disturbances are due to inertial instability. It is also shown that negative PV occurs more than 30% of the time in winter, in a zonally elongated region of 238‐ 298N in the western Pacific, on an isentropic surface of 345 K (;10 km altitude). Such a high frequency of negative PV is not observed at other longitudes in this latitude band. To determine the origin of the anomalous PV, backward trajectories were analyzed. For EOF2 disturbances, air parcels having mostly negative PV are traced back to the equatorial region in the longitude band 208W‐1408E within a few days. This is due to a strong northward branch of the Hadley circulation associated with deep convection over the Maritime Continent and a strong northeastward subtropical jet stream. On the other hand, the background PV is low but scarcely negative for EOF1 disturbances. Air parcels at EOF1 stations are traced back to the far west because they are advected mostly by a strong eastward jet stream. Thus, it is inferred that the EOF1 disturbances may be due to inertia‐gravity waves trapped in a duct of the westerly jet core.

Horizontal wind disturbances induced by inertial instability in the equatorial middle atmosphere as seen in rocketsonde observations

Rocketsonde observations at Kwajalein (8.7°N, 167.7°E) were used for investigation of horizontal wind disturbances induced by inertial instability. Two characteristic cases were found in the 1978–1979 northern winter during which the limb infrared monitor of the stratosphere (LIMS) made observations. In both the cases the eastward component and the northward component of horizontal winds are negatively correlated in the vertical direction near the stratopause level, which is thought to be due to inertial instability. The wind disturbances have a wavelength of about 10 km, and their maximum amplitudes are estimated as over 10 ms−1. Examinations of the LIMS temperatures support a possibility that the wind disturbances are induced by inertial instability. It was revealed that temperature disturbances characteristic of inertial instability, called “pancake structures,” appear in the same height and time as the wind disturbances do. The relationship between the rocketsonde wind disturbances and the LIMS pancake structures is 90° out of phase, as expected by the theory of inertial instability. In addition, it was confirmed that the two inertial instability events follow enhancements of the midlatitude planetary wave. This is consistent with a mechanism of the inertially unstable disturbances in the equatorial region inferred in some observational and numerical studies. Analyses of rocketsonde data were extended to the entire observation period at Kwajalein, which suggests that the occurrence of inertially unstable disturbances is biased toward the winter season. However, at some other stations in the tropics, wind disturbances which may be induced by inertial instability do not appear so frequently as they do at Kwajalein. This seasonality and regionality of inertially unstable disturbances would be due to the seasonality and regionality of planetary wave breakings at midlatitude.

Kelvin waves in stratospheric temperature observed by the Microwave Limb Sounder

The three‐dimensional (3‐D) structure of stratospheric Kelvin waves is revealed using data from the Microwave Limb Sounder for the period July 1992 to April 1993. Four Kelvin wave modes are identified, two for zonal wave number 1 (k = 1) and two for k = 2, using extended empirical orthogonal functions. The 3‐D structures of the modes agree with linear theory and satisfy the dispersion relation for Kelvin waves, and with periods ranging from 4.5 to 10 days the modes mostly fall near the boundary between “fast” and “slow” Kelvin waves [Canziani et al., 1998]. The analysis also identifies a feature that may correspond with the “pancake structures” associated with inertial instability.