Inertio-gravity Waves Research Articles

Interactions between Moisture and Tropical Convection. Part II: The Convective Coupling of Equatorial Waves

AbstractThe exponential increase in precipitation with increasing column saturation fraction (CSF) is used to investigate the role of moisture in convective coupling. This simple empirical relationship between precipitation and CSF is shown to capture nearly all MJO-related variability in TRMM precipitation, ~80% of equatorial Rossby wave–related variability, and ~75% of east Pacific easterly wave–related variability. In contrast, this empirical relationship only captures roughly half of TRMM precipitation variability associated with Kelvin waves, African easterly waves, and mixed Rossby–gravity waves, suggesting coupling mechanisms other than moisture are playing leading roles in these phenomena. These latter phenomena have strong adiabatically forced vertical motions that could reduce static stability and convective inhibition while simultaneously moistening, creating a more favorable convective environment. Cross-spectra of precipitation and column-integrated dry static energy show enhanced coherence and an out-of-phase relationship in the Kelvin wave, mixed Rossby–gravity wave, and eastward inertio-gravity wave bands, supporting this narrative. The cooperative modulation of precipitation by moisture and temperature anomalies is shown to shorten the convective adjustment time scale (i.e., time scale by which moisture and precipitation are relaxed toward their “background” state) of these phenomena. Speeding the removal of moisture anomalies relative to that of temperature anomalies may allow the latter to assume a more important role in driving moist static energy fluctuations, helping promote the gravity wave character of these phenomena.

Deep sea floor observations of typhoon driven enhanced ocean turbulence

The impact of large atmospheric disturbances on deep benthic communities is not well known quantitatively. Observations are scarce but may reveal specific processes leading to turbulent disturbances. Here, we present high-resolution deep-ocean observations to study potential turbulent mixing by a large atmospheric disturbance. We deployed an array of 100-Hz sampling-rate geophysical broadband Ocean Bottom Seismometers (OBSs) on the seafloor. Within the footprint of this array we also deployed an oceanographic 0.5-Hz sampling-rate vertical temperature sensor string covering the water phase between 7 and 207 m above the seafloor at about 3000 m depth off eastern Taiwan between June 2017 and April 2018. In September 2017, all instruments recorded Category 4 cyclone Typhoon Talim’s passage northeast of the array one day ahead of the cyclone’s closest approach when the cyclone’s eye was more than 1,000 km away. For 10 days, a group of near-inertial motions appeared most clearly in temperature. The group contained the largest inertial amplitudes in the ten month time series, and which led to turbulence dissipation rates O(10−7 m2 s−3). The observation reflects the importance of barotropic response to a cyclone and the propagation of inertio-gravity waves in weak density stratification. In addition to internal tides, these waves drove turbulent overturns larger than 200 m that were concurrently recorded by OBSs. The turbulent signals were neither due to seismic activity nor to ocean-surface wave action. Cyclones can generate not only microseisms and earth hums, as well as turbulence in the water column, producing additional ground motions. Quantified turbulence processes may help constrain models on sediment resuspension and its effect on deep-sea benthic life.

Nonlinear interaction of gravity and acoustic waves

Here we have investigated the possibility of an inertio-acoustic wave-mode to be unstable with regards to gravity mode perturbations through non-linear triad interactions in the context of a shallow non-hydrostatic model. We have considered highly truncated Galerkin expansions of the perturbations around a resting, hydrostatic and isothermal background state in terms of the eigensolutions of the linear problem. For a single interacting wave triplet, we have shown that an acoustic mode cannot amplify a pair of inertio-gravity perturbations due to the high mismatch among the eigenfrequencies of the three interacting wave-modes, which requires an unrealistically high amplitude of the acoustic mode in order for pump wave instability to occur. In contrast, it has been demonstrated by analysing the dynamics of two triads coupled by a single mode that a non-hydrostatic gravity wave-mode participating in a nearly resonant interaction with two acoustic modes can be unstable to small amplitude perturbations associated with a pair of two hydrostatically balanced inertio-gravity wave-modes. This linear instability yields significant inter-triad energy exchanges if the nonlinearity associated with the second triplet containing the two hydrostatically balanced inertio-gravity modes is restored. Therefore, this inter-triad energy exchanges lead the acoustic modes to yield significant energy modulations in hydrostatic inertio-gravity wave modes. Consequently, our theory suggests that acoustic waves might play an important role in the transient phase of the three-dimensional adjustment process of the atmosphere to both hydrostatic and geostrophic balances.

Modal Decomposition of the Global Response to Tropical Heating Perturbations Resembling MJO

Abstract The paper presents four ensembles of numerical experiments that compare the response to monopole and dipole heating perturbations resembling different phases of the Madden–Julian oscillation (MJO). The results quantify the Rossby and inertio-gravity (IG) wave response using the normal-mode function decomposition. The day 3 response is characterized by about 60% variance in the IG modes, with about 85% of it belonging to the Kelvin waves. On day 14, only 10% of the response variance is due to the Kelvin waves. Although the n = 1 Rossby mode is the main contributor to the Rossby variance at all time scales, the n > 1 Rossby modes contribute over 50% of the balanced response to the MJO heating. In the short range, dipole perturbations produce a response with the maximal variance in zonal wavenumbers k = 2–3 whereas in the medium range the response maximizes at k = 1 in all experiments. Furthermore, the medium-range response to the heating perturbation mimicking MJO phase 6 is found also over Europe.

A Systematic Comparison of Tropical Waves over Northern Africa. Part II: Dynamics and Thermodynamics

AbstractThis study presents the first systematic comparison of the dynamics and thermodynamics associated with all major tropical wave types causing rainfall modulation over northern tropical Africa: the Madden–Julian oscillation (MJO), equatorial Rossby waves (ERs), tropical disturbances (TDs, including African easterly waves), Kelvin waves, mixed Rossby–gravity waves (MRGs), and eastward inertio-gravity waves (EIGs). Reanalysis and radiosonde data were analyzed for the period 1981–2013 based on space–time filtering of outgoing longwave radiation. The identified circulation patterns are largely consistent with theory. The slow modes, MJO and ER, mainly impact precipitable water, whereas the faster TDs, Kelvin waves, and MRGs primarily modulate moisture convergence. Monsoonal inflow intensifies during wet phases of the MJO, ERs, and MRGs, associated with a northward shift of the intertropical discontinuity for MJO and ERs. This study reveals that MRGs over Africa have a distinct dynamical structure that differs significantly from AEWs. During passages of vertically tilted imbalanced wave modes, such as the MJO, TDs, Kelvin waves, and partly MRG waves, increased vertical wind shear and improved conditions for up- and downdrafts facilitate the organization of mesoscale convective systems. The balanced ERs are not tilted, and rainfall is triggered by large-scale moistening and stratiform lifting. The MJO and ERs interact with intraseasonal variations of the Indian monsoon and extratropical Rossby wave trains. The latter causes a trough over the Atlas Mountains associated with a tropical plume and rainfall over the Sahara. The presented results unveil which dynamical processes need to be modeled realistically to represent the coupling between tropical waves and rainfall in northern tropical Africa.

Systematic decomposition of the MJO and its Northern Hemispheric extratropical response into Rossby and inertio‐gravity components

The Madden–Julian Oscillation (MJO) is the dominant form of intraseasonal variability in the Tropics. The MJO is a complex convectively coupled phenomenon, which is still poorly represented in the current generation of climate models, and our understanding of its essential dynamics and its influence on the midlatitude circulation is still incomplete. Here, we use a normal‐mode decomposition method to decompose the MJO systematically into Kelvin, inertio‐gravity (IG), and Rossby‐wave components in the ERA‐Interim reanalysis data for the period 1980–2015 to provide a climatology of the eight MJO phases for the Kelvin, IG, and Rossby‐wave components.Our analysis shows that the Rossby modes provide a larger contribution to the magnitude of the MJO in terms of geopotential height and winds than the Kelvin wave and IG modes. Moreover, the kinetic energy associated with the Rossby modes of the MJO accounts for about 93% of the kinetic energy. Our decomposition also shows that the Kelvin wave is the dominant mode in the unbalanced wave part, which is flanked by Rossby waves on both sides of the Equator, consistent with previous studies. The extratropical response to the MJO also consists of both IG and Rossby‐wave components in the Northern Hemisphere (NH). The midlatitude MJO response is also linked to well‐known teleconnection patterns like the North Atlantic Oscillation and the Pacific–North American pattern. The transient NH atmospheric response is fast, of the order of 5–7 days. While the extratropical response is dominated by Rossby waves, IG waves also show a prominent response in the NH.

A Systematic Comparison of Tropical Waves over Northern Africa. Part I: Influence on Rainfall

Abstract Low-latitude rainfall variability on the daily to intraseasonal time scale is often related to tropical waves, including convectively coupled equatorial waves, the Madden–Julian oscillation (MJO), and tropical disturbances (TDs). Despite the importance of rainfall variability for vulnerable societies in tropical Africa, the relative influence of tropical waves for this region is largely unknown. This article presents the first systematic comparison of the impact of six wave types on precipitation over northern tropical Africa during the transition and full monsoon seasons, using two satellite products and a dense rain gauge network. Composites of rainfall anomalies in the different datasets show comparable modulation intensities in the West Sahel and at the Guinea Coast, varying from less than 2 to above 7 mm day−1 depending on the wave type. African easterly waves (AEWs) and Kelvin waves dominate the 3-hourly to daily time scale and explain 10%–30% locally. On longer time scales (7–20 days), only the MJO and equatorial Rossby (ER) waves remain as modulating factors and explain about up to one-third of rainfall variability. Eastward inertio-gravity waves and mixed Rossby–gravity (MRG) waves are comparatively unimportant. An analysis of wave superposition shows that low-frequency waves (MJO, ER) in their wet phase amplify the activity of high-frequency waves (TD, MRG) and suppress them in the dry phase. The results stress that more attention should be paid to tropical waves when forecasting rainfall over northern tropical Africa.

Momentum Flux of Convective Gravity Waves Derived from an Offline Gravity Wave Parameterization. Part II: Impacts on the Quasi-Biennial Oscillation

Abstract The characteristics of small-scale convective gravity waves (CGWs; horizontal wavelengths <100 km) and their contributions to the large-scale flow in the stratosphere, including the quasi-biennial oscillation (QBO), are investigated using an offline calculation of a source-dependent, physically based CGW parameterization with global reanalysis data from 1979 to 2010. The CGW momentum flux (CGWMF) and CGW drag (CGWD) are calculated from the cloud top (source level) to the upper stratosphere using a Lindzen-type wave propagation scheme. The 32-yr-mean CGWD exhibits large magnitudes in the tropical upper stratosphere and near the stratospheric polar night jet (~60°). The maximum positive drag is 0.1 (1.5) m s−1 day−1, and the maximum negative drag is −0.9 (−0.7) m s−1 day−1 in January (July) between 3 and 1 hPa. In the tropics, the momentum forcing by CGWs at 30 hPa associated with the QBO in the westerly shear zone is 3.5–6 m s−1 month−1, which is smaller than that by Kelvin waves, while that by CGWs in the easterly shear zone (3.1–6 m s−1 month−1) is greater than that by any other equatorial planetary waves or inertio-gravity waves (inertio-GWs). Composite analyses of the easterly QBO (EQBO) and westerly QBO (WQBO) phases reveal that the zonal CGWMF is concentrated near 10°N and that the negative (positive) CGWD extends latitudinally to ±20° (±10°) at 30 hPa. The strongest (weakest) negative CGWD is in March–May (September–November) during the EQBO, and the strongest (weakest) positive CGWD is in June–August (March–May) during the WQBO. The CGWMF and CGWD are generally stronger during El Niño than during La Niña in the equatorial region.

Jupiter's Mesoscale Waves Observed at 5 μm by Ground-based Observations and Juno JIRAM.

We characterize the origin and evolution of a mesoscale wave pattern in Jupiter's North Equatorial Belt (NEB), detected for the first time at 5 μm using a 2016-17 campaign of "lucky imaging" from the VISIR instrument on the Very Large Telescope and the NIRI instrument on the Gemini observatory, coupled with M-band imaging from Juno's JIRAM instrument during the first seven Juno orbits. The wave is compact, with a 1°.1-1°.4 longitude wavelength (wavelength 1300-1600 km, wavenumber 260-330) that is stable over time, with wave crests aligned largely north-south between 14°N and 17°N (planetographic). The waves were initially identified in small (10° longitude) packets immediately west of cyclones in the NEB at 16°N but extended to span wider longitude ranges over time. The waves exhibit a 7-10 K brightness temperature amplitude on top of an ∼210 K background at 5 μm. The thermal structure of the NEB allows for both inertio-gravity waves and gravity waves. Despite detection at 5 μm, this does not necessarily imply a deep location for the waves, and an upper tropospheric aerosol layer near 400-800 mbar could feature a gravity wave pattern modulating the visible-light reflectivity and attenuating the 5-μm radiance originating from deeper levels. Strong rifting activity appears to obliterate the pattern, which can change on timescales of weeks. The NEB underwent a new expansion and contraction episode in 2016-17 with associated cyclone-anticyclone formation, which could explain why the mesoscale wave pattern was more vivid in 2017 than ever before.

Small-Scale Wind Fluctuations in the Tropical Tropopause Layer from Aircraft Measurements: Occurrence, Nature, and Impact on Vertical Mixing

Abstract The contribution of turbulent mixing to heat and tracer transport in the tropical tropopause layer (TTL) is poorly constrained, partly owing to a lack of direct observations. Here, the authors use high-resolution (20 Hz) airborne measurements to study the occurrence and properties of small-scale (<100 m) wind fluctuations in the TTL (14–19 km) over the tropical Pacific. The fluctuations are highly intermittent and appear localized within shallow (100 m) patches. Furthermore, active turbulent events are more frequent at low altitude, near deep convection, and within layers of low gradient Richardson number. A case study emphasizes the link between the turbulent events and the occurrence of inertio-gravity waves having small horizontal or vertical scale. To evaluate the impact of the observed fluctuations on tracer mixing, their characteristics are examined. During active events, they are in broad agreement with inertial-range turbulence theory: the motions are close to 3D isotropic and the spectra follow a −5/3 power-law scaling. The diffusivity induced by turbulent bursts is estimated to be on the order of 10−1 m2 s−1 and increases from the top to the bottom of the TTL (from ~2 × 10−2 to ~3 × 10−1 m2 s−1). Given the uncertainties involved in the estimate, this is in reasonable agreement (about a factor of 3–4 lower) with the parameterized turbulent diffusivity in ERA-Interim, but it disagrees with other observational estimates from radar and radiosondes. The magnitude of the consequent vertical transport depends on the altitude and the tracer; for the species considered, it is generally smaller than that induced by the mean tropical upwelling.

Ocean mixing in deep-sea trenches: New insights from the Challenger Deep, Mariana Trench

Reliable very deep shipborne SBE 911plus Conductivity Temperature Depth (CTD) data to within 60m from the bottom and Kongsberg EM122 0.5° × 1° multibeam echosounder data are collected in the Challenger Deep, Mariana Trench. A new position and depth are given for the deepest point in the world's ocean. The data provide insight into the interplay between topography and internal waves in the ocean that lead to mixing of the lowermost water masses on Earth. Below 5000m, the vertical density stratification is weak, with a minimum buoyancy frequency N = 1.0 ± 0.6 cpd, cycles per day, between 6500 and 8500m. In that depth range, the average turbulence is coarsely estimated from Thorpe-overturning scales, with limited statistics to be ten times higher than the mean values of dissipation rate εT = 3 ± 2 × 10–11m2s−3 and eddy diffusivity KzT = 2 ± 1.5 × 10−4m2s−1 estimated for the depth range between 10,300 and 10,850m, where N = 2.5 ± 0.6 cpd. Inertial and meridionally directed tidal inertio-gravity waves can propagate between the differently stratified layers. These waves are suggested to be responsible for the observed turbulence. The turbulence values are similar to those recently estimated from CTD and moored observations in the Puerto Rico Trench. Yet, in contrast to the Puerto Rico Trench, seafloor morphology in the Mariana Trench shows up to 500m-high fault scarps on the incoming tectonic plate and a very narrow trench, suggesting that seafloor topography does not play a crucial role for mixing.

Inertio-gravity waves under the non-traditional -plane approximation: singularity in the large-scale limit

The low horizontal wavenumber limit of waves on a plane under a constant rotation rate (the so-called $f$-plane) is degenerate: all wave frequencies asymptotically approach the inertial frequency. This degeneracy has no serious consequence when the rotation axis is perpendicular to the plane (traditional $f$-plane approximation). However, when the rotation axis is tilted from the vertical direction (non-traditional $f$-plane approximation), we encounter a type of ‘singularity’ in the sense that each term of the Taylor expansion of the wave frequency in the horizontal Coriolis parameter diverges in the limit of low horizontal wavenumber. Such a drastic change of the solution behaviour by adding the horizontal Coriolis parameter in the low horizontal wavenumber limit is rather counter-intuitive, because the conventional scale analysis suggests that the horizontal Coriolis effect is negligible in this limit. However, the degeneracy of the system makes this effect critical with a need for considering higher-order terms. Two possible asymptotic limits are proposed for resolving this degeneracy. One of them, as it turns out, amounts to a representation of the wave frequency by a Taylor expansion in the horizontal wavenumber.

The Relationship between Equatorial Mixed Rossby–Gravity and Eastward Inertio-Gravity Waves. Part I

Abstract The relationship between n = 0 mixed Rossby–gravity waves (MRGs) and eastward inertio-gravity waves (EIGs) from Matsuno’s shallow-water theory on an equatorial beta plane is studied using statistics of satellite brightness temperature Tb and dynamical fields from ERA-Interim data. Unlike other observed convectively coupled equatorial waves, which have spectral signals well separated into eastward and westward modes, there is a continuum of MRG–EIG power standing above the background that peaks near wavenumber 0. This continuum is also present in the signals of dry stratospheric MRGs. While hundreds of papers have been written on MRGs, very little work on EIGs has appeared in the literature to date. The authors attribute this to the fact that EIG circulations are much weaker than those of MRGs for a given amount of divergence, making them more difficult to observe even though they strongly modulate convection. Empirical orthogonal function (EOF) and cross-spectral analysis of 2–6-day-filtered Tb isolate zonally standing modes of synoptic-scale convection originally identified by Wallace in 1971. These display antisymmetric Tb signals about the equator that propagate poleward with a period of around 4 days, along with westward-propagating MRG-like circulations that move through the Tb patterns. Further analysis here and in Part II shows that these signatures are not artifacts of the EOF approach but result from a mixture of MRG or EIG modes occurring either in isolation or at the same time.

The Relationship between Equatorial Mixed Rossby–Gravity and Eastward Inertio-Gravity Waves. Part II

Abstract Space–time spectral analysis of tropical cloudiness data shows strong evidence that convectively coupled n = 0 mixed Rossby–gravity waves (MRGs) and eastward inertio-gravity waves (EIGs) occur primarily within the western/central Pacific Ocean. Spectral filtering also shows that MRG and EIG cloudiness patterns are antisymmetric with respect to the equator, and they propagate coherently toward the west and east, respectively, with periods between 3 and 5 days, in agreement with Matsuno’s linear shallow-water theory. In contrast to the spectral approach, in a companion paper it has been shown that empirical orthogonal functions (EOFs) of 2–6-day-filtered cloudiness data within the tropical Pacific Ocean also suggest an antisymmetric pattern, but with the leading EOFs implying a zonally standing but poleward-propagating oscillation, along with the associated tropospheric flow moving to the west. In the present paper, these two views are reconciled by applying an independent approach based on a tracking method to assess tropical convection organization. It is shown that, on average, two-thirds of MRG and EIG events develop independently of one another, and one-third of the events overlap in space and time. This analysis also verifies that MRG and EIG cloudiness fields tend to propagate meridionally away from the equator. It is demonstrated that the lack of zonal propagation implied from the EOF analysis is likely due to the interference between eastward- and westward-propagating disturbances. In addition, it is shown that the westward-propagating circulation associated with the leading EOF is consistent with the expected theoretical behavior of an interference between MRGs and EIGs.

Assessing the Equatorial Long-Wave Approximation: Asymptotics and Observational Data Analysis*

Abstract Equatorial long-wave theory applies where a small horizontal aspect ratio between meridional and zonal length scales is assumed. In an idealized setting, the theory suggests that (i) meridional wind is small, (ii) geostrophic balance holds in the meridional direction, and (iii) inertio-gravity waves are small in amplitude or “filtered out.” In this paper a spectral data analysis method is used to quantitatively assess the spatial and temporal scales on which each of these aspects of long-wave dynamics is observed in reanalysis data. Three different perspectives are used in this assessment: primitive variables, characteristic variables, and wave variables. To define each wave variable, the eigenvectors and theoretical wave structures of the equatorial shallow-water equations are used. Evidence is presented that the range of spatial and temporal scales on which long-wave dynamics holds depends on which aspect of the dynamics is considered. For example, while meridional winds are an order of magnitude smaller than zonal winds over only a very narrow range of spatial scales (planetary wavenumber ), an examination of meridional geostrophic balance and inertio-gravity waves indicates long-wave dynamics for a broader range of scales (). A simple prediction is also presented for this range of scales based on physical and mathematical reasoning.

Offshore Propagation of Coastal Precipitation

Abstract This work focuses on the seaward propagation of coastal precipitation with and without mountainous terrain nearby. Offshore of India, diurnal propagation of precipitation is observed over the Bay of Bengal. On the eastern side of the bay, a diurnal but nonpropagating signal is observed near the west coast of Burma. This asymmetry is consistent with the inertio-gravity wave mechanism. Perturbations generated by diurnal heating over the coastal mountains of India propagate offshore, amplify in the upwind direction, and dissipate in the downwind direction relative to the steering wind, owing to critical-level considerations. A linear model is applied to evaluate sensitivity to gravity waves, as these affect deep moist convection and propagation. Analyses are performed for various heating depths, mountain widths, stability, Coriolis effect, background mean wind, and friction. Calculations reveal how these factors affect the amplitude, dissipation, initiation phase, and propagation speed of the diurnal disturbance. The propagation of precipitation triggered by land–sea breezes is distinguishable from that triggered by a mountain–plains circulation. Convection resulting purely from mountain heating begins earlier, propagates slower, and damps faster than that of the land–sea breeze. For mountains near a coast, slower propagation and stronger earlier convection result from a resonance-like combination of two dynamical mechanisms. The propagation of precipitation is initially triggered by the mountain breeze near the coastal mountain. Over the open ocean, the dominant signal propagates as that of the land breeze but with stronger convection.

Wave motions in a stably-neutrally stratified ocean

Wave spectrum of rotating stably-neutrally stratified fluid consisting of the stably stratified upper layer and the homogeneous lower one is studied. The density and other fields are assumed to be continuous at the interface between the layers. The study does not use the traditional (when the horizontal component of the Earth’s rotation is neglected) and hydrostatic approximations. The spectrum is rather complicated and consists of the super-inertial internal waves, the sub-inertial gyroscopic waves, and the sub- and super-inertial internal inertio-gravity waves. In the long-wave approximation the internal and internal inertio-gravity waves span both the layers, whereas the gyroscopic waves are localized in the lower layer and are close to the inertial oscillations. The sub-inertial wave motions observed in the nearly barotropic deep Western Mediterranean can be related to the gyroscopic waves.

A Systematic Relationship between the Representations of Convectively Coupled Equatorial Wave Activity and the Madden–Julian Oscillation in Climate Model Simulations

Abstract The relationship between a model’s performance in simulating the Madden–Julian oscillation (MJO) and convectively coupled equatorial wave (CCEW) activity during wintertime is examined by analyzing precipitation from 26 general circulation models (GCMs) participating in the MJO Task Force/Global Energy and Water Cycle Experiment (GEWEX) Atmospheric System Study (GASS) MJO model intercomparison project as well as observations based on the Tropical Rainfall Measuring Mission (TRMM). A model’s performance in simulating the MJO is determined by how faithfully it reproduces the eastward propagation of the large-scale intraseasonal variability (ISV) compared to TRMM observations. Results suggest that models that simulate a better MJO tend to 1) have higher fractional variances for various high-frequency wave modes (Kelvin, mixed Rossby–gravity, and westward and eastward inertio-gravity waves), which are defined by the ratios of wave variances of specific wave modes to the “total” variance, and 2) exhibit stronger CCEW variances in association with the eastward-propagating ISV precipitation anomalies for these high-frequency wave modes. The former result is illustrative of an alleviation in the good MJO models of the widely reported GCM deficiency in simulating the correct distribution of variance in tropical convection [i.e., typically too weak (strong) variance in the high- (low-) frequency spectrum of the precipitation]. The latter suggests better coherence and stronger interactions between these aforementioned high-frequency CCEWs and the ISV envelope in good MJO models. Both factors likely contribute to the improved simulation of the MJO in a GCM.

Contributions of equatorial wave modes and parameterized gravity waves to the tropical QBO in HadGEM2

AbstractThe contributions of the equatorial waves to the quasi‐biennial oscillation (QBO) are investigated using Hadley Centre Global Environment Model version 2 (HadGEM2). A gravity wave parameterization that couples its source spectrum to the convection is used. The equatorial wave modes are identified in the spectral domain, based on their distinct characteristics associated with momentum and heat fluxes. The Kelvin waves and parameterized gravity waves (PGWs) transport westerly momentum into the equatorial stratosphere by ∼0.35 and 0.8 mPa, respectively, while easterly momentum is carried primarily by the PGWs (∼0.75 mPa). The resolved inertio‐gravity (IG) waves transport both easterly and westerly momentum by ∼0.2 mPa. In the lowermost stratosphere, gradual dissipation of the Kelvin waves occurs, and the remaining waves induce eastward forcing in the westerly shear layer by 3–5 m s−1 month−1. The PGWs primarily dissipate within the sheared layer and provide large easterly and westerly forcing in the middle stratosphere (∼17 m s−1 month−1), while the forcing in the lower stratosphere is comparable to the Kelvin wave forcing. The IG wave forcing is small because of the small wave dissipation rate. The Rossby and mixed Rossby‐gravity (MRG) waves contribute to the westerly‐to‐easterly QBO transition by ∼2 m s−1 month−1. The magnitudes of the simulated Kelvin and Rossby wave forcings are comparable with the Modern‐Era Retrospective Analysis for Research and Applications, whereas the MRG and IG wave forcings are underestimated in the lower stratosphere. Differences between the simulation and reanalysis and the uncertainties in both are discussed.

The breaking of transient inertio-gravity waves in a shear flow using the Gaussian beam approximation

AbstractThe propagation of transient inertio-gravity waves in a shear flow is examined using the Gaussian beam formulation. This formulation assumes Gaussian wavepackets in the spectral space and uses a second-order Taylor expansion of the phase of the wave field. In this sense, the Gaussian beam formulation is also an asymptotic approximation like spatial ray tracing; however, the first one is free of the singularities found in spatial ray tracing at caustics. Therefore, the Gaussian beam formulation permits the examination of the evolution of transient inertio-gravity wavepackets from the initial time up to the destabilization of the flow close to the critical levels. We show that the transience favours the development of the dynamical instability relative to the convective instability. In particular, there is a well-defined threshold for which small initial amplitude transient inertio-gravity waves never reach the convective instability criterion. This threshold does not exist for steady-state inertio-gravity waves for which the wave amplitude increases indefinitely towards the critical level. The Gaussian beam formulation is shown to be a powerful tool to treat analytically several aspects of inertio-gravity waves in simple shear flows. In more realistic shear flows, its numerical implementation is readily available and the required numerical calculations have a low computational cost.