Rossby Modes Research Articles

Planetary wave induced wind and airglow oscillations in the middle latitude MLT region

Upper mesosphere airglow emissions and temperature observed at Rikubetsu (43.5°N,143.8°E) and mesospheric winds observed at Wakkanai (45.4°N,141.8°E), Japan, from January to December 2005 were used to analyze periodic oscillations of 2–16 days. During the January to March period and after September, both winds and airglow demonstrated clear 8-, 10- and 16-day oscillations. Downward phase progressions observed in the oscillations indicate that these are a signature of Rossby mode planetary waves. The 16-day wave was more evident in the zonal wind than the meridional. The 10-day wave was observed in January and March, on the basis of only a few cycles superposed on the 16-day wave. Airglow OI 557.7nm, O2 and OH(6,2) band emissions and O2 rotational temperature also showed significant amplitude of oscillation induced by the wave passages. For the 10-day wave, OI557.7nm showed an amplitude of oscillation equals to or more than 50% of the mean intensity level, O2 ∼45% and OH ∼25%. Large amplitudes of oscillation of the airglow during the passage of planetary waves suggest the possible vertical transport of atomic oxygen in addition to the density and temperature variations intrinsic to the wave events.

Pacific Decadal Variability: Paced by Rossby Basin Modes?

Abstract A systematic study is presented of decadal climate variability in the North Pacific. In particular, the hypothesis is addressed that oceanic Rossby basin modes are responsible for enhanced energy at decadal and bidecadal time scales. To this end, a series of statistical analyses are performed on a 500-yr control integration of the Community Climate System Model, version 3 (CCSM3). In particular, a principal oscillation pattern (POP) analysis is performed to identify modal behavior in the subsurface pressure field. It is found that the dominant energy of sea surface temperature (SST) variability at 25 yr (the model equivalent of the Pacific decadal oscillation) cannot be explained by the resonant excitation of an oceanic basin mode. However, significant energy in the subsurface pressure field at time scales of 17 and 10 yr appears to be related to internal ocean oscillations. However, these oscillations lack the characteristics of the classical basin modes, and must either be deformed beyond recognition by the background circulation and inhomogeneous stratification or have another dynamical origin altogether. The 17-yr oscillation projects onto the Pacific decadal oscillation and, if present in the real ocean, has the potential to enhance the predictability of low-frequency climate variability in the North Pacific.

The Aqua-Planet Experiment (APE): CONTROL SST Simulation

Climate simulations by 16 atmospheric general circulation models (AGCMs) are compared on an aqua-planet, a water-covered Earth with prescribed sea surface temperature varying only in latitude. The idealised configuration is designed to expose differences in the circulation simulated by different models. Basic features of the aqua-planet climate are characterised by comparison with Earth. The models display a wide range of behaviour. The balanced component of the tropospheric mean flow, and mid-latitude eddy covariances subject to budget constraints, vary relatively little among the models. In contrast, differences in damping in the dynamical core strongly influence transient eddy amplitudes. Historical uncertainty in modelled lower stratospheric temperatures persists in APE.Aspects of the circulation generated more directly by interactions between the resolved fluid dynamics and parameterized moist processes vary greatly. The tropical Hadley circulation forms either a single or double inter-tropical convergence zone (ITCZ) at the equator, with large variations in mean precipitation. The equatorial wave spectrum shows a wide range of precipitation intensity and propagation characteristics. Kelvin mode-like eastward propagation with remarkably constant phase speed dominates in most models. Westward propagation, less dispersive than the equatorial Rossby modes, dominates in a few models or occurs within an eastward propagating envelope in others. The mean structure of the ITCZ is related to precipitation variability, consistent with previous studies.The aqua-planet global energy balance is unknown but the models produce a surprisingly large range of top of atmosphere global net flux, dominated by differences in shortwave reflection by clouds. A number of newly developed models, not optimised for Earth climate, contribute to this. Possible reasons for differences in the optimised models are discussed.The aqua-planet configuration is intended as one component of an experimental hierarchy used to evaluate AGCMs. This comparison does suggest that the range of model behaviour could be better understood and reduced in conjunction with Earth climate simulations. Controlled experimentation is required to explore individual model behavior and investigate convergence of the aqua-planet climate with increasing resolution.

Controlling the Computational Modes of the Arbitrarily Structured C Grid

Abstract The arbitrarily structured C grid, Thuburn–Ringler–Skamarock–Klemp (TRiSK), is being used in the Model for Prediction Across Scales (MPAS) and is being considered by the Met Office for their next dynamical core. However, the hexagonal C grid supports a branch of spurious Rossby modes, which lead to erroneous grid-scale oscillations of potential vorticity (PV). It is shown how these modes can be harmlessly controlled by using upwind-biased interpolation schemes for PV. A number of existing advection schemes for PV are tested, including that used in MPAS, and none are found to give adequate results for all grids and all cases. Therefore a new scheme is proposed; continuous, linear-upwind stabilized transport (CLUST), a blend between centered and linear-upwind with the blend dependent on the flow direction with respect to the cell edge. A diagnostic of grid-scale oscillations is proposed that gives further discrimination between schemes than using potential enstrophy alone. Indeed, some schemes are found to destroy potential enstrophy while grid-scale oscillations grow. CLUST performs well on hexagonal-icosahedral grids and unrotated skipped latitude–longitude grids of the sphere for various shallow-water test cases. Despite the computational modes, the hexagonal icosahedral grid performs well since these modes are easy and harmless to filter. As a result, TRiSK appears to perform better than a spectral shallow-water model.

An experimental study of the Atlantic variability on interdecadal timescales

Abstract. A series of laboratory experiments has been carried out to model the basic dynamics of the multidecadal variability observed in North Atlantic sea surface temperature (SST) records. According to the minimal numerical sector model introduced by te Raa and Dijkstra (2002), the three key components to excite such a low-frequency variability are rotation, meridional temperature gradient and additive thermal noise in the surface heat forcing. If these components are present, periodic perturbations of the overturning background flow are excited, leading to thermal Rossby mode like propagation of anomalous patches in the SST field. Our tabletop scale setup was built to capture this phenomenon, and to test whether the aforementioned three components are indeed sufficient to generate a low-frequency variability in the system. The results are compared to those of the numerical models, as well as to oceanic SST reanalysis records. To the best of our knowledge, the experiment described here is the very first to investigate the dynamics of the North Atlantic multidecadal variability in a laboratory-scale setup.

Analysis of wave-like oscillations in parameters of sporadic E layer and neutral atmosphere

The present study mainly concerns the wave-like activity in the ionospheric sporadic E layer (Es) and in the lower lying stratosphere. The proposed analysis involves parameters describing the state of plasma in the sporadic E layer. Critical frequencies foEs and layer heights hEs were measured at the Pruhonice station (50°N, 14.5°E) during summer campaigns 2004, 2006 and 2008. Further, we use neutral atmosphere (temperature data at 10hPa) data from the same time interval. The analysis concentrates on vertically propagating wave-like structures within distant atmospheric regions. By means of continuous wavelet transform (CWT) we have detected significant wave-like oscillation at periods covering tidal and planetary oscillation domains both in the Es layer parameters (some of them were reported earlier, for instance in works of Abdu et al., 2003; Pancheva and Mitchel, 2004; Pancheva et al., 2003; Šauli and Bourdillon, 2008) and in stratospheric temperature variations. Further analyses using cross wavelet transform (XWT) and wavelet coherence analysis (WTC) show that despite high wave-like activity in a wide period range, there are only limited coherent wave-like bursts present in both spectra. Such common coherent wave bursts occur on periods close to eigen-periods of the terrestrial atmosphere. We suppose that vertical coupling between atmospheric regions realized by vertically propagating planetary waves occurs predominantly on periods close to those of Rossby modes. Analysis of the phase shift between data from distant atmospheric regions reveals high variability and very likely supports the non-linear scenario of the vertical coupling provided by planetary waves.

Rossby wave instability in 3D discs

The Rossby wave instability (RWI) is a promising mechanism for producing large-scale vortices in protoplanetary discs. The instability operates around a density bump in the disc, and the resulting vortices may facilitate planetesimal formation and angular momentum transfer in the disc dead zone. Most previous works on the RWI deal with 2D (height-integrated) discs. However, vortices in 3D may have different dynamical behaviours from those in 2D. Recent numerical simulations of the RWI in 3D global discs by Meheut et al. have revealed intriguing vertical structure of the vortices, including appreciable vertical velocities. In this paper we present a linear analysis of the RWI, in 3D global models of isothermal discs. We calculate the growth rates of the Rossby modes (of various azimuthal wave numbers m= 2–6) trapped around the fiducial density bump and carry out 3D numerical simulations to compare with our linear results. We show that the 3D RWI growth rates are only slightly smaller than the 2D growth rates, and the velocity structures seen in the numerical simulations during the linear phase are in agreement with the velocity eigenfunctions obtained in our linear calculations. This numerical benchmark shows that numerical simulations can accurately describe the instability. The angular momentum transfer rate associated with Rossby vortices is also studied.

Large-Scale Rossby Normal Modes during Some Recent Northern Hemisphere Winters

Abstract Large-scale Rossby normal modes are studied for the Northern Hemisphere winters of 2005, 2006, 2008, and 2009 using global observational meteorological analyses spanning the 0–92-km altitude range. Spectral analysis of geopotential height fields shows pronounced peaks at westward-propagating zonal wavenumber 1 near the theoretical locations of the free Rossby waves at 25, 16, 10, and 5 days that, in some cases, have amplitudes significantly larger than the estimated background spectrum. Evidence is also found for a wavenumber-2 free mode near 4 days. A coherence analysis is used to extract the amplitude and phase of the waves, and to isolate those regions of the latitude/altitude plane where the signals are statistically significant. Although the spectral location, temporal evolution, and vertical structure of several of these waves are suggestive of the presence of Rossby normal modes, this study shows that in the real atmosphere the waves only occasionally have the global properties of classical normal modes. Moreover, no evidence is found that the amplitudes of these modes are enhanced during stratospheric sudden warmings.

A dynamo driven by zonal jets at the upper surface: Applications to giant planets

We present a dynamo mechanism arising from the presence of barotropically unstable zonal jet currents in a rotating spherical shell. The shear instability of the zonal flow develops in the form of a global Rossby mode, whose azimuthal wavenumber depends on the width of the zonal jets. We obtain self-sustained magnetic fields at magnetic Reynolds numbers greater than 103. We show that the propagation of the Rossby waves is crucial for dynamo action. The amplitude of the axisymmetric poloidal magnetic field depends on the wavenumber of the Rossby mode, and hence on the width of the zonal jets. We discuss the plausibility of this dynamo mechanism for generating the magnetic field of the giant planets. Our results suggest a possible link between the topology of the magnetic field and the profile of the zonal winds observed at the surface of the giant planets. For narrow Jupiter-like jets, the poloidal magnetic field is dominated by an axial dipole whereas for wide Neptune-like jets, the axisymmetric poloidal field is weak.

The onset of strongly localized thermal convection in rotating spherical shells

AbstractA Boussinesq fluid of kinematic velocity$\nu $and thermal diffusivity$\kappa $is confined within a rapidly rotating shell with inner and outer sphere boundary radii${ r}_{i}^{\ensuremath{\ast} } $and${ r}_{o}^{\ensuremath{\ast} } $, respectively. The boundaries of the shell corotate at angular velocity${ \Omega }_{io}^{\ensuremath{\ast} } $and a continuously varying stratification profile is applied which is unstable in${ r}_{i}^{\ensuremath{\ast} } \lt {r}^{\ensuremath{\ast} } \lt { r}_{n}^{\ensuremath{\ast} } \equiv \mathop{ (1+ {\varepsilon }^{2} )}\nolimits ^{1/ 2} { r}_{i}^{\ensuremath{\ast} } $and stable in${ r}_{n}^{\ensuremath{\ast} } \lt {r}^{\ensuremath{\ast} } \lt { r}_{o}^{\ensuremath{\ast} } $. When$\varepsilon \ll 1$, the unstable zone attached to the inner boundary is thin. As in previous small Ekman number$E= \nu / (2{ \Omega }_{io}^{\ensuremath{\ast} } {{ r}_{i}^{\ensuremath{\ast} } }^{2} )$studies, convection at the onset of instability takes on the familiar ‘cartridge belt’ structure, which is localized within a narrow layer adjacent to, but outside, the cylinder tangent to the inner sphere at its equator (Dormyet al. J. Fluid Mech., 2004, vol. 501, pp. 43–70), with estimated radial width of order$ \mathop{ (E{\varepsilon }^{4} )}\nolimits ^{2/ 9} { r}_{i}^{\ensuremath{\ast} } $. The azimuthally propagating convective columns, described by the cartridge belt, reside entirely within the unstable layer when${E}^{1/ 5} \ll \varepsilon $, and extend from the equatorial plane an axial distance$\varepsilon { r}_{i}^{\ensuremath{\ast} } $along the tangent cylinder as far as its intersection with the neutrally stable spherical surface${r}^{\ensuremath{\ast} } = { r}_{n}^{\ensuremath{\ast} } $. We investigate the eigensolutions of the ordinary differential equation governing the axial structure of the cartridge belt both numerically for moderate-to-small values of the stratification parameter$\varepsilon $and analytically when$\varepsilon \ll 1$. At the lowest order of the expansion in powers of$\varepsilon $, the eigenmodes resemble those for classical plane layer convection, being either steady (exchange of stabilities) or, for small Prandtl number$P\equiv \nu / \kappa \hspace{0.167em} \lt 1$, oscillatory (overstability) with a frequency$\pm {\Omega }^{\ensuremath{\ast} } $. At the next order, the axial variation of the basic state removes any plane layer degeneracies. First, the exchange of stabilities modes oscillate at a low frequency causing the short axial columns to propagate as a wave with a small angular velocity, termed slow modes. Second, the magnitudes of both the Rayleigh number and frequency of the two overstable modes, termed fast modes, split. When$P\lt 1$the slow modes that exist at large azimuthal wavenumbers$M$make a continuous transition to the preferred fast modes at small$M$. At all values of$P$the critical Rayleigh number corresponds to a mode exhibiting prograde propagation, whether it be a fast or slow mode. This feature is shared by the uniform classical convective shell models, as well as Busse’s celebrated annulus model. None of them possess any stable stratification and typically are prone to easily excitable Rossby or inertial modes of convection at small$P$. By way of contrast these structures cannot exist in our model for small$\varepsilon $due to the viscous damping in the outer thick stable region.

Stratospheric Sudden Warmings as Self-Tuning Resonances. Part II: Vortex Displacement Events

Abstract Vortex displacement stratospheric sudden warmings (SSWs) are studied in an idealized model of a quasigeostrophic columnar vortex in an anelastic atmosphere. Motivated by the fact that observed events occur at a fixed orientation to the earth’s surface and have a strongly baroclinic vertical structure, vortex Rossby waves are forced by a stationary topographic forcing designed to minimize excursions of the vortex from its initial position. Variations in the background stratospheric “climate” are represented by means of an additional flow in solid body rotation. The vortex response is determined numerically as a function of the forcing strength M and the background flow strength Ω. At moderate M it is found that a large response, with many features resembling observed displacement SSWs, occurs only for a narrow range of Ω. Linear analysis reveals that for this range of Ω the first baroclinic azimuthal wave-1 Rossby wave mode is close to being resonantly excited. A forced nonlinear oscillator equation is proposed to describe the nonlinear behavior, and a method for determining the relevant coefficients numerically, using unforced calculations of steadily propagating vortex “V states,” is adopted. The nonlinear equation predicts some qualitative details of the variation in the response at finite M. However, it is concluded that strongly nonlinear processes, such as wave breaking and filament formation, are necessarily quantitatively important in determining the amplitude of the near-resonant response at finite M.

A time splitting scheme for the nonhydrostatic atmospheric model

A semi-implicit finite difference scheme with time splitting corresponding to the multi-scale nature of atmospheric dynamics is developed for the nonhydrostatic atmospheric model. The fast acoustic and gravity waves are approximated implicitly, while relatively slow advective terms and Rossby modes are treated explicitly. The used level of implicitness requires a solution of the three-dimensional linear elliptic equation at each time step, which is accomplished efficiently by vertical decoupling and subsequent application of fast and accurate multigrid solvers for the most significant vertical modes, and fast and simpler solvers for the secondary ones. Analysis of the linear stability of the scheme reveals that the Courant–Friedrichs–Lewy condition on the time step associated with gravity and acoustic waves can be circumvented and the maximum stable time step can be brought into closer agreement with the time step limitations arising from accuracy considerations. The performed numerical experiments show the computational efficiency of the designed scheme and accuracy of the predicted atmospheric fields.

Rossby–Khantadze electromagnetic planetary vortical motions in the ionospheric E-layer

AbstractIt is shown that in the earth's conductive ionospheric E-region, large-scale ultra low-frequency Rossby and Khantadze electromagnetic waves can propagate. Along with the prevalent effect of Hall conductivity for these waves, the latitudinal inhomogeneity of both the earth's angular velocity and the geomagnetic field becomes essential. Action of these effects leads to the coupled propagation of electromagnetic Rossby and Khantadze modes. Linear propagation properties of these waves are given in detail. It is shown that the waves lose the dispersing property for large values of wave numbers. Corresponding nonlinear solitary vortical structures are constructed. Conditions for such self-organization are given. It is shown that nonlinear large-scale vortices generate the stronger pulses of the geomagnetic field than the corresponding linear waves. Previous investigations are revised.

The Relative Roles of Different Physical Processes in Unstable Midlatitude Ocean–Atmosphere Interactions

Abstract Following Goodman and Marshall (hereinafter GM), an improved intermediate midlatitude coupled ocean–atmosphere model linearized around a basic state is developed. The model assumes a two-layer quasigeostrophic atmosphere overlying a quasigeostrophic upper ocean that consists of a constant-depth mixed layer, a thin entrainment layer, and a thermocline layer. The SST evolution is determined within the mixed layer by advection, entrainment, and air–sea flux. The atmospheric heating is specified at midlevel, which is parameterized in terms of both the SST and atmospheric temperature anomalies. With this coupled model, the dynamical features of unstable ocean–atmosphere interactions in the midlatitudes are investigated. The coupled model exhibits two types of coupled modes: the coupled oceanic Rossby wave mode and the SST-only mode. The SST-only mode decays over the entire range of wavelengths, whereas the coupled oceanic Rossby wave mode destabilizes over a certain range of wavelengths (∼10 500 km) when the atmospheric response to the heating is equivalent barotropic. The relative roles of different physical processes in destabilizing the coupled oceanic Rossby wave are examined. The main processes emphasized are the influence of entrainment and advection for determining SST evolution, and the atmospheric heating profile. Although either entrainment or advection can lead to unstable growth of the coupled oceanic Rossby wave with similar wavelength dependence for each case, the advection process is found to play the more important role, which differs from GM’s results in which the entrainment process is dominant. The structure of the unstable coupled mode is sensitive to the atmospheric heating profile. The inclusion of surface heating largely reduces the growth rate and stabilizes the coupled oceanic Rossby wave. In comparison with observations, it is demonstrated that the structure of the growing coupled mode derived from the authors’ model is closer to reality than that from the previous model.

Energy Spectra of Rossby and Gravity Waves

The characteristics of energy spectrum based on 3D normal mode energetics are investigated with the global analysis dataset provided by Japan Meteorological Agency (JMA) with the resolution of TL959L60. The energy spectrum of gravity modes exactly follows the -5/3 power law in the synoptic and mesoscales. In the synoptic scale, the spectral slope of total energy follows the -3 power law because Rossby waves are dominant compared to gravity waves. The energy level of gravity modes becomes larger than that of Rossby modes around the zonal wavenumber k = 80. This scale corresponds to 350 km in 45°circle. The total energy spectrum does not show a clear transition from -3 power slope to -5/3 power slope because the energy level of Rossby and gravity modes become comparable near the transition wavenumbers.

Characteristics and origin of quasi‐biweekly oscillation over the western North Pacific during boreal summer

This study investigates the structure, energetic, and origin of quasi‐biweekly oscillation (QBWO) over the western North Pacific (WNP), using NCEP reanalyses for the years 2000–2007. In the context of vorticity there appears to be a significant QBWO mode over the WNP during the summer. QBWO emerges from the equatorial region and propagates northwestward. Its horizontal structure exhibits a slight southwest‐northeast tilt but mainly longitudinal elongation. In the vertical the QBWO has a northwest tilt with height that gives rise to a structure of the first baroclinic mode. The centers of vorticity and vertical motion near the equator show a phase lag of about one‐quarter wavelength, consistent with the characteristics of equatorial waves, whereas the cyclonic circulation is tightly coupled with anomalous convection as the wave moves away from the equator. Energetic analysis of the QBWO reveals that diabatic heating in the tropics and baroclinic processes in the subtropics play important roles in the generation of eddy available potential energy (EAPE). In turn, the conversion from EAPE to eddy kinetic energy (EKE) and the barotropic conversion are major sources for EKE to compensate the loss by EKE redistribution and dissipation. Tracing the QBWO to equatorial disturbances, our results show some features of equatorially trapped n = 1 Rossby mode, such as phase speed and group velocity. This mode is generally characterized by a zonal planetary wave number of about 6 and nearly symmetric circulation about the equator. A typical case from 2002 is chosen to illustrate that the origin of the QBWO is closely associated with the theoretical equatorial Rossby wave.

Alternating zonal flows in a two-layer wind-driven ocean

Alternating zonal flows in an idealized wind-driven double-gyre ocean circulation have been investigated using a two-layer shallow-water eddy-permitting numerical model. While the alternating zonal flows are found almost everywhere in the time-mean zonal velocity field, their meridional scales differ from region to region. In the subpolar western boundary region, where the energetic eddy activity induces quasi two-dimensional turbulence, the alternating zonal flows are generated by the inverse energy cascade and its arrest by Rossby waves, and the meridional scale of the flows corresponds well to the Rhines scale. In the eastern part of the basin, where barotropic basin modes are dominant, the zonal structure is formed through the nonlinear effect of the basin modes and is wider than the Rhines scale. Both effects are likely to form zonal structure between the two regions. These results show that Rossby basin modes become an important factor in the formation of alternating zonal flows in a closed basin in addition to the arrest of the inverse energy cascade by Rossby waves. The wind-driven general circulation associated with eddy activities plays an essential role in determining which mechanism of the alternating zonal flows is possible in each region.

Modal Interpretation for the Ekman Destabilization of Inviscidly Stable Baroclinic Flow in the Phillips Model

Abstract Ekman boundary layers can lead to the destabilization of baroclinic flow in the Phillips model that, in the absence of dissipation, is nonlinearly stable in the sense of Liapunov. It is shown that the Ekman-induced instability of inviscidly stable baroclinic flow in the Phillips model occurs if and only if the kinematic phase velocity associated with the dissipation lies outside the interval bounded by the greatest and least neutrally stable Rossby wave phase velocities. Thus, Ekman-induced destabilization does not correspond to a coalescence of the barotropic and baroclinic Rossby modes as in classical inviscid baroclinic instability. The differing modal mechanisms between the two instability processes is the reason why subcritical baroclinic shears in the classical theory can be destabilized by an Ekman layer, even in the zero dissipation limit of the theory.

Interaction of equatorial waves through resonance with the diurnal cycle of tropical heating

In this work, a new theoretical mechanism is presented in which equatorial Rossby and inertio-gravity wave modes may interact with each other through resonance with the diurnal cycle of tropical deep convection.We have adopted the two-layer incompressible equatorial primitive equations forced by a parametric heating that roughly represents deep convection activity in the tropical atmosphere. The heat source was parametrized in the simplest way according to the hypothesis that it is proportional to the lower-troposphere moisture convergence, with the background moisture state functionmimicking the structure of the ITCZ. In this context, we have investigated the possibility of resonant interaction between equatorially trapped Rossby and inertio-gravity modes through the diurnal cycle of the background moisture state function. The reduced dynamics of a single resonant duo shows that when this diurnal variation is considered, a Rossby wave mode can undergo significant amplitude modulations when interacting with an inertio-gravity wave mode, which is not possible in the context of the resonant triad non-linear interaction. Therefore, the results suggest that the diurnal variation of the ITCZ can be a possible dynamical mechanism that leads the Rossby waves to be significantly affected by high frequency modes.

Studies of inertio‐gravity waves on midlatitude beta‐plane without the traditional approximation

AbstractThe role of the Rossby parameter β due to the meridional variation of the Coriolis parameter f is investigated for inertio‐gravity waves in midlatitudes based on a linear Boussinesq model without the traditional approximation, namely including the role of the horizontal component of the Coriolis vector of the Earth's rotation. Without the β‐effect, it is well established that the non‐traditional Coriolis effects give rise to an additional mode of inertio‐gravity (IG) waves whose frequencies are slightly smaller than the local Coriolis frequency f unlike the traditional IG‐mode whose frequencies are larger than f. The addition of the β‐effect modifies the properties of the sub‐inertial and super‐inertial IG‐modes. These modifications are examined by calculating the model normal modes for a given vertical profile of the buoyancy frequency N. Inclusion of the β‐effect yields the external and internal Rossby modes in addition to the IG‐modes. Presence of the external Rossby mode in this model is a new result, since it does not occur in the traditional version with β nor in the non‐traditional version without β. The normal‐mode properties, including wave frequencies and eigenfunctions, are presented for various values of N. The normal‐mode analysis is complemented by the initial‐value approach to study the evolution of waves generated by forcing. The results of numerical time‐integrations of wave generation in the ocean forced by atmospheric disturbances and by the interaction of tidal flows with bottom topography are presented to reveal a notable role of β for the IG‐waves. Application to atmospheric problems is proposed. Copyright © 2010 Royal Meteorological Society