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Riwal Plougonven and Fuqing Zhang

Abstract

Studies on the spontaneous emission of gravity waves from jets, both observational and numerical, have emphasized that excitation of gravity waves occurred preferentially near regions of imbalance. Yet a quantitative relation between the several large-scale diagnostics of imbalance and the excited waves is still lacking.

The purpose of the present note is to investigate one possible way to relate quantitatively the gravity waves to diagnostics of the large-scale flow that is exciting them. Scaling arguments are used to determine how the large-scale flow may provide a forcing on the right-hand side of a wave equation describing the linear dynamics of the excited waves. The residual of the nonlinear balance equation plays an important role in this forcing.

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Riwal Plougonven and Chris Snyder

Abstract

The spontaneous generation of inertia–gravity waves in idealized life cycles of baroclinic instability is investigated using the Weather Research and Forecasting Model. Two substantially different life cycles of baroclinic instability are obtained by varying the initial zonal jet. The wave generation depends strongly on the details of the baroclinic wave’s development. In the life cycle dominated by cyclonic behavior, the most conspicuous gravity waves are excited by the upper-level jet and are broadly consistent with previous simulations of O’Sullivan and Dunkerton. In the life cycle that is dominated by anticyclonic behavior, the most conspicuous gravity waves even in the stratosphere are excited by the surface fronts, although the fronts are no stronger than in the cyclonic life cycle. The anticyclonic life cycle also reveals waves in the lower stratosphere above the upper-level trough of the baroclinic wave; these waves have not been previously identified in idealized simulations. The sensitivities of the different waves to both resolution and dissipation are discussed.

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Riwal Plougonven, David J. Muraki, and Chris Snyder

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Normal modes of a linear vertical shear (Eady shear) are studied within the linearized primitive equations for a rotating stratified fluid above a rigid lower boundary. The authors' interest is in modes having an inertial critical layer present at some height within the flow. Below this layer, the solutions can be closely approximated by balanced edge waves obtained through an asymptotic expansion in Rossby number. Above, the solutions behave as gravity waves. Hence these modes are an example of a spatial coupling of balanced motions to gravity waves.

The amplitude of the gravity waves relative to the balanced part of the solutions is obtained analytically and numerically as a function of parameters. It is shown that the waves are exponentially small in Rossby number. Moreover, their amplitude depends in a nontrivial way on the meridional wavenumber. For modes having a radiating upper boundary condition, the meridional wavenumber for which the gravity wave amplitude is maximal occurs when the tilts of the balanced edge wave and gravity waves agree.

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Riwal Plougonven, Chris Snyder, and Fuqing Zhang
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Riwal Plougonven, Alexis Foussard, and Guillaume Lapeyre

Abstract

In a recent study, O’Neill et al. analyzed the divergence of surface winds above the northwest Atlantic. In the time mean, a band of convergence is found, overlying the southern flank of the Gulf Stream. To quantify the impact of synoptic storms, the authors proposed to compare the time-mean divergence with the divergence averaged in the absence of rain. In the resulting conditional-average field, divergence was found to be positive nearly everywhere. O'Neill et al. concluded that this absence of convergence precludes the Ekman-balanced mass adjustment to be responsible for the atmospheric response above the Gulf Stream. Using a simplistic toy model as well as a numerical simulation representative of a storm track, we show that the absence of negative divergence values purely results from the correlation between rain and convergence: the conditional average based on the absence of rain necessarily implies a shift toward positive divergence values. In consequence, we argue that conditional statistics (based on the absence of rain or removing extreme values in the divergence field), as produced by O’Neill et al., do not allow conclusions on the mechanisms underlying the atmospheric response to the Gulf Stream. They nevertheless highlight the essential role of synoptic storms in shaping the divergence field in instantaneous fields.

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François Lott, Riwal Plougonven, and Jacques Vanneste

Abstract

The gravity waves (GWs) generated by potential vorticity (PV) anomalies in a rotating stratified shear flow are examined under the assumptions of constant vertical shear, two-dimensionality, and unbounded domain. Near a PV anomaly, the associated perturbation is well modeled by quasigeostrophic theory. This is not the case at large vertical distances, however, and in particular beyond the two inertial layers that appear above and below the anomaly; there, the perturbation consists of vertically propagating gravity waves. This structure is described analytically, using an expansion in the continuous spectrum of the singular modes that results from the presence of critical levels.

Several explicit results are obtained. These include the form of the Eliassen–Palm (EP) flux as a function of the Richardson number N22, where N is the Brunt–Väisälä frequency and Λ the vertical shear. Its nondimensional value is shown to be approximately exp(−πN/Λ)/8 in the far-field GW region, approximately twice that between the two inertial layers. These results, which imply substantial wave–flow interactions in the inertial layers, are valid for Richardson numbers larger than 1 and for a large range of PV distributions. In dimensional form they provide simple relationships between the EP fluxes and the large-scale flow characteristics.

As an illustration, the authors consider a PV disturbance with an amplitude of 1 PVU and a depth of 1 km, and estimate that the associated EP flux ranges between 0.1 and 100 mPa for a Richardson number between 1 and 10. These values of the flux are comparable with those observed in the lower stratosphere, which suggests that the mechanism identified in this paper provides a substantial gravity wave source, one that could be parameterized in GCMs.

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Riwal Plougonven, David J. Muraki, and Chris Snyder
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Chris Snyder, Riwal Plougonven, and David J. Muraki

Abstract

Previous simulations of dipole vortices propagating through rotating, stratified fluid have revealed small-scale inertia–gravity waves that are embedded within the dipole near its leading edge and are approximately stationary relative to the dipole. The mechanism by which these waves are generated is investigated, beginning from the observation that the dipole can be reasonably approximated by a balanced quasigeostrophic (QG) solution. The deviations from the QG solution (including the waves) then satisfy linear equations that come from linearization of the governing equations about the QG dipole and are forced by the residual tendency of the QG dipole (i.e., the difference between the time tendency of the QG solution and that of the full primitive equations initialized with the QG fields). The waves do not appear to be generated by an instability of the balanced dipole, as homogeneous solutions of the linear equations amplify little over the time scale for which the linear equations are valid. Linear solutions forced by the residual tendency capture the scale, location, and pattern of the inertia–gravity waves, although they overpredict the wave amplitude by a factor of 2. There is thus strong evidence that the waves are generated as a forced linear response to the balanced flow. The relation to and differences from other theories for wave generation by balanced flows, including those of Lighthill and Ford et al., are discussed.

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Albert Hertzog, M. Joan Alexander, and Riwal Plougonven

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In this article, long-duration balloon and spaceborne observations, and mesoscale numerical simulations are used to study the intermittency of gravity waves in the lower stratosphere above Antarctica and the Southern Ocean; namely, the characteristics of the gravity wave momentum-flux probability density functions (pdfs) obtained with these three datasets are described. The pdfs consistently exhibit long tails associated with the occurrence of rare and large-amplitude events. The pdf tails are even longer above mountains than above oceanic areas, which is in agreement with previous studies of gravity wave intermittency in this region. It is moreover found that these rare, large-amplitude events represent the main contribution to the total momentum flux during the winter regime of the stratospheric circulation. In contrast, the wave intermittency significantly decreases when stratospheric easterlies develop in late spring and summer. It is also shown that, except above mountainous areas in winter, the momentum-flux pdfs tend to behave like lognormal distributions. Monte Carlo simulations are undertaken to examine the role played by critical levels in influencing the shape of momentum-flux pdfs. In particular, the study finds that the lognormal shape may result from the propagation of a wave spectrum into a varying background wind field that generates the occurrence of frequent critical levels.

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François Lott, Riwal Plougonven, and Jacques Vanneste

Abstract

The gravity waves (GWs) produced by three-dimensional potential vorticity (PV) anomalies are examined under the assumption of constant vertical shear, constant stratification, and unbounded domain. As in the two-dimensional case analyzed in an earlier paper, the disturbance near the PV anomaly is well modeled by quasigeostrophic theory. At larger distances the nature of the disturbance changes across the two inertial layers that are located above and below the anomaly, and it takes the form of a vertically propagating GW beyond these.

For a horizontally monochromatic PV anomaly of infinitesimal depth, the disturbance is described analytically using both an exact solution and a WKB approximation; the latter includes an exponentially small term that captures the change of the solution near the PV anomaly induced by the radiation boundary condition in the far field. The analytical results reveal a strong sensitivity of the emission to the Richardson number and to the orientation of the horizontal wavenumber: the absorptive properties of the inertial layers are such that the emission is maximized in the Northern Hemisphere for wavenumbers at negative angles to the shear.

For localized PV anomalies, numerical computations give the temporal evolution of the GW field. Analytical and numerical results are also used to establish an explicit form for the Eliassen–Palm flux that could be used to parameterize GW sources in GCMs. The properties of the Eliassen–Palm flux vector imply that in a westerly shear, the GWs exert a drag in a southwest direction in the upper inertial layer, and in a northwest direction at the altitudes where the GWs dissipate aloft.

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