Rossby Kelvin Research Articles

Equatorial Waves and Superrotation in the Stratosphere of a Titan General Circulation Model

We investigate the characteristics of equatorial waves associated with the maintenance of superrotation in the stratosphere of a Titan general circulation model. A variety of equatorial waves are present in the model atmosphere, including equatorial Kelvin waves, equatorial Rossby waves, and mixed Rossby–gravity waves. In the upper stratosphere, acceleration of superrotation is strongest around solstice and is due to interaction between equatorial Kelvin waves and Rossby-type waves in winter hemisphere midlatitudes. The existence of this “Rossby–Kelvin”-type wave appears to depend on strong meridional shear of the background zonal wind that occurs in the upper stratosphere at times away from the equinoxes. In the lower stratosphere, acceleration of superrotation occurs throughout the year and is partially induced by equatorial Rossby waves, which we speculate are generated by quasigeostrophic barotropic instability. Acceleration of superrotation is generally due to waves with phase speeds close to the zonal velocity of the mean flow. Consequently, they have short vertical wavelengths that are close to the model’s vertical grid scale and therefore likely to be not properly represented. We suggest that this may be a common issue among Titan general circulation models that should be addressed by future model development.

Atmospheric Dynamics of Temperate Sub-Neptunes. I. Dry Dynamics

Abstract Sub-Neptunes (planets with radii between 2 and 4 R ⊕) are abundant around M-dwarf stars, yet the atmospheric dynamics of these planets is relatively unexplored. In this paper, we aim to provide a basic underpinning of the dry dynamics of general low-mean-molecular-weight, temperate sub-Neptune atmospheres. We use the ExoFMS general circulation model (GCM) with an idealized gray-gas radiation scheme to simulate planetary atmospheres with different levels of instellation and rotation rates, using the atmosphere of K2-18b as our control. We find that the atmospheres of tidally locked (TL), temperate sub-Neptunes have weak horizontal temperature gradients owing to their slow rotation rates and hydrogen-dominated composition. The zonal wind structure is dominated by high-latitude cyclostrophic jets driven by the conservation of angular momentum. At low pressures we observe superrotating equatorial jets, which we propose are driven by a Rossby–Kelvin instability similar to the type seen in simulations of idealized atmospheres with axisymmetric forcing. By viewing the flow in TL coordinates, we find the predominant overturning circulation to be between the day side and night side, and we derive scaling relations linking the TL stream function and vertical velocities to instellation. Comparing our results to the only other GCM study of K2-18b, we find significant qualitative differences in dynamics, highlighting the need for further collaboration and investigation into the effects of different dynamical cores and physical parameterizations. This paper provides a baseline for studying the dry dynamics of temperate sub-Neptunes, which will be built on in part II with the introduction of moist effects.

Asymmetry and Variability in the Transmission Spectra of Tidally Locked Habitable Planets

Spatial heterogeneity and temporal variability are general features in planetary weather and climate, due to the effects of planetary rotation, uneven stellar flux distribution, fluid motion instability, etc. In this study, we investigate the asymmetry and variability in the transmission spectra of 1:1 spin–orbit tidally locked (or called synchronously rotating) planets around low-mass stars. We find that for rapidly rotating planets, the transit atmospheric thickness of the evening terminator (east of the substellar region) is significantly larger than that of the morning terminator (west of the substellar region). The asymmetry is mainly related to the spatial heterogeneity in ice clouds, as the contributions of liquid clouds and water vapor are smaller. The underlying mechanism is that there are always more ice clouds on the evening terminator, due to the combined effect of coupled Rossby–Kelvin waves and equatorial superrotation that advect vapor and clouds to the east, especially at high levels of the atmosphere. For slowly rotating planets, the asymmetry reverses (the morning terminator has a larger transmission depth than the evening terminator), but the magnitude is small or even negligible. For both rapidly and slowly rotating planets, there is strong variability in the transmission spectra. The asymmetry signal is nearly impossible to be observed by the James Webb Space Telescope (JWST), because the magnitude of the asymmetry (about 10 ppm) is smaller than the instrumental noise and the high variability further increases the challenge.

Oceanic Superrotation on Tidally Locked Planets

Abstract Is there oceanic superrotation on exoplanets? Atmospheric superrotation, characterized by west-to-east winds over the equator, is a common phenomenon in the atmospheres of Venus, Titan, Saturn, Jupiter, and tidally locked exoplanets. The stratospheric atmosphere of Earth is also superrotating during the westerly phase of the quasi-biennial oscillation. However, whether the same phenomenon can occur in the ocean is poorly known. Through numerical simulations, here we show that oceanic superrotation does occur on tidally locked terrestrial planets around low-mass stars. Its formation (spun up from rest) is associated with surface winds, the equatorward momentum convergence by Rossby waves, and the eastward propagation of Kelvin waves in the ocean. Its maintenance is driven by equatorward momentum transports of coupled Rossby–Kelvin waves in the ocean excited from the uneven stellar radiation distribution. The width of the superrotation is mainly constrained by the Rossby deformation radius in the ocean, while its strength is more complex. Many factors can influence the strength, including planetary rotation rate, stellar flux, greenhouse gas concentration, seawater salinity, and bottom drag, but a scaling theory for the strength of the oceanic superrotation is lacking. This work confirms that oceanic superrotation can occur on tidally locked terrestrial planets with seawater oceans and suggests that it may also occur on tidally locked hot planets with magma oceans that will possibly be observed in the near future.

The instability of vertically curved fronts in a two-layer shallow water model

This paper investigates frontal instabilities in the context of a two-layer shallow water model with both linear and curved interfaces. First, we generalize the model previously established to allow for curved interfaces. Second, we revisit the linear interface case but with higher spatial resolution and study the impact of no-normal flow or radiation boundary conditions. The results show that the former prevents a baroclinic mode from occurring. Third, we investigate the novel problem of curved interfaces and deduce that it does not have a significant impact on a baroclinic instability; however, it does alter the regions of Kelvin–Helmholtz and Rossby–Kelvin instabilities. Furthermore, it introduces a new type of baroclinic instability that we refer to as the vertically curved-interface baroclinic instability.

Tropical Deep Convection Impact on Southern Winter Stationary Waves and Its Modulation by the Quasi-Biennial Oscillation

Abstract The impact of tropical deep convection on southern winter stationary waves and its modulation by the quasi-biennial oscillation (QBO) have been investigated in a long (210 year) climate model simulation and in ERA-Interim reanalysis data for the period 1979–2018. Model results reveal that tropical deep convection over the region of its climatological maximum modulates high-latitude stationary planetary waves in the southern winter hemisphere, corroborating the dominant role of tropical thermal forcing in the generation of these waves. In the tropics, deep convection enhancement leads to wavenumber-1 eddy anomalies that reinforce the climatological Rossby–Kelvin wave couplet. The Rossby wave propagates toward the extratropical southern winter hemisphere and upward through the winter stratosphere reinforcing wavenumber-1 climatological eddies. As a consequence, stronger tropical deep convection is related to greater upward wave propagation and, consequently, to a stronger Brewer–Dobson circulation and a warmer polar winter stratosphere. This linkage between tropical deep convection and the Southern Hemisphere (SH) winter polar vortex is also found in the ERA-Interim reanalysis. Furthermore, model results indicate that the enhancement of deep convection observed during the easterly phase of the QBO (E-QBO) gives rise to a similar modulation of the southern winter extratropical stratosphere, which suggests that the QBO modulation of convection plays a fundamental role in the transmission of the QBO signature to the southern stratosphere during the austral winter, revealing a new pathway for the QBO–SH polar vortex connection. ERA-Interim corroborates a QBO modulation of deep convection; however, the shorter data record does not allow us to assess its possible impact on the SH polar vortex.

Planetary scale selection of the Madden–Julian Oscillation in an air-sea coupled dynamic moisture model

The authors present an air–sea coupled dynamic moisture (ASDM) model to explore the mechanism of preferred planetary scale of the Madden–Julian Oscillation (MJO). This ASDM model, extended from the original frictionally coupled dynamic moisture model and a mixed layer model, can present a good simulation of planetary-scale characteristics of the MJO, including a slow eastward propagation of 5 m s−1, coupled Rossby–Kelvin wave-like structure, and phase leading of convective center by warm sea surface temperature (SST). It is interesting that the planetary-scale selection in terms of instability is only found in the nonlinear ASDM model with the assumption of positive-only heating. Such a scale selection, however, cannot be found in the ASDM model with linear heating or in an uncoupled atmosphere model. The essential mechanism for the scale selection is nonlinear positive-only heating, and the air-sea interaction primarily provides an instability source to support this scale selection. This scale selection is attributed to different phase speeds of coupled moist Rossby–Kelvin waves and dry Kelvin waves. From short-wave initial perturbations, the easterly wind anomalies of eastward-propagating dry Kelvin waves from a stronger wave component will catch up with other weaker moist components and suppress their westerly wind anomalies, resulting in weak SST gradient as well as reduced moisture convergence and precipitation for these suppressed components. As a result, the wavenumber-one structure is selected. The Warm Pool-like mean state will select the stronger component among the initial short-wave perturbations and accelerate this scale selection process. These results provide new insight into MJO mechanism in terms of air-sea interaction.

Monitoring the Madden–Julian oscillation with geopotential height

This paper examines the three-dimensional geopotential height structure of the Madden–Julian oscillation (MJO) and proposes that the MJO convection signals can be well reflected by upper-tropospheric zonal anomalous height gradient (ZAHG, $$\nabla_{x} z'$$ ). A case study in 2011 and composite analyses have been done by applying a wavenumber-frequency filtering method on daily variable anomalies derived from different reanalysis datasets. Results show that the upper-level eastward-moving intraseasonal geopotential height anomaly does not exactly display a Rossby–Kelvin wave structure of the Gill model. Instead, it shows a height quadrupole pattern and is well associated with temperature and zonal wind anomalies. The notable tilted upper-tropospheric temperature structure can be derived from the height anomalies by the hydrostatic balance relationship. The first baroclinic mode vertical structure of zonal wind anomalies can be approximated from the height anomalies by the geostrophic equation. A highlight of the paper is the proposal of tracing the MJO convection center by the upper-tropospheric ZAHG ( $$\nabla_{x} z'$$ ). Composite analyses of all MJO events during extended winter (NDJFM) from 1979 to 2013 suggest that positive upper-tropospheric ZAHG is exactly in phase with negative outgoing longwave radiation (OLR) anomalies in the eastern Indian Ocean and Maritime Continent during a MJO event. On the other hand, positive upper-tropospheric ZAHG leads (lags) negative OLR anomalies by 1 (2) days in the western Indian Ocean (western Pacific Ocean), where MJO events generally initiate (dissipate). ZAHG can also be applied to modeling data and observation data before the satellite era. This study provides a new diagnostic parameter option to monitor MJO events, and an alternative for studying MJOs before the satellite era and model evaluation.

Frontal instabilities and waves in a differentially rotating fluid

AbstractWe present an experimental investigation of the stability of a baroclinic front in a rotating two-layer salt-stratified fluid. A front is generated by the spin-up of a differentially rotating lid at the fluid surface. In the parameter space set by rotational Froude number, $F$, dissipation number, $d$ (i.e. the ratio between disk rotation time and Ekman spin-down time) and flow Rossby number, a new instability is observed that occurs for Burger numbers larger than the critical Burger number for baroclinic instability. This instability has a much smaller wavelength than the baroclinic instability, and saturates at a relatively small amplitude. The experimental results for the instability regime and the phase speed show overall a reasonable agreement with the numerical results of Gula, Zeitlin & Plougonven (J. Fluid Mech., vol. 638, 2009, pp. 27–47), suggesting that this instability is the Rossby–Kelvin instability that is due to the resonance between Rossby and Kelvin waves. Comparison with the results of Williams, Haines & Read (J. Fluid Mech., vol. 528, 2005, pp. 1–22) and Hart (Geophys. Fluid Dyn., vol. 3, 1972, pp. 181–209) for immiscible fluid layers in a small experimental configuration shows continuity in stability regimes in $(F, d)$ space, but the baroclinic instability occurs at a higher Burger number than predicted according to linear theory. Small-scale perturbations are observed in almost all regimes, either locally or globally. Their non-zero phase speed with respect to the mean flow, cusped-shaped appearance in the density field and the high values of the Richardson number for the observed wavelengths suggest that these perturbations are in many cases due to Hölmböe instability.

Instabilities of two-layer shallow-water flows with vertical shear in the rotating annulus

Being motivated by the recent experiments on instabilities of the two-layer flows in the rotating annulus with super-rotating top, we perform a full stability analysis for such system in the shallow-water approximation. We use the collocation method which is benchmarked by comparison with analytically solvable one-layer shallow-water equations linearized about a state of cyclogeostrophic equilibrium. We describe different kinds of instabilities of the cyclogeostrophically balanced state of solid-body rotation of each layer (baroclinic, Rossby–Kelvin (RK) and Kelvin–Helmholtz (KH) instabilities), and give the corresponding growth rates and the structure of the unstable modes. We obtain the full stability diagram in the space of parameters of the problem and demonstrate the existence of crossover regions where baroclinic and RK, and RK and KH instabilities, respectively, compete having similar growth rates.

Ageostrophic instabilities of fronts in a channel in a stratified rotating fluid

It is known that for finite Rossby numbers geostrophically balanced flows develop specific ageostrophic instabilities. We undertake a detailed study of the Rossby–Kelvin (RK) instability, previously studied by Sakai (J. Fluid Mech., vol. 202, 1989, pp. 149–176) in a two-layer rotating shallow-water model. First, we benchmark our method by reproducing the linear stability results obtained by Sakai (1989) and extend them to more general configurations. Second, in order to determine the relevance of RK instability in more realistic flows, simulations of the evolution of a front in a continuously stratified fluid are carried out. They confirm the presence of RK instability with characteristics comparable to those found in the two-layer case. Finally, these simulations are used to study the nonlinear saturation of the RK modes. It is shown that saturation is achieved through the development of small-scale instabilities along the front which modify the mean flow so as to stabilize the RK mode. Remarkably, the developing instability leads to conversion of kinetic energy of the basic flow to potential energy, contrary to classical baroclinic instability.

Decoupling of Balanced and Unbalanced Motions and Inertia–Gravity Wave Emission: Small versus Large Rossby Numbers

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.

The Boreal Summer Intraseasonal Oscillation Simulated in the NCEP Climate Forecast System: The Effect of Sea Surface Temperature

Abstract Observational evidence has indicated the important role of the interaction of the atmosphere with the sea surface in the development and maintenance of the tropical intraseasonal oscillation (ISO). However, improvements in ISO simulations with fully coupled atmosphere–ocean general circulation models are limited and model dependent. This study further examines the effect of air–sea coupling and the basic-state sea surface temperature (SST) associated with the boreal summer intraseasonal oscillation (BSISO) in a 21-yr free run with the recently developed NCEP coupled Climate Forecast System (CFS) model. For this, the CFS run is compared with an Atmospheric Model Intercomparison Project–type long-term simulation forced by prescribed SST in the NCEP Global Forecast System (GFS) model and flux-corrected version of CFS (referred to as CFSA). The GFS run simulates significantly unorganized BSISO convection anomalies, which exhibit an erroneous standing oscillation. The CFS run with interactive air–sea coupling has limited improvements, including the generation of intraseasonal SST variation preceding the convection anomaly by ∼10 days. However, this simulation still does not show the observed continuous northward propagation over the Indian Ocean due to a cold model bias. The CFSA run removes the cold bias in the Indian Ocean and the simulation of the development and propagation of BSISO anomalies are significantly improved. Enhanced and suppressed convection anomalies exhibit the observed quadrupole-like configuration, and phase relationships between precipitation and surface dynamic and thermodynamic variables for the northward propagation are shown to be coherent and consistent with the observations. It is shown that the surface meridional moisture convergence is an important factor for the northward propagation of the BSISO. On the other hand, both the GFS and CFS runs do not realistically simulate an eastward-propagating equatorial mode. The CFSA run produces a more realistic eastward-propagation mode only over the Indian Ocean and Java Sea due to the improved mean state in SST, low-level winds, and vertical wind shear. Reasons for the failure of farther eastward propagation into the west Pacific in CFSA are discussed. This study reconfirms the significance of air–sea interactions. More importantly, however, the results suggest that in order for the influence of the coupled air–sea interaction to be properly communicated, the mean state SST in the coupled model should be reasonably simulated. This is because the basic-state SST itself acts to sustain BSISO convection and it makes the large-scale dynamical environment (i.e., easterly vertical wind shear or low-level westerly zonal wind) more favorable for the propagation of the moist Rossby–Kelvin wave packet.

Shear Instability in a Shallow Water Model with Implications for the Venus Atmosphere

Abstract The shear instability problem in the spherical shallow water system is investigated for three types of wind profiles that are observed at the upper cloud level in Venus. Destabilized Kelvin modes are obtained for all profiles, even when the wind profile is barotropically and inertially stable. The eigenfunctions of these unstable modes are a hybrid of Kelvin modes and continuous modes, which have singularity at the critical latitude. Destabilized Rossby–Kelvin modes are also obtained for the barotropically unstable profile with strong jets. When Lamb parameter ε = (2aΩ)2/gH is large, together with other destabilized gravity modes, these modes have the property of inertial instability modes, which are described by preceding studies on the tropical inertial instability. The destabilizing mechanism of unstable modes is described using resonance theory. It is found that the angular-momentum flux is equatorward for almost all growing modes obtained in this study; this result is consistent with what the resonance theory predicts. This momentum transport may contribute to the mechanism of producing the superrotation of the Venus atmosphere based on the meridional circulation. The destabilized Kelvin modes may be considered as a source of the 4-day waves observed in the equatorial region at the cloud top of Venus.

The global response to tropical heating in the Madden–Julian oscillation during the northern winter

AbstractA life cycle of the Madden–Julian oscillation (MJO) was constructed, based on 21 years of outgoing long‐wave radiation data. Regression maps of NCEP–NCAR reanalysis data for the northern winter show statistically significant upper‐tropospheric equatorial wave patterns linked to the tropical convection anomalies, and extratropical wave patterns over the North Pacific, North America, the Atlantic, the Southern Ocean and South America. To assess the cause of the circulation anomalies, a global primitive‐equation model was initialized with the observed three‐dimensional (3D) winter climatological mean flow and forced with a time‐dependent heat source derived from the observed MJO anomalies. A model MJO cycle was constructed from the global response to the heating, and both the tropical and extratropical circulation anomalies generally matched the observations well. The equatorial wave patterns are established in a few days, while it takes approximately two weeks for the extratropical patterns to appear. The model response is robust and insensitive to realistic changes in damping and basic state. The model tropical anomalies are consistent with a forced equatorial Rossby–Kelvin wave response to the tropical MJO heating, although it is shifted westward by approximately 20° longitude relative to observations. This may be due to a lack of damping processes (cumulus friction) in the regions of convective heating. Once this shift is accounted for, the extratropical response is consistent with theories of Rossby wave forcing and dispersion on the climatological flow, and the pattern correlation between the observed and modelled extratropical flow is up to 0.85. The observed tropical and extratropical wave patterns account for a significant fraction of the intraseasonal circulation variance, and this reproducibility as a response to tropical MJO convection has implications for global medium‐range weather prediction. Copyright © 2004 Royal Meteorological Society