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## Abstract

Using a two-dimensional Fourier decomposition and a four-dimensional ray-tracing technique, the propagating characteristics and source mechanisms of mesoscale gravity waves simulated in idealized baroclinic jet-front systems are investigated. The Fourier decomposition successfully separates the simulated gravity waves from a complex background flow in the troposphere. Four groups of gravity waves in the lower stratosphere are identified from the spectral decomposition. One is a northward-propagating short-scale wave packet with horizontal wavelength of ∼150 km, and another is a northeastward-propagating medium-scale wave packet with horizontal wavelength of ∼350 km. Both of these are most pronounced in the exit region of the upper-tropospheric jet. A third group exists in the deep trough region above (and nearly perpendicular to) the jet, and a fourth group far to the south of the jet right above the surface cold front, both of which are short-scale waves and have a horizontal wavelength of ∼100–150 km.

Ray-tracing analysis suggests that the medium-scale gravity waves originate from the upper-tropospheric jet-front system where there is maximum imbalance, though contributions from the surface fronts cannot be completely ruled out. The shorter-scale, northward-propagating gravity waves in the jet-exit region, on the other hand, may originate from both the upper-tropospheric jet-front system and the surface frontal system. The shorter-scale gravity waves in the deep trough region across the jet (and those right above the surface cold fronts) are almost certain to initiate from the surface frontal system. Ray-tracing analysis also reveals a very strong influence of the spatial and temporal variability of the complex background flow on the characteristics of gravity waves as they propagate.

## Abstract

Using a two-dimensional Fourier decomposition and a four-dimensional ray-tracing technique, the propagating characteristics and source mechanisms of mesoscale gravity waves simulated in idealized baroclinic jet-front systems are investigated. The Fourier decomposition successfully separates the simulated gravity waves from a complex background flow in the troposphere. Four groups of gravity waves in the lower stratosphere are identified from the spectral decomposition. One is a northward-propagating short-scale wave packet with horizontal wavelength of ∼150 km, and another is a northeastward-propagating medium-scale wave packet with horizontal wavelength of ∼350 km. Both of these are most pronounced in the exit region of the upper-tropospheric jet. A third group exists in the deep trough region above (and nearly perpendicular to) the jet, and a fourth group far to the south of the jet right above the surface cold front, both of which are short-scale waves and have a horizontal wavelength of ∼100–150 km.

Ray-tracing analysis suggests that the medium-scale gravity waves originate from the upper-tropospheric jet-front system where there is maximum imbalance, though contributions from the surface fronts cannot be completely ruled out. The shorter-scale, northward-propagating gravity waves in the jet-exit region, on the other hand, may originate from both the upper-tropospheric jet-front system and the surface frontal system. The shorter-scale gravity waves in the deep trough region across the jet (and those right above the surface cold fronts) are almost certain to initiate from the surface frontal system. Ray-tracing analysis also reveals a very strong influence of the spatial and temporal variability of the complex background flow on the characteristics of gravity waves as they propagate.

## Abstract

This paper discusses some of the mechanisms whereby fast inertia–gravity waves can be generated spontaneously by slow, balanced atmospheric and oceanic flows. In the small Rossby number regime relevant to midlatitude dynamics, high-accuracy balanced models, which filter out inertia–gravity waves completely, can in principle describe the evolution of suitably initialized flows up to terms that are exponentially small in the Rossby number ε, that is, of the form exp(−*α*/ε) for some *α* > 0. This suggests that the mechanisms of inertia–gravity wave generation, which are not captured by these balanced models, are also exponentially weak. This has been confirmed by explicit analytical results obtained for a few highly simplified models. These results are reviewed, and some of the exponential-asymptotic techniques that have been used in their derivation are presented. Two types of mechanisms are examined: spontaneous-generation mechanisms, which generate exponentially small waves from perfectly balanced initial conditions, and unbalanced instability mechanisms, which amplify unbalanced initial perturbations of steady flows. The relevance of the results to realistic flows is discussed.

## Abstract

This paper discusses some of the mechanisms whereby fast inertia–gravity waves can be generated spontaneously by slow, balanced atmospheric and oceanic flows. In the small Rossby number regime relevant to midlatitude dynamics, high-accuracy balanced models, which filter out inertia–gravity waves completely, can in principle describe the evolution of suitably initialized flows up to terms that are exponentially small in the Rossby number ε, that is, of the form exp(−*α*/ε) for some *α* > 0. This suggests that the mechanisms of inertia–gravity wave generation, which are not captured by these balanced models, are also exponentially weak. This has been confirmed by explicit analytical results obtained for a few highly simplified models. These results are reviewed, and some of the exponential-asymptotic techniques that have been used in their derivation are presented. Two types of mechanisms are examined: spontaneous-generation mechanisms, which generate exponentially small waves from perfectly balanced initial conditions, and unbalanced instability mechanisms, which amplify unbalanced initial perturbations of steady flows. The relevance of the results to realistic flows is discussed.

## Abstract

Although it is now accepted that imbalance in the atmosphere and ocean is generic, the feedback of the unbalanced motion on the balanced flow has not received much attention. In this work the parameterization problem is examined in the context of rotating stratified turbulence, that is, with a nonhydrostatic Boussinesq model. Using the normal modes as a first approximation to the balanced and unbalanced flow, the growth of ageostrophic perturbations to the quasigeostrophic flow and the associated feedback are studied. For weak stratification, there are analogies with the three-dimensionalization of decaying 2D turbulence: the growth rate of the ageostrophic perturbation follows a linear estimate, geostrophic energy is extracted from the base flow, and the associated damping on the geostrophic base flow (the “eddy viscosity”) is peaked at large horizontal scales. For strong stratification, the transfer spectra and eddy viscosities maintain this structure if there is synoptic-scale motion and the buoyancy scale is adequately resolved. This has been confirmed for global Rossby and Froude numbers of *O*(0.1). Implications for atmospheric and oceanic modeling are discussed.

## Abstract

Although it is now accepted that imbalance in the atmosphere and ocean is generic, the feedback of the unbalanced motion on the balanced flow has not received much attention. In this work the parameterization problem is examined in the context of rotating stratified turbulence, that is, with a nonhydrostatic Boussinesq model. Using the normal modes as a first approximation to the balanced and unbalanced flow, the growth of ageostrophic perturbations to the quasigeostrophic flow and the associated feedback are studied. For weak stratification, there are analogies with the three-dimensionalization of decaying 2D turbulence: the growth rate of the ageostrophic perturbation follows a linear estimate, geostrophic energy is extracted from the base flow, and the associated damping on the geostrophic base flow (the “eddy viscosity”) is peaked at large horizontal scales. For strong stratification, the transfer spectra and eddy viscosities maintain this structure if there is synoptic-scale motion and the buoyancy scale is adequately resolved. This has been confirmed for global Rossby and Froude numbers of *O*(0.1). Implications for atmospheric and oceanic modeling are discussed.

## Abstract

Results from new experiments on baroclinic instability of a coastal jet demonstrate that this almost balanced flow spontaneously emits inertial waves when the Rossby radius of deformation is relatively small such that the characteristics of baroclinic meanders match the dispersion relation for the inertial waves. The energy of the waves is small compared to the energy of the flow. A single event of wave emission is identified in the experiment with larger radius of deformation and is interpreted in terms of vorticity dynamics. The flows are generated on a laboratory polar *β* plane where the Coriolis parameter varies quadratically with latitude. A new method for imaging the rotating flows, which the authors call “altimetric imaging velocimetry,” is employed. Optical color coding of slopes of the free-surface elevation field allows the authors to derive the fields of pressure, surface elevation, geostrophic velocity, or the “gradient wind” velocity with very high spatial resolution (typically several million vectors) limited largely by the pixel resolution of the available imaging sensors. The technique is particularly suited for the investigations of small-amplitude waves, which are often difficult to detect by other methods.

## Abstract

Results from new experiments on baroclinic instability of a coastal jet demonstrate that this almost balanced flow spontaneously emits inertial waves when the Rossby radius of deformation is relatively small such that the characteristics of baroclinic meanders match the dispersion relation for the inertial waves. The energy of the waves is small compared to the energy of the flow. A single event of wave emission is identified in the experiment with larger radius of deformation and is interpreted in terms of vorticity dynamics. The flows are generated on a laboratory polar *β* plane where the Coriolis parameter varies quadratically with latitude. A new method for imaging the rotating flows, which the authors call “altimetric imaging velocimetry,” is employed. Optical color coding of slopes of the free-surface elevation field allows the authors to derive the fields of pressure, surface elevation, geostrophic velocity, or the “gradient wind” velocity with very high spatial resolution (typically several million vectors) limited largely by the pixel resolution of the available imaging sensors. The technique is particularly suited for the investigations of small-amplitude waves, which are often difficult to detect by other methods.

## Abstract

Inertial gravity wave radiation from an unsteady rotational flow (spontaneous radiation) is investigated numerically in an *f*-plane shallow water system for a wide range of Rossby numbers, 1 ≤ Ro ≤ 1000, and Froude numbers, 0.1 ≤ Fr ≤ 0.8. A barotropically unstable jet flow is initially balanced and maintained by forcing so that spontaneous gravity wave radiation is generated continuously. The amount of gravity wave flux is proportional to Fr for large Ro(≥30), which is consistent with the power law of the aeroacoustic sound wave radiation theory (the Lighthill theory). In contrast, for small Ro(≤10) this power law does not hold because of the vortex stabilization due to the small deformation radius. In the case of fixed Fr, gravity wave flux is almost constant for larger Ro(>30) and decreases rapidly for smaller Ro(<5). There is a local maximum value between these Ro(∼10). Spectral frequency analysis of the gravity wave source shows that for Ro = 10, while the source term related to the earth’s rotation is larger than that related to unsteady rotational flow, the inertial cutoff frequency is still lower than the peak frequency of the dominant source. The results suggest that the effect of the earth’s rotation may intensify spontaneous gravity wave radiation for Ro ∼ 10.

## Abstract

Inertial gravity wave radiation from an unsteady rotational flow (spontaneous radiation) is investigated numerically in an *f*-plane shallow water system for a wide range of Rossby numbers, 1 ≤ Ro ≤ 1000, and Froude numbers, 0.1 ≤ Fr ≤ 0.8. A barotropically unstable jet flow is initially balanced and maintained by forcing so that spontaneous gravity wave radiation is generated continuously. The amount of gravity wave flux is proportional to Fr for large Ro(≥30), which is consistent with the power law of the aeroacoustic sound wave radiation theory (the Lighthill theory). In contrast, for small Ro(≤10) this power law does not hold because of the vortex stabilization due to the small deformation radius. In the case of fixed Fr, gravity wave flux is almost constant for larger Ro(>30) and decreases rapidly for smaller Ro(<5). There is a local maximum value between these Ro(∼10). Spectral frequency analysis of the gravity wave source shows that for Ro = 10, while the source term related to the earth’s rotation is larger than that related to unsteady rotational flow, the inertial cutoff frequency is still lower than the peak frequency of the dominant source. The results suggest that the effect of the earth’s rotation may intensify spontaneous gravity wave radiation for Ro ∼ 10.

## Abstract

Vortex dipoles provide a simple representation of localized atmospheric jets. Numerical simulations of a synoptic-scale dipole in surface potential temperature are considered in a rotating, stratified fluid with approximately uniform potential vorticity. Following an initial period of adjustment, the dipole propagates along a slightly curved trajectory at a nearly steady rate and with a nearly fixed structure for more than 50 days. Downstream from the jet maximum, the flow also contains smaller-scale, upward-propagating inertia–gravity waves that are embedded within and stationary relative to the dipole. The waves form elongated bows along the leading edge of the dipole. Consistent with propagation in horizontal deformation and vertical shear, the waves’ horizontal scale shrinks and the vertical slope varies as they approach the leading stagnation point in the dipole’s flow. Because the waves persist for tens of days despite explicit dissipation in the numerical model that would otherwise damp the waves on a time scale of a few hours, they must be inherent features of the dipole itself, rather than remnants of imbalances in the initial conditions. The wave amplitude varies with the strength of the dipole, with waves becoming obvious once the maximum vertical vorticity in the dipole is roughly half the Coriolis parameter. Possible mechanisms for the wave generation are spontaneous wave emission and the instability of the underlying balanced dipole.

## Abstract

Vortex dipoles provide a simple representation of localized atmospheric jets. Numerical simulations of a synoptic-scale dipole in surface potential temperature are considered in a rotating, stratified fluid with approximately uniform potential vorticity. Following an initial period of adjustment, the dipole propagates along a slightly curved trajectory at a nearly steady rate and with a nearly fixed structure for more than 50 days. Downstream from the jet maximum, the flow also contains smaller-scale, upward-propagating inertia–gravity waves that are embedded within and stationary relative to the dipole. The waves form elongated bows along the leading edge of the dipole. Consistent with propagation in horizontal deformation and vertical shear, the waves’ horizontal scale shrinks and the vertical slope varies as they approach the leading stagnation point in the dipole’s flow. Because the waves persist for tens of days despite explicit dissipation in the numerical model that would otherwise damp the waves on a time scale of a few hours, they must be inherent features of the dipole itself, rather than remnants of imbalances in the initial conditions. The wave amplitude varies with the strength of the dipole, with waves becoming obvious once the maximum vertical vorticity in the dipole is roughly half the Coriolis parameter. Possible mechanisms for the wave generation are spontaneous wave emission and the instability of the underlying balanced dipole.