## Abstract

This study investigates gravity wave generation and propagation from jets within idealized vortex dipoles using a nonhydrostatic mesoscale model. Two types of initially balanced and localized jets induced by vortex dipoles are examined here. These jets have their maximum strength either at the surface or in the middle levels of a uniformly stratified atmosphere. Within these dipoles, inertia–gravity waves with intrinsic frequencies 1–2 times the Coriolis parameter are simulated in the jet exit region. These gravity waves are nearly phase locked with the jets as shown in previous studies, suggesting spontaneous emission of the waves by the localized jets. A ray tracing technique is further employed to investigate the propagation effects of gravity waves. The ray tracing analysis reveals strong variation of wave characteristics along ray paths due to variations (particularly horizontal variations) in the propagating environment.

The dependence of wave amplitude on the jet strength (and thus on the Rossby number of the flow) is examined through experiments in which the two vortices are initially separated by a large distance but subsequently approach each other and form a vortex dipole with an associated amplifying localized jet. The amplitude of the stationary gravity waves in the simulations with 90-km grid spacing increases as the square of the Rossby number (Ro), when Ro falls in a small range of 0.05–0.15, but does so significantly more rapidly when a smaller grid spacing is used.

## Abstract

This study investigates gravity wave generation and propagation from jets within idealized vortex dipoles using a nonhydrostatic mesoscale model. Two types of initially balanced and localized jets induced by vortex dipoles are examined here. These jets have their maximum strength either at the surface or in the middle levels of a uniformly stratified atmosphere. Within these dipoles, inertia–gravity waves with intrinsic frequencies 1–2 times the Coriolis parameter are simulated in the jet exit region. These gravity waves are nearly phase locked with the jets as shown in previous studies, suggesting spontaneous emission of the waves by the localized jets. A ray tracing technique is further employed to investigate the propagation effects of gravity waves. The ray tracing analysis reveals strong variation of wave characteristics along ray paths due to variations (particularly horizontal variations) in the propagating environment.

The dependence of wave amplitude on the jet strength (and thus on the Rossby number of the flow) is examined through experiments in which the two vortices are initially separated by a large distance but subsequently approach each other and form a vortex dipole with an associated amplifying localized jet. The amplitude of the stationary gravity waves in the simulations with 90-km grid spacing increases as the square of the Rossby number (Ro), when Ro falls in a small range of 0.05–0.15, but does so significantly more rapidly when a smaller grid spacing is used.

## Abstract

After reviewing the background, this article discusses the recently discovered examples of hybrid propagating structures consisting of vortex dipoles and comoving gravity waves undergoing wave capture. It is shown how these examples fall outside the scope of the Lighthill theory of spontaneous imbalance and, concomitantly, outside the scope of shallow-water dynamics. Besides the fact that going from shallow-water to continuous stratification allows disparate vertical scales—small for inertia–gravity waves and large for vortical motion—the key points are 1) that by contrast with cases covered by the Lighthill theory, the wave source feels a substantial radiation reaction when Rossby numbers *R* ≳ 1, so that the source cannot be prescribed in advance; 2) that examples of this sort may supply exceptions to the general rule that spontaneous imbalance is exponentially small in *R*; and 3) that unsteady vortical motion in continuous stratification can stay close to balance thanks to three quite separate mechanisms. These are as follows: first, the near-suppression, by the Lighthill mechanism, of large-scale imbalance (inertia–gravity waves of large horizontal scale), where “large” means large relative to a Rossby deformation length *L _{D}* characterizing the vortical motion; second, the flaccidity, and hence near-steadiness, of

*L*-wide jets that meander and form loops, Gulf-Stream-like, on streamwise scales ≫

_{D}*L*; and third, the dissipation of small-scale imbalance by wave capture leading to wave breaking, which is generically probable in an environment of random shear and straining. Shallow-water models include the first two mechanisms but exclude the third.

_{D}## Abstract

After reviewing the background, this article discusses the recently discovered examples of hybrid propagating structures consisting of vortex dipoles and comoving gravity waves undergoing wave capture. It is shown how these examples fall outside the scope of the Lighthill theory of spontaneous imbalance and, concomitantly, outside the scope of shallow-water dynamics. Besides the fact that going from shallow-water to continuous stratification allows disparate vertical scales—small for inertia–gravity waves and large for vortical motion—the key points are 1) that by contrast with cases covered by the Lighthill theory, the wave source feels a substantial radiation reaction when Rossby numbers *R* ≳ 1, so that the source cannot be prescribed in advance; 2) that examples of this sort may supply exceptions to the general rule that spontaneous imbalance is exponentially small in *R*; and 3) that unsteady vortical motion in continuous stratification can stay close to balance thanks to three quite separate mechanisms. These are as follows: first, the near-suppression, by the Lighthill mechanism, of large-scale imbalance (inertia–gravity waves of large horizontal scale), where “large” means large relative to a Rossby deformation length *L _{D}* characterizing the vortical motion; second, the flaccidity, and hence near-steadiness, of

*L*-wide jets that meander and form loops, Gulf-Stream-like, on streamwise scales ≫

_{D}*L*; and third, the dissipation of small-scale imbalance by wave capture leading to wave breaking, which is generically probable in an environment of random shear and straining. Shallow-water models include the first two mechanisms but exclude the third.

_{D}## Abstract

The gravity wave (GW)–resolving capabilities of 118-GHz saturated thermal radiances acquired throughout the stratosphere by the Microwave Limb Sounder (MLS) on the *Aura* satellite are investigated and initial results presented. Because the saturated (optically thick) radiances resolve GW perturbations from a given altitude at different horizontal locations, variances are evaluated at 12 pressure altitudes between ∼21 and 51 km using the 40 saturated radiances found at the bottom of each limb scan. Forward modeling simulations show that these variances are controlled mostly by GWs with vertical wavelengths *λ _{z}* > 5 km and horizontal along-track wavelengths of

*λ*∼ 100–200 km. The tilted cigar-shaped three-dimensional weighting functions yield highly selective responses to GWs of high intrinsic frequency that propagate toward the instrument. The latter property is used to infer the net meridional component of GW propagation by differencing the variances acquired from ascending (A) and descending (D) orbits. Because of improved vertical resolution and sensitivity,

_{y}*Aura*MLS GW variances are ∼5–8 times larger than those from the

*Upper Atmosphere Research Satellite*(

*UARS*) MLS. Like

*UARS*MLS variances, monthly-mean

*Aura*MLS variances in January and July 2005 are enhanced when local background wind speeds are large, due largely to GW visibility effects. Zonal asymmetries in variance maps reveal enhanced GW activity at high latitudes due to forcing by flow over major mountain ranges and at tropical and subtropical latitudes due to enhanced deep convective generation as inferred from contemporaneous MLS cloud-ice data. At 21–28-km altitude (heights not measured by the UARS MLS), GW variance in the tropics is systematically enhanced and shows clear variations with the phase of the quasi-biennial oscillation, in general agreement with GW temperature variances derived from radiosonde, rocketsonde, and limb-scan vertical profiles. GW-induced temperature variances at ∼44-km altitude derived from operational global analysis fields of the ECMWF Integrated Forecast System in August 2006 reveal latitudinal bands of enhanced GW variance and preferred GW meridional propagation directions that are similar to those inferred from the MLS variances, highlighting the potential of MLS GW data for validating the stratospheric GWs simulated and/or parameterized in global models.

## Abstract

The gravity wave (GW)–resolving capabilities of 118-GHz saturated thermal radiances acquired throughout the stratosphere by the Microwave Limb Sounder (MLS) on the *Aura* satellite are investigated and initial results presented. Because the saturated (optically thick) radiances resolve GW perturbations from a given altitude at different horizontal locations, variances are evaluated at 12 pressure altitudes between ∼21 and 51 km using the 40 saturated radiances found at the bottom of each limb scan. Forward modeling simulations show that these variances are controlled mostly by GWs with vertical wavelengths *λ _{z}* > 5 km and horizontal along-track wavelengths of

*λ*∼ 100–200 km. The tilted cigar-shaped three-dimensional weighting functions yield highly selective responses to GWs of high intrinsic frequency that propagate toward the instrument. The latter property is used to infer the net meridional component of GW propagation by differencing the variances acquired from ascending (A) and descending (D) orbits. Because of improved vertical resolution and sensitivity,

_{y}*Aura*MLS GW variances are ∼5–8 times larger than those from the

*Upper Atmosphere Research Satellite*(

*UARS*) MLS. Like

*UARS*MLS variances, monthly-mean

*Aura*MLS variances in January and July 2005 are enhanced when local background wind speeds are large, due largely to GW visibility effects. Zonal asymmetries in variance maps reveal enhanced GW activity at high latitudes due to forcing by flow over major mountain ranges and at tropical and subtropical latitudes due to enhanced deep convective generation as inferred from contemporaneous MLS cloud-ice data. At 21–28-km altitude (heights not measured by the UARS MLS), GW variance in the tropics is systematically enhanced and shows clear variations with the phase of the quasi-biennial oscillation, in general agreement with GW temperature variances derived from radiosonde, rocketsonde, and limb-scan vertical profiles. GW-induced temperature variances at ∼44-km altitude derived from operational global analysis fields of the ECMWF Integrated Forecast System in August 2006 reveal latitudinal bands of enhanced GW variance and preferred GW meridional propagation directions that are similar to those inferred from the MLS variances, highlighting the potential of MLS GW data for validating the stratospheric GWs simulated and/or parameterized in global models.

## Abstract

Intensive radiosonde observations were performed at Syowa Station (69.0°S, 39.6°E) over about 10 days in each of March, June, October, and December 2002 to examine inertia–gravity wave characteristics in the Antarctic lower stratosphere. Based on the 3-hourly observation data, two-dimensional (i.e., vertical wavenumber versus frequency) spectra of wind fluctuations were examined, utilizing a double Fourier transform method. Clear signals of gravity waves whose phases propagate upward, suggesting downward energy propagation, are detected in June and October when the polar night jet (PNJ) was present. On the other hand, downward phase propagation (i.e., upward energy propagation) components are dominant in all months. There is a spectral peak around the inertial frequency in a wide range of vertical wavenumbers in December when the background wind was weak, whereas large spectral densities are distributed over lower-frequency regions in June and October. These spectral characteristics are consistent with the results obtained using a gravity wave–resolving global circulation model (GCM) by Sato et al. Dynamical characteristics are examined separately for upward- and downward-propagating gravity waves in June, using a hodograph analysis method. As a result, it is found that upward- and downward-propagating wave packets observed simultaneously in the same height regions have similar horizontal wavelengths and phase velocities. This fact suggests that these gravity waves are generated from the same source with a similar mechanism. When the wave packets were observed, both the local Rossby number and the residual in the nonlinear balance equation estimated using NCEP–NCAR reanalysis data are large around the PNJ situated slightly to the lower latitudes of Syowa Station. Therefore, it is likely that the observed inertia–gravity waves are generated by a spontaneous adjustment around the geostrophically unbalanced PNJ and propagate toward Syowa Station. The possibility of spontaneous gravity wave generation around the PNJ is confirmed by comparison with the GCM simulation by Sato et al.

## Abstract

Intensive radiosonde observations were performed at Syowa Station (69.0°S, 39.6°E) over about 10 days in each of March, June, October, and December 2002 to examine inertia–gravity wave characteristics in the Antarctic lower stratosphere. Based on the 3-hourly observation data, two-dimensional (i.e., vertical wavenumber versus frequency) spectra of wind fluctuations were examined, utilizing a double Fourier transform method. Clear signals of gravity waves whose phases propagate upward, suggesting downward energy propagation, are detected in June and October when the polar night jet (PNJ) was present. On the other hand, downward phase propagation (i.e., upward energy propagation) components are dominant in all months. There is a spectral peak around the inertial frequency in a wide range of vertical wavenumbers in December when the background wind was weak, whereas large spectral densities are distributed over lower-frequency regions in June and October. These spectral characteristics are consistent with the results obtained using a gravity wave–resolving global circulation model (GCM) by Sato et al. Dynamical characteristics are examined separately for upward- and downward-propagating gravity waves in June, using a hodograph analysis method. As a result, it is found that upward- and downward-propagating wave packets observed simultaneously in the same height regions have similar horizontal wavelengths and phase velocities. This fact suggests that these gravity waves are generated from the same source with a similar mechanism. When the wave packets were observed, both the local Rossby number and the residual in the nonlinear balance equation estimated using NCEP–NCAR reanalysis data are large around the PNJ situated slightly to the lower latitudes of Syowa Station. Therefore, it is likely that the observed inertia–gravity waves are generated by a spontaneous adjustment around the geostrophically unbalanced PNJ and propagate toward Syowa Station. The possibility of spontaneous gravity wave generation around the PNJ is confirmed by comparison with the GCM simulation by Sato et al.

## Abstract

This paper provides a brief review of recent results on decoupling of fast [inertia–gravity wave (IGW)] and slow (vortex) motions at small Rossby numbers obtained in the framework of the geostrophic adjustment of localized perturbations. Special attention is paid to the IGW emission and its interpretation in the context of “spontaneous imbalance.” Several mechanisms that lead to spontaneous IGW emission and, thus, to violations of fast–slow splitting at large Rossby numbers are reviewed: Lighthill radiation, symmetric/inertial instability, and ageostrophic shear (Rossby–Kelvin) instability. New results on the saturation of symmetric instability and on the existence of Rossby–Kelvin instability in continuously stratified fluid are presented.

## Abstract

This paper provides a brief review of recent results on decoupling of fast [inertia–gravity wave (IGW)] and slow (vortex) motions at small Rossby numbers obtained in the framework of the geostrophic adjustment of localized perturbations. Special attention is paid to the IGW emission and its interpretation in the context of “spontaneous imbalance.” Several mechanisms that lead to spontaneous IGW emission and, thus, to violations of fast–slow splitting at large Rossby numbers are reviewed: Lighthill radiation, symmetric/inertial instability, and ageostrophic shear (Rossby–Kelvin) instability. New results on the saturation of symmetric instability and on the existence of Rossby–Kelvin instability in continuously stratified fluid are presented.

## Abstract

This paper describes laboratory observations of inertia–gravity waves emitted from balanced fluid flow. In a rotating two-layer annulus experiment, the wavelength of the inertia–gravity waves is very close to the deformation radius. Their amplitude varies linearly with Rossby number in the range 0.05–0.14, at constant Burger number (or rotational Froude number). This linear scaling challenges the notion, suggested by several dynamical theories, that inertia–gravity waves generated by balanced motion will be exponentially small. It is estimated that the balanced flow leaks roughly 1% of its energy each rotation period into the inertia–gravity waves at the peak of their generation.

The findings of this study imply an inevitable emission of inertia–gravity waves at Rossby numbers similar to those of the large-scale atmospheric and oceanic flow. Extrapolation of the results suggests that inertia–gravity waves might make a significant contribution to the energy budgets of the atmosphere and ocean. In particular, emission of inertia–gravity waves from mesoscale eddies may be an important source of energy for deep interior mixing in the ocean.

## Abstract

This paper describes laboratory observations of inertia–gravity waves emitted from balanced fluid flow. In a rotating two-layer annulus experiment, the wavelength of the inertia–gravity waves is very close to the deformation radius. Their amplitude varies linearly with Rossby number in the range 0.05–0.14, at constant Burger number (or rotational Froude number). This linear scaling challenges the notion, suggested by several dynamical theories, that inertia–gravity waves generated by balanced motion will be exponentially small. It is estimated that the balanced flow leaks roughly 1% of its energy each rotation period into the inertia–gravity waves at the peak of their generation.

The findings of this study imply an inevitable emission of inertia–gravity waves at Rossby numbers similar to those of the large-scale atmospheric and oceanic flow. Extrapolation of the results suggests that inertia–gravity waves might make a significant contribution to the energy budgets of the atmosphere and ocean. In particular, emission of inertia–gravity waves from mesoscale eddies may be an important source of energy for deep interior mixing in the ocean.

## Abstract

A new method of clear-air turbulence (CAT) forecasting based on the Lighthill–Ford theory of spontaneous imbalance and emission of inertia–gravity waves has been derived and applied on episodic and seasonal time scales. A scale analysis of this shallow-water theory for midlatitude synoptic-scale flows identifies advection of relative vorticity as the leading-order source term. Examination of leading- and second-order terms elucidates previous, more empirically inspired CAT forecast diagnostics. Application of the Lighthill–Ford theory to the Upper Mississippi and Ohio Valleys CAT outbreak of 9 March 2006 results in good agreement with pilot reports of turbulence. Application of Lighthill–Ford theory to CAT forecasting for the 3 November 2005–26 March 2006 period using 1-h forecasts of the Rapid Update Cycle (RUC) 2 1500 UTC model run leads to superior forecasts compared to the current operational version of the Graphical Turbulence Guidance (GTG1) algorithm, the most skillful operational CAT forecasting method in existence. The results suggest that major improvements in CAT forecasting could result if the methods presented herein become operational.

## Abstract

A new method of clear-air turbulence (CAT) forecasting based on the Lighthill–Ford theory of spontaneous imbalance and emission of inertia–gravity waves has been derived and applied on episodic and seasonal time scales. A scale analysis of this shallow-water theory for midlatitude synoptic-scale flows identifies advection of relative vorticity as the leading-order source term. Examination of leading- and second-order terms elucidates previous, more empirically inspired CAT forecast diagnostics. Application of the Lighthill–Ford theory to the Upper Mississippi and Ohio Valleys CAT outbreak of 9 March 2006 results in good agreement with pilot reports of turbulence. Application of Lighthill–Ford theory to CAT forecasting for the 3 November 2005–26 March 2006 period using 1-h forecasts of the Rapid Update Cycle (RUC) 2 1500 UTC model run leads to superior forecasts compared to the current operational version of the Graphical Turbulence Guidance (GTG1) algorithm, the most skillful operational CAT forecasting method in existence. The results suggest that major improvements in CAT forecasting could result if the methods presented herein become operational.

## Abstract

Balance dynamics are proposed in a probabilistic framework, assuming that the state variables and the master, or control, variables are random variables described by continuous probability density functions. Balance inversion, defined as recovering the state variables from the control variables, is achieved through Bayes’ theorem. Balance dynamics are defined by the propagation of the joint probability of the state and control variables through the Liouville equation. Assuming Gaussian statistics, balance inversion reduces to linear regression of the state variables onto the control variables, and assuming linear dynamics, balance dynamics reduces to a Kalman filter subject to perfect observations given by the control variables.

Example solutions are given for an elliptical vortex in shallow water having unity Rossby and Froude numbers, which produce an outward-propagating pulse of inertia–gravity wave activity. Applying balance inversion to the potential vorticity reveals that, because potential vorticity and divergence share well-defined patterns of covariability, the inertia–gravity wave field is recovered in addition to the vortical field. Solutions for a probabilistic balance dynamics model applied to the elliptical vortex reveal smaller errors (“imbalance”) for height control compared to potential vorticity control.

Important attributes of the probabilistic balance theory include quantification of the concept of balance manifold “fuzziness,” and clear state-independent definitions of balance and imbalance in terms of the range of the probabilistic inversion operators. Moreover, the theory provides a generalization of the notion of balance that may prove useful for problems involving moist physics, chemistry, and tropical circulations.

## Abstract

Balance dynamics are proposed in a probabilistic framework, assuming that the state variables and the master, or control, variables are random variables described by continuous probability density functions. Balance inversion, defined as recovering the state variables from the control variables, is achieved through Bayes’ theorem. Balance dynamics are defined by the propagation of the joint probability of the state and control variables through the Liouville equation. Assuming Gaussian statistics, balance inversion reduces to linear regression of the state variables onto the control variables, and assuming linear dynamics, balance dynamics reduces to a Kalman filter subject to perfect observations given by the control variables.

Example solutions are given for an elliptical vortex in shallow water having unity Rossby and Froude numbers, which produce an outward-propagating pulse of inertia–gravity wave activity. Applying balance inversion to the potential vorticity reveals that, because potential vorticity and divergence share well-defined patterns of covariability, the inertia–gravity wave field is recovered in addition to the vortical field. Solutions for a probabilistic balance dynamics model applied to the elliptical vortex reveal smaller errors (“imbalance”) for height control compared to potential vorticity control.

Important attributes of the probabilistic balance theory include quantification of the concept of balance manifold “fuzziness,” and clear state-independent definitions of balance and imbalance in terms of the range of the probabilistic inversion operators. Moreover, the theory provides a generalization of the notion of balance that may prove useful for problems involving moist physics, chemistry, and tropical circulations.

## Abstract

This paper discusses recent progress toward understanding the instability of a monotonic vortex at high Rossby number, due to the radiation of spiral inertia–gravity (IG) waves. The outward-propagating IG waves are excited by inner undulations of potential vorticity that consist of one or more vortex Rossby waves. An individual vortex Rossby wave and its IG wave emission have angular pseudomomenta of opposite sign, positive and negative, respectively. The Rossby wave therefore grows in response to producing radiation. Such growth is potentially suppressed by the resonant absorption of angular pseudomomentum in a critical layer, where the angular phase velocity of the Rossby wave matches the angular velocity of the mean flow. Suppression requires a sufficiently steep radial gradient of potential vorticity in the critical layer. Both linear and nonlinear steepness requirements are reviewed.

The formal theory of radiation-driven instability, or “spontaneous imbalance,” is generalized in isentropic coordinates to baroclinic vortices that possess active critical layers. Furthermore, the rate of angular momentum loss by IG wave radiation is reexamined in the hurricane parameter regime. Numerical results suggest that the negative radiation torque on a hurricane has a smaller impact than surface drag, despite recent estimates of its large magnitude.

## Abstract

This paper discusses recent progress toward understanding the instability of a monotonic vortex at high Rossby number, due to the radiation of spiral inertia–gravity (IG) waves. The outward-propagating IG waves are excited by inner undulations of potential vorticity that consist of one or more vortex Rossby waves. An individual vortex Rossby wave and its IG wave emission have angular pseudomomenta of opposite sign, positive and negative, respectively. The Rossby wave therefore grows in response to producing radiation. Such growth is potentially suppressed by the resonant absorption of angular pseudomomentum in a critical layer, where the angular phase velocity of the Rossby wave matches the angular velocity of the mean flow. Suppression requires a sufficiently steep radial gradient of potential vorticity in the critical layer. Both linear and nonlinear steepness requirements are reviewed.

The formal theory of radiation-driven instability, or “spontaneous imbalance,” is generalized in isentropic coordinates to baroclinic vortices that possess active critical layers. Furthermore, the rate of angular momentum loss by IG wave radiation is reexamined in the hurricane parameter regime. Numerical results suggest that the negative radiation torque on a hurricane has a smaller impact than surface drag, despite recent estimates of its large magnitude.

## Abstract

Several existing sets of smaller-scale ocean and atmospheric data appear to display Kolmogorov–Obukov–Corrsin inertial ranges in horizontal spectra for length scales up to at least a few hundred meters. It is argued here that these data are inconsistent with the assumptions for these inertial range theories. Instead, it is hypothesized that the dynamics of stratified turbulence explain these data. If valid, these dynamics may also explain the behavior of strongly stratified flows in similar dynamic ranges of other geophysical flows.

## Abstract

Several existing sets of smaller-scale ocean and atmospheric data appear to display Kolmogorov–Obukov–Corrsin inertial ranges in horizontal spectra for length scales up to at least a few hundred meters. It is argued here that these data are inconsistent with the assumptions for these inertial range theories. Instead, it is hypothesized that the dynamics of stratified turbulence explain these data. If valid, these dynamics may also explain the behavior of strongly stratified flows in similar dynamic ranges of other geophysical flows.