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We review our current knowledge of the atmospheric dynamics of Venus prior to the Akatsuki mission, in the altitude range from the surface to approximately the cloud tops located at about 100 km altitude. The three-dimensional structure of the wind field in this region has been determined with a variety of techniques over a broad range of spatial and temporal scales (from the mesoscale to planetary, from days to years, in daytime and nighttime), spanning a period of about 50 years (from the 1960s to the present). The global panorama is that the mean atmospheric motions are essentially zonal, dominated by the so-called super-rotation (an atmospheric rotation that is 60 to 80 times faster than that of the planetary body). The zonal winds blow westward (in the same direction as the planet rotation) with a nearly constant speed of ∼ 100 m s − 1 at the cloud tops (65–70 km altitude) from latitude 50°N to 50°S, then decreasing their speeds monotonically from these latitudes toward the poles. Vertically, the zonal winds decrease with decreasing altitude towards velocities ∼ 1 – 3 m s − 1 in a layer of thickness ∼ 10 km close to the surface. Meridional motions with peak speeds of ∼ 15 m s − 1 occur within the upper cloud at 65 km altitude and are related to a Hadley cell circulation and to the solar thermal tide. Vertical motions with speeds ∼ 1 – 3 m s − 1 occur in the statically unstable layer between altitudes of ∼ 50 – 55 km . All these motions are permanent with speed variations of the order of ∼ 10 % . Various types of wave, from mesoscale gravity waves to Rossby-Kelvin planetary scale waves, have been detected at and above cloud heights, and are considered to be candidates as agents for carrying momentum that drives the super-rotation, although numerical models do not fully reproduce all the observed features. Momentum transport by atmospheric waves and the solar tide is thought to be an indispensable component of the general circulation of the Venus atmosphere. Another conspicuous feature of the atmospheric circulation is the presence of polar vortices. These are present in both hemispheres and are regions of warmer and lower clouds, seen prominently at infrared wavelengths, showing a highly variable morphology and motions. The vortices spin with a period of 2–3 days. The South polar vortex rotates around a geographical point which is itself displaced from the true pole of rotation by ∼ 3  degrees. The polar vortex is surrounded and constrained by the cold collar, an infrared-dark region of lower temperatures. We still lack detailed models of the mechanisms underlying the dynamics of these features and how they couple (or not) to the super-rotation. The nature of the super-rotation relates to the angular momentum stored in the atmosphere and how it is transported between the tropics and higher latitudes, and between the deep atmosphere and upper levels. The role of eddy processes is crucial, but likely involves the complex interaction of a variety of different types of eddy, either forced directly by radiative heating and mechanical interactions with the surface or through various forms of instability. Numerical models have achieved some significant recent success in capturing some aspects of the observed super-rotation, consistent with the scenario discussed by Gierasch (J. Atmos. Sci. 32:1038–1044, 1975 ) and Rossow and Williams (J. Atmos. Sci. 36:377–389, 1979 ), but many uncertainties remain, especially in the deep atmosphere. The theoretical framework developed to explain the circulation in Venus’s atmosphere is reviewed, as well as the numerical models that have been built to elucidate the super-rotation mechanism. These tools are used to analyze the respective roles of the different waves in the processes driving the observed motions. Their limitations and suggested directions for improvements are discussed.

Over the course of his career, Fuqing Zhang drew vital new insights into the dynamics of meteorologically significant mesoscale gravity waves (MGWs), including their generation by unbalanced jet streaks, their interaction with fronts and organized precipitation, and their importance in midlatitude weather and predictability. Zhang was the first to deeply examine “spontaneous balance adjustment”—the process by which MGWs are continuously emitted as baroclinic growth drives the upper-level flow out of balance. Through his pioneering numerical model investigation of the large-amplitude MGW event of 4 January 1994, he additionally demonstrated the critical role of MGW–moist convection interaction in wave amplification. Zhang’s curiosity-turned-passion in atmospheric science covered a vast range of topics and led to the birth of new branches of research in mesoscale meteorology and numerical weather prediction. Yet, it was his earliest studies into midlatitude MGWs and their significant impacts on hazardous weather that first inspired him. Such MGWs serve as the focus of this review, wherein we seek to pay tribute to his groundbreaking contributions, review our current understanding, and highlight critical open science issues. Chief among such issues is the nature of MGW amplification through feedback with moist convection, which continues to elude a complete understanding. The pressing nature of this subject is underscored by the continued failure of operational numerical forecast models to adequately predict most large-amplitude MGW events. Further research into such issues therefore presents a valuable opportunity to improve the understanding and forecasting of this high-impact weather phenomenon, and in turn, to preserve the spirit of Zhang’s dedication to this subject.

This study documents the contribution of equatorial waves and mesoscale gravity waves to the momentum budget of the quasi-biennial oscillation (QBO) in a 110-level version of the Whole Atmosphere Community Climate Model. The model has high vertical resolution, 500 m, above the boundary layer and through the lower and middle stratosphere, decreasing gradually to about 1.5 km near the stratopause. Parameterized mesoscale gravity waves and resolved equatorial waves contribute comparable easterly and westerly accelerations near the equator. Westerly acceleration by resolved waves is due mainly to Kelvin waves of zonal wavenumber in the range k = 1–15 and is broadly distributed about the equator. Easterly acceleration near the equator is due mainly to Rossby–gravity (RG) waves with zonal wavenumbers in the range k = 4–12. These RG waves appear to be generated in situ during both the easterly and westerly phases of the QBO, wherever the meridional curvature of the equatorial westerly jet is large enough to produce reversals of the zonal-mean barotropic vorticity gradient, suggesting that they are excited by the instability of the jet. The RG waves produce a characteristic pattern of Eliassen–Palm flux divergence that includes strong easterly acceleration close to the equator and westerly acceleration farther from the equator, suggesting that the role of the RG waves is to redistribute zonal-mean vorticity such as to neutralize the instability of the westerly jet. Insofar as unstable RG waves might be present in the real atmosphere, mixing due to these waves could have important implications for transport in the tropical stratosphere.

This study investigated the daily cycle of the wind and divergence fields observed off the southwestern coast of Sumatra during a field campaign of the Years of the Maritime Continent pilot study. An algorithm was developed to retrieve kinematic variables from the single-Doppler data collected aboard the Research Vessel Mirai from 24 November to 13 December 2015. The observed daily cycles of the wind and divergence fields consisted of diurnal, semidiurnal, and short-term variations. Diurnal wind variation was characterized by deep and three-dimensional circulation. There was an approximate phase locking of the semidiurnal variation to the diurnal variation, both in the wind and divergence fields. The short-term wind variation occurred at a time scale of ∼1–3 h, and this pattern was associated with density currents or mesoscale gravity waves. Up to 73% of the daily vertical motion variance can be attributed to the diurnal and semidiurnal vertical motion variations with comparable strengths. Concurrently, precipitation propagated offshore in phase with density currents and mesoscale gravity waves. Our results suggest that diurnal and semidiurnal wind variations dominate the daily evolution of precipitation, whereas density currents and mesoscale gravity waves control offshore propagation. Additionally, it appears that the daily precipitation cycle is modulated by multiple-time-scale wind variabilities of less than a day, which is also responsible for the development of strong nocturnal convection off the southwestern coast of Sumatra.

The mesosphere and lower thermosphere (MLT) is a dynamic layer of the earth's atmosphere. This region marks the interface at which neutral atmosphere dynamics begin to influence the upper atmosphere and ionosphere. However, our understanding of this region and our ability to accurately simulate it in global circulation models (GCMs) is limited by a lack of observations, especially in remote locations. To this end, a meteor radar was deployed from 2016 to 2020 on the remote mountainous island of South Georgia (54∘ S, 36∘ W) in the Southern Ocean. In this study we use these new measurements to characterise the fundamental dynamics of the MLT above South Georgia including large-scale winds, solar tides, planetary waves (PWs), and mesoscale gravity waves (GWs). We first present an improved method for time–height localisation of radar wind measurements and characterise the large-scale MLT winds. We then determine the amplitudes and phases of the diurnal (24 h), semidiurnal (12 h), terdiurnal (8 h), and quardiurnal (6 h) solar tides at this latitude. We find very large amplitudes up to 30 m s−1 for the quasi 2 d PW in summer and, combining our measurements with the meteor SAAMER radar in Argentina, show that the dominant modes of the quasi 5, 10, and 16 d PWs are westward 1 and 2. We investigate and compare wind variance due to both large-scale “resolved” GWs and small-scale “sub-volume” GWs in the MLT and characterise their seasonal cycles. Last, we use our radar observations and satellite temperature observations from the Microwave Limb Sounder to test a climatological simulation of the Whole Atmosphere Community Climate Model (WACCM). We find that WACCM exhibits a summertime mesopause near 80 km altitude that is around 10 K warmer and 10 km lower in altitude than observed. Above 95 km altitude, summertime meridional winds in WACCM reverse to poleward, but this not observed in radar observations in this altitude range. More significantly, we find that wintertime zonal winds between 85 to 105 km altitude are eastward up to 40 m s−1 in radar observations, but in WACCM they are westward up to 20 m s−1. We propose that this large discrepancy may be linked to the impacts of secondary GWs (2GWs) on the residual circulation, which are not included in most global models, including WACCM. These radar measurements can therefore provide vital constraints that can guide the development of GCMs as they extend upwards into this important region of the atmosphere.

This paper compares two different approaches for the efficient modeling of subgrid-scale inertia–gravity waves in a rotating compressible atmosphere. The first approach, denoted as the pseudomomentum scheme, exploits the fact that in a Lagrangian-mean reference frame the response of a large-scale flow can only be due to forcing momentum. Present-day gravity wave parameterizations follow this route. They do so, however, in an Eulerian-mean formulation. Transformation to that reference frame leads, under certain assumptions, to pseudomomentum-flux convergence by which the momentum is to be forced. It can be shown that this approach is justified if the large-scale flow is in geostrophic and hydrostatic balance. Otherwise, elastic and thermal effects might be lost. In the second approach, called the direct scheme and not relying on such assumptions, the large-scale flow is forced both in the momentum equation, by anelastic momentum-flux convergence and an additional elastic term, and in the entropy equation, via entropy-flux convergence. A budget analysis based on one-dimensional wave packets suggests that the comparison between the abovementioned two schemes should be sensitive to the following two parameters: 1) the intrinsic frequency and 2) the wave packet scale. The smaller the intrinsic frequency is, the greater their differences are. More importantly, with high-resolution wave-resolving simulations as a reference, this study shows conclusive evidence that the direct scheme is more reliable than the pseudomomentum scheme, regardless of whether one-dimensional or two-dimensional wave packets are considered. In addition, sensitivity experiments are performed to further investigate the relative importance of each term in the direct scheme, as well as the wave–mean flow interactions during the wave propagation.

The momentum forcing of the QBO (quasi-biennial oscillation) by equatorial waves is estimated using recent reanalyses. Based on the estimation using the conventional pressure-level data sets, the forcing by the Kelvin waves (3–9 m s−1 month−1) dominates the net forcing by all equatorial wave modes (3–11 m s−1 month−1) in the easterly-to-westerly transition phase at 30 hPa. In the opposite phase, the net forcing by equatorial wave modes is small (1–5 m s−1 month−1). By comparing the results with those from the native model-level data set of the ERA-Interim reanalysis, it is suggested that the use of conventional-level data causes the Kelvin wave forcing to be underestimated by 2–4 m s−1 month−1. The momentum forcing by mesoscale gravity waves, which are unresolved in the reanalyses, is deduced from the residual of the zonal wind tendency equation. In the easterly-to-westerly transition phase at 30 hPa, the mesoscale gravity wave forcing is found to be smaller than the resolved wave forcing, whereas the gravity wave forcing dominates over the resolved wave forcing in the opposite phase. Finally, we discuss the uncertainties in the wave forcing estimates using the reanalyses.

A series of cloud-permitting simulations with the Weather Research and Forecast model (WRF) are performed to study the characteristics and source mechanisms of mesoscale gravity waves in moist baroclinic jet–front systems with varying degrees of convective instability. These idealized experiments are initialized with the same baroclinic jet but with different initial moisture content, which produce different life cycles of moist baroclinic waves, to investigate the relative roles of moist processes and baroclinicity in the generation and propagation of mesoscale gravity waves. The dry experiment with no moisture or convection simulates gravity waves that are consistent with past modeling studies. An experiment with a small amount of moisture produces similar baroclinic life cycles to the dry experiment but with the introduction of weak convective instability. Subsequent initiation of convection, although weak, may considerably amplify the gravity waves that are propagating away from the upper-level jet exit region crossing the ridge to the jet entrance region. The weak convection also generates a new wave mode of shorter-scale wave packets that are believed to interact with, strengthen, and modify the dry gravity wave modes. Further increase of the moisture content (up to 5 times) leads to strong convective instability and vigorous moist convection. Besides a faster-growing moist baroclinic wave, the convectively generated gravity waves emerge much earlier, are more prevalent, and are larger in amplitude; they are fully coupled with, and hardly separable from, the dry gravity wave modes under the complex background moist baroclinic waves.

The characteristics of the mesoscale gravity waves during a snowfall event on November 30, 2018 over the Ili Valley and the northern slope of the Tianshan Mountains are analyzed based on the Weather Research and Forecasting model simulation. The vertical distribution of R o is similar to that of the residual of the nonlinear balance equation ( Δ N B E ), with their high-value areas located over the leeward slope and the fluctuations extending upwardly with time, indicating the characteristics of strong ageostrophy and non-equilibrium of atmospheric motions. In addition, the R o and Δ N B E are first developed in the lower layers over the leeward slope, revealing that the generation of the gravity waves is closely related to the topography. Thus, the topographic uplifting greatly affects this snowfall, and the ageostrophic motion in the whole troposphere and the lower stratosphere, as well as the unbalanced motions between convergence and divergence over the peak and the leeward slope are conductive to the development of the inertia-gravity waves. In terms of the horizontal scale of the gravity waves, the Barnes’ band-pass filter is applied to separate the mesoscale waves and the synoptic-scale basic flow. The vertical distributions of the vorticity and divergence perturbations have a phase difference of π/2, indicating the polarization state of gravity waves. The analyses on the sources and sinks of gravity waves by the non-hydrostatic wave equation show that the main forcing term for orographic gravity waves is the second-order nonlinear term, whose magnitude mainly depends on the nonlinear thermal forcing. This term is mainly related to the vertical transport of potential temperature perturbations. During the snowfall, the potential temperature perturbations are mainly caused by the topographic relief and the release of condensation latent heat. Therefore, the gravity waves in this snowfall are caused by the topographic forcing and condensation latent heating.

An idealized cloud-system-resolving model simulation is used to examine the coupling between a tropical cloud population and the mesoscale gravity waves that it generates. Spectral analyses of the cloud and gravity wave fields identify a clear signal of coupling between the clouds and a deep tropospheric gravity wave mode with a vertical wavelength that matches the depth of the convection, which is about two-thirds of the tropospheric depth. This vertical wavelength and the period of the waves, defined by a characteristic convective time scale, means that the horizontal wavelength is constrained through the dispersion relation. Indeed, the wave–convection coupling manifests at the appropriate wavelength, with the emergence of quasi-regular cloud-system spacing of order 100 km. It is shown that cloud systems at this spacing achieve a quasi-resonant state, at least for a few convective life cycles. Such regular spacing is a key component of cloud organization and is likely a contributor to the processes controlling the upscale growth of convective systems. Other gravity wave processes are also elucidated, including their apparent role in the maintenance of convective systems by providing a mechanism for renewed convective activity and system longevity.