Wave-mean Flow Interaction Research Articles

Numerical experiments on the behavior of Rossby waves in the critical layer

The barotropic vorticity equation is numerically integrated in time to study the behavior of Rossby waves in the vicinity of the critical latitude. The integrations are conducted with linear, quasi-linear (wave-mean flow interaction), and nonlinear models on a sphere for both the inviscid and viscous cases. The meridional resolution required for the correct representation of a vorticity overturning is determined for both the inviscid and viscous cases. The Stewartson–Warn–Warn (SWW) analytical solution is reexamined by comparison with the present numerical results. The cat's eye represented by the closed streamfunction is tilted in the present model results, unlike that in a ‘scaled model’ based on the SWW solution. It is shown that this discrepancy is due to the omission of the meridional structure of the disturbance in the first-order matched asymptotic expansions in the SWW solutions.

Convectively Generated Internal Gravity Waves in the Lower Atmosphere of Venus. Part II: Mean Wind Shear and Wave–Mean Flow Interaction

Abstract This paper is the second of a two-part study that numerically investigates internal gravity wave generation by convection in the lower atmosphere of Venus. Part I of this study considers gravity wave generation and propagation in the absence of mean wind shear. In Part II, the Venus westward superrotation is included, and wave–mean flow interaction is assessed. Both lower-atmosphere convection and cloud-level convection play active roles in the dynamics of the stable layer from 31- to 47-km altitude when mean wind shear is present. This result contrasts with the simulation without mean wind shear presented in Part I where cloud-level convection was primarily responsible for gravity wave generation in the stable layer. In the presence of mean wind shear, upward entrainment from lower-atmosphere convection and downward penetration from cloud-level convection are comparable in magnitude. Convectively generated internal gravity waves have horizontal wavelengths (∼25–30 km) comparable to horizontal sc...

A Simple Model for the Baroclinic Life Cycle of Meridionally Elongated Eddies in Uniform Shear

Abstract A highly simplified model for the wave–mean flow interaction in a baroclinic wave life cycle is derived from the quasigeostrophic two-layer system. The simplification is based on a sheared disturbance embedded in a zonal mean flow with uniform vertical and meridional shear. This system, referred to as the uniform shear model, can only be justified in the limit of large meridional eddy elongation. However, the model captures well-known features of baroclinic wave life cycles. These include the excitation of a baroclinic growth and a barotropic decay phase where the zonal mean flow is effectively stabilized by the barotropic governor effect. This effect is a consequence of a nonlinear tilting instability where enstrophy is driven to decreasing scales while the kinetic energy is transformed into the zonal mean barotropic shear flow. A detailed examination of the uniform shear model reveals that the wave evolution depends sensitively on the initial barotropic shear, wave amplitude, and wave tilt. The...

Nonlinear Behavior in the Propagation of Atmospheric Gravity Waves

Abstract The nonlinear behavior of quasi-monochromatic gravity wave breaking events is studied using a high-resolution, two-dimensional, fully nonlinear numerical model. A suite of supporting models is used alongside the nonlinear model to separate the effects of wave–wave and wave–mean flow interactions. The focus of this study is the breaking of initially monochromatic waves at two different frequencies. The results are used to address some of the issues central to the role that nonlinear effects play in gravity wave propagation and saturation. It is found that the presence or absence of wave–mean flow interactions influences the nature of wave breaking. Comparison of the results from the fully nonlinear model with those from a model from which the wave–mean flow interactions are removed indicates that wave overturning and breaking occur at lower altitudes when wave–mean flow interactions are included. This influence is found to be frequency dependent with the effect being stronger at the higher frequen...

The Role of Tropical Cyclones in the Formation of Tropical Upper-Tropospheric Troughs

Tropical upper-tropospheric troughs (TUTTs), also known as midoceanic troughs, are elongated troughs that appear in summer monthly averaged maps of the upper-tropospheric flow over the oceans. The transient part of these climatological features is composed of TUTT cells and their origin is the subject of this study. TUTT cells often occur to the east of tropical cyclones. A nonlinear shallow water model on the sphere was used in a simplified study of the interactions between tropical cyclones and the circumpolar vortex. Based on the results of these simulations and keeping in mind their limitations, it is proposed that dispersion of short Rossby wave energy is a possible mechanism to explain the formation of TUTT cells to the east of tropical cyclones. The model simulations suggest that two types of TUTT cells may form to the east of tropical cyclones. When embedded in cyclonic or weak anticyclonic shear, the trough to the east of the tropical cyclone may broaden, resulting in the formation of an intense TUTT cell that has a strong signature in the wind and mass fields. In the presence of stronger anticyclonic shear, the trough to the east of the tropical cyclone may become a thin and elongated TUTT cell that has a comparatively negligible signature in the mass and flow fields. Moreover, the model simulations indicate that the mode of evolution of TUTT cells that form to the east of a tropical cyclone is strongly dependent on the intensity and relative location of midlatitude waves. Wave–mean flow interaction calculations indicated that tropical cyclones produced a westerly acceleration of the mean zonal flow in the latitudinal band through which they move and an easterly acceleration elsewhere. These calculations also indicated that broadening TUTT cells may cause an easterly acceleration of the zonal mean flow.

Simulation of planetary waves and their influence on the zonally averaged circulation in the middle atmosphere

A linearized numerical model is used to simulate the propagation of stationary planetary waves through the stratosphere and mesosphere into the lower thermosphere. Wave forcing at the lower boundary has been specified by the perturbation of the geopotential height for January. The dependence of planetary wave structure on the zonally averaged wind is investigated through the analysis of results of simulation with different background wind distributions. The global model of stationary planetary waves has been modified to simulate traveling planetary waves, and the spectrum of resonant planetary modes has been obtained by forcing the model with a periodic perturbation of the vertical velocity near the surface. Wave-activity density, Eliassen-Palm flux, and its divergence are used as a diagnostics of wave propagation and wave-mean flow interaction. It is found that planetary waves can provide substantial acceleration of the mean flow which is comparable to that one associated with gravity wave and atmospheric tide breaking and/or saturation. Results of numerical simulation are compared with the climatological model of stationary planetary waves in the stratosphere and with the preliminary results of wind observations using WINDII instrument on the UARS.

Vortex Rossby Waves and Hurricane Intensification in a Barotropic Model

In this study the balanced evolution of small but finite as well as large-amplitude asymmetries in a rapidly rotating hurricane-like vortex is investigated. In particular, the wave kinematics and wave–mean flow interaction of vortex Rossby waves in a barotropic nonlinear asymmetric balance (AB) model are examined. By diagnosing the evolution of different asymmetric initial potential vorticity (PV) disturbances and their effect on the symmetric vortex, recent linear and quasi-linear predictions are verified and the proposed AB model is shown to be a viable balance model for azimuthal wavenumbers >1. For disturbance amplitudes that are 40% of the basic-state PV at the radius of maximum wind, a discrete normal mode propagating cyclonically around the vortex is excited as a by-product of the process by which energy is transferred from the asymmetries into the basic state (axisymmetrization). In addition we are able to show that even a strong disturbance axisymmetrizes in a circular flow and is able to intensify the basic state. Side-by-side comparison with some experiments from a primitive equation model show good agreement for both weak and strong asymmetric disturbances. The results raise intriguing questions about the dynamical role of discrete and continuous spectrum vortex Rossby waves in the moist convective dynamics of the hurricane. The application of the results to hurricane intensification will be addressed.

Potential Vorticity Thickness Fluxes and Wave–Mean Flow Interaction

The use of eddy flux of thickness between density surfaces has become a familiar starting point in oceanographic studies of adiabatic eddy effects on the mean density distribution. In this study, a dynamical analogy with the density thickness flux approach is explored to reexamine the theory of nonzonal wave‐mean flow interaction in two-dimensional horizontal flows. By analogy with the density thickness flux, the flux of thickness between potential vorticity (PV) surfaces is used as a starting point for a residual circulation formulation for nonzonal mean flows. Mean equations for barotropic PV dynamics are derived in which a modified mean velocity with an eddy-induced component advects a modified mean PV that also has an eddy-induced component. For smallamplitude eddies, the results are analogous to recent results of McDougall and McIntosh derived for stratified flow. The dynamical implications of this approach are then examined. The modified mean PV equation provides a decomposition of the eddy forcing of the mean flow into contributions from wave transience, wave dissipation, and wave-induced mass redistribution between PV contours. If the mean flow is along the mean PV contours, the contribution from wave-induced mass redistribution is ‘‘workless’’ in Plumb’s sense that it is equivalent to an eddy-induced stress that is perpendicular to the mean flow. This contribution is also associated with the convergence along the mean streamlines of a modified PV flux that is equal to the difference between the PV flux and the rotational PV flux term identified by Illari and Marshall. The cross-stream component of the modified PV flux is related to wave transience and dissipation.

Linear and Nonlinear Vortex Motion in an Asymmetric Balance Shallow Water Model

Abstract This work extends asymmetric balance (AB) theory to the beta plane (β-AB). The physical problem examined is the motion of a coherent vortex on a beta plane in a finite depth fluid in the absence of an environmental steering flow. A useful attribute of the β-AB formulation is that it allows one to separate the linear and nonlinear balance contributions to the vortex motion when the standard Rossby number is not small compared to unity. It is therefore well suited for testing the hurricane-motion paradigm proposed by Willoughby for equivalent barotropic dynamics. The β-AB model is formulated first for linear shallow water dynamics on a circular vortex forced by the meridional gradient of planetary vorticity (the beta effect) in an earth-based coordinate system. The linear dynamics precludes wave–wave and wave–mean flow interactions. From incipient vortices to hurricanes, the β-AB model correctly develops the wavenumber-one asymmetries (the “beta” gyres) necessary for vortex self-advection. Cyclonic...

Numerical experiments on internal gravity waves in an accelerating shear flow

Abstract The influence of an accelerating shear flow on the propagation of an internal gravity wave in a continuously stratified fluid is studied by means of two-dimensional numerical simulations. These are motivated by earlier laboratory experiments [Thorpe, S.A. 1978b. On internal gravity waves in an accelerating shear flow, Vol. 88. J. Fluid Mech. pp. 623–639]. In these experiments the mean flow is an accelerated Couette flow and the mean density profile is linear. The laboratory experiments revealed the striking effect of the unsteady shear flow in the evolution of an internal gravity wave leading to the wave focusing in a region where the flow is extremum. This phenomenon is associated with the growth of small scale density fluctuations. As a result density overturns are sometimes observed. This behaviour is well reproduced by the numerical simulations. We provide insights on the flow dynamics in particular on the possible occurrence of wavebreaking. We show that the dynamics is characterized by two competitive mechanisms that is a damping of the wave and a local enhancement of its steepness leading sometimes to density overturns. The budget for the energy of the wave reveals that the initial damping of the wave results from wave-mean flow interactions. These interactions lead to the development of a fine scale vertical density structure which is associated with high vertical shear. We find that in some cases wavebreaking occurs as a result of shear instability. The value of the acceleration of the mean flow is very likely to influence the onset of the instability. The scaling laws of the wave evolution, in particular the rate of decrease of its energy, are determined. From these laws the lifetime of the wave is found as a function of the acceleration of the shear. It may be expected that, in the ocean, this development will result in the largest fluctuations derived from wave-flow interactions occurring where the mean flow in the wave direction is greatest. Waves travelling normal to a two-dimensional shear flow will be unchanged. Waves travelling parallel will be damped. This may have particular application at the continental shelf where flow, mainly parallel to the isobaths, will damp waves travelling along-slope, but allows waves travelling normal to the isobaths (e.g., directly across the shelf-break) to be transmitted without attenuation. Similar effects are expected for the evolution of a high frequency wave interacting with a lower frequency (e.g., near inertial) motion.

Two‐day wave structure and mean flow interactions observed by radar and High Resolution Doppler Imager

Data obtained with four MF and meteor radars at equatorial and subtropical sites and with the High Resolution Doppler Imager (HRDI) instrument aboard the UARS satellite were used to examine the structure, wave‐mean flow interactions, and potential sources of the 2‐day wave in the middle atmosphere during three southern hemisphere summers. The three wave events were highly transient, having typical durations of 20 to 30 days and exhibiting modulation at shorter periods. Temporal variations were found to exhibit good correlations between radar and HRDI data. Radar and HRDI data were used to estimate those components of the Eliassen‐Palm flux that could be assessed with these data. Meridional fluxes of momentum and heat were computed using HRDI data and agree reasonably with the momentum fluxes computed from radar data at discrete locations. These fluxes were found to exhibit consistent latitudinal structures each year, suggesting systematic wave excitation and wave‐mean flow interactions. Meridional momentum flux gradients were seen to be anticorrelated with zonal wind accelerations in a manner consistent with wave forcing of the large‐scale circulation. The apparent wave‐mean flow interactions suggest that the 2‐day wave could be a transient response to baroclinic instability of the summer hemisphere mesospheric jet. A calculation of the meridional gradient of quasi‐geostrophic potential vorticity using HRDI winds and the COSPAR International Reference Atmosphere (CIRA 1986) temperatures exhibits a region of instability in the lower and middle mesosphere extending into subtropical latitudes and provides additional evidence of a possible source of this motion via baroclinic instability of the summer hemisphere jet structure.

A comparison of reanalyses in the tropical stratosphere. Part 2: the quasi-biennial oscillation

Reanalysis datasets potentially offer the opportunity to examine the tropical quasi-biennial oscillation (QBO) in greater detail than in the past, including the associated meridional circulation and the links with other parts of the atmosphere. For such studies to be useful, the QBO represented by the reanalyses should be realistic. In this work, the QBO in the ERA and NCEP reanalyses is validated against rawinsonde observations from Singapore. Monthly mean data are used. In the lower stratosphere (at 50 hPa and 30 hPa) the ERA QBO is reasonable, although the wind extrema in both phases are too weak and the vertical shear and the temperature anomalies are too small. The NCEP QBO is weaker still. At 10 hPa neither reanalysis system performs well, both systems failing to reproduce the westerlies, possibly because of the proximity of the upper boundary. The Singapore wind is representative of the zonal means in the reanalyses. The weak wind extrema in the reanalyses would not support a wave-mean flow interaction theory of the QBO, because a large portion of the gravity wave spectrum which would be absorbed in reality would be transmitted beyond 10 hPa. The stronger shear zones captured in the ERA data are associated with larger, more realistic temperature perturbations near 30 hPa. The northward velocities in the NCEP data show a more realistic structure than in the ERA reanalysis, where they are dominated by a vertical “gridpoint wave” structure in the lowermost stratosphere. Despite the shortcomings of the reanalyses, the high correlations of the wind at 30 hPa and 50 hPa with the observations at Singapore mean that the reanalyses could potentially be used to examine the effects of the QBO away from the tropical stratosphere. Future reanalyses need to take full account of the wind shears evident in the rawinsonde observations and use models with an adequate resolution to capture these vertical scales.

Wave–Mean Flow Interaction Associated with a QBO-like Oscillation Simulated in a Simplified GCM

Abstract The interaction between convectively excited waves and the mean zonal wind in the equatorial lower stratosphere is investigated with a simplified general circulation model (GCM). The model has T42 truncation, and the vertical resolution is about 700 m in the stratosphere. Although it is an “aquaplanet” model with uniform sea surface temperature, cumulus convection in low latitudes has realistic hierarchical structures with reasonable space–time spectral distributions. The model produced an oscillation having quite similar features to the equatorial quasi-biennial oscillation (QBO), although the period is 400 days. Waves in the equatorial lower stratosphere of the model are excited mainly by the cumulus convection in low latitudes. The energy of these waves is a little larger than that observed in the real atmosphere. The dominant waves are gravity waves having an equivalent depth of about 200 m and those of 40–100 m. About half of the transport and deposition of zonal momentum contributing to the...

Self-consistent Hamiltonian dynamics of wave mean-flow interaction for a rotating stratified incompressible fluid

We derive a hierarchy of approximate models of wave mean-flow interaction (WMFI) by using asymptotic expansions and phase averages either in Euler's equations for a stratified rotating inviscid incompressible fluid, or in Hamilton's principle for these equations. Two small dimensionless parameters are used in these expansions. The first parameter is the ratio of time scales between internal waves at most wave numbers and the mesoscale mean flow of the fluid. This “adiabatic ratio” is small and is comparable to the corresponding ratio of space scales for the class of initial conditions that support internal waves. The other small parameter used in these expansions is the ratio of the amplitude of the internal wave to its wavelength. An application of Noether's theorem to the phase-averaged Hamilton's principle shows that the resulting equations conserve the wave action, convect a potentional vorticity and can, depending on the order of approximation, convect wave angular momentum. Passage from the phase-averaged Hamilton's principle to the Hamiltonian formulation brings the WMFI theory into the Lie-Poisson framework in which formal and nonlinear stability analysis may be applied. This framework also suggests a two-fluid model of the interaction of waves and mean flow similar to that for the superfluid and normal fluid components of liquid He 4 without vortices. We also discuss the relations of these results to the Charney-Drazin nonacceleration theorem, Whitham averaging, WKB stability theory, and Lagrangian-mean fluid equations for prescribed wave displacements.

Simulation of the influence of stationary planetary waves on the zonally averaged circulation of the mesosphere/lower thermosphere region

A linearised numerical model has been used to simulate the stationary planetary waves (SPW) structure and investigate its influence on a zonally averaged circulation in the mesosphere and lower thermosphere. The wave-activity density. Eliassen-Palm flux, and its divergence cross-sections are used as a diagnostic of wave propagation and wave-mean flow interaction. The results of numerical simulations show that SPW can provide the substantial accelerations of the mean flow which are comparable with the accelerations due to the breakdown of internal gravity waves and atmospheric tides, and it is necessary to develop three-dimensional models of the general circulation of the lower thermosphere, taking account of the effects of gravity wave and tidal drag. The influence of the eddy thermal conduction and viscosity on the formation of SPW structure in the mesosphere and lower thermosphere and on the distribution of the mean flow accelerations due to SPW dissipation is discussed.

The impact of changing the horizontal diffusion scheme on the northern winter climatology of a general circulation model

A general circulation model was used in perpetual January mode, to study the wintertime climatological sensitivity to changes in the horizontal hyper-Laplacian diffusion scheme at both spectral T21 and T42 horizontal resolutions. Analysis of the global energy cycle revealed a large impact especially on the conversion of eddy to zonal kinetic energy. Less diffusion resulted in less zonal available potential energy, weaker baroclinic conversions and caused the barotropic conversion of eddy to zonal kinetic energy to become significantly weaker. It was found that by weakening the diffusion in the T21 model, the eddy kinetic energy increased and became more realistic yet at the same time the conversion of eddy to zonal kinetic energy decreased and became less realistic. Weakening the horizontal diffusion caused a northern hemisphere tropospheric response similar to that obtained by increasing the upper-level orographic gravity wave drag in the model. The zonal-mean zonal winds weakened poleward of the subtropical jets, the Ferrel cells weakened and the troposphere warmed up at high latitudes. The weakening of the zonal wind and the Ferrel cells was associated with a weakening of the upper-level convergence of the poleward eddy momentum flux and the wave-mean flow interaction was demonstrated using Eliassen–Palm diagnostics. A substantial part of the change in the poleward eddy momentum flux was due to large changes in the poleward momentum flux of the transient eddies in the mid-latitude stormtracks and changes in their horizontal phase tilt. A large northern hemisphere stationary-wave change appeared in these regions and had a similar structure in the Atlantic sector to that seen when strengthening upper-level gravity wave drag.

On Triad Interactions in a Linearly Stratified Ocean

Abstract Triad interactions in a linearly stratified ocean are studied numerically using a Garrett–Munk energy spectrum as the initial condition. It is found by bispectrum analysis that wave–mean flow interactions dominate and resonant interactions are limited to very large scales. Resonant triads of parametric subharmonic instability type play an insignificant role in the energy distribution. Local sum resonant triads provide the most effective energy transfer at very large scales. The analysis of triadic energy transfer rates suggests that triad configuration determines the energy flow pattern. When the modes with zero horizontal wavenumber are set to zero, resonant interactions arise. Thus, over most of the Garrett–Munk spectrum the energy level is low enough for resonance, but due to strong nonlinearities induced by horizontal currents, resonance is destroyed and wave–mean flow interactions dominate. If the energy level is reduced by a factor of 100, the number of resonant modes increases but wave–mea...

Topographic Wave Modification and the Angular Momentum Balance of the Antarctic Troposphere. Part II: Baroclinic Flows

Abstract It has been demonstrated in Part I of this paper that synoptic-scale waves propagating around Antarctica are modified by the Antarctic topography such that they transport westerly angular momentum out of Antarctica. These transports are necessary to maintain a vigorous slope wind regime, which generates westerly angular momentum through surface friction. The results of Part I are based on a quasi-barotropic wave-mean flow interaction model where the mean flow equations are averaged over the Antarctic domain. Frequency and wave-length of the waves are prescribed according to observations. Here, the authors relax many of the constraints imposed in Part I. The model atmosphere is now fully three-dimensional and extends from the South Pole to 30°S. A wave perturbation is inserted in the baroclinic zone to the north of Antarctica. Initially the wave grows due to baroclinic instability, while cooling at the slopes induces downslope winds. After an initial phase of intensification the slope wind regime ...

Antarctic slope winds and the polar stratospheric vortex

A wave mean-flow interaction model is used to investigate the coupling of the Antarctic slope winds and the polar vortex in the lower stratosphere in winter. The model is restricted to the Antarctic domain but synoptic waves of fixed frequency and zonal wavenumber can be prescribed at the northern boundary. They represent southward moving midlatitude perturbations. Cooling at the slope of the Antarctic continent induces southeasterly flow near the surface which acts as a source of westerly angular momentum to the atmosphere. The momentum so generated must be transported out of the Antarctic domain by these synoptic waves. It is found that the polar vortex is intense in the troposphere and lower stratosphere, and that the slope winds are weak when these waves are ineffective in transporting angular momentum. If, on the other hand, the momentum transport is sufficiently strong, the polar vortex is relatively weak and the slope winds are vigorous. Such a coupling of vortex and slope winds has been observed for the troposphere [Yasunari and Kodama (1992) J. geophys. Res. (in press)] and our results suggest that it extends into the lower stratosphere.

Heat Transport by Mesoscale Eddies in an Ocean Circulation Model

Abstract The role of mesoscale eddies in the poleward heat transport in the ocean is investigated; in particular, the compensation of poleward eddy heat transport by an eddy-induced mean meridional circulation is examined. A multilayer isopycnic primitive equation model of an idealized western North Atlantic is presented to test whether compensation also occurs within an isopycnic model and when the poleward eddy heat transport becomes comparable to the mean transport. Also, in this model configuration compensation of the poleward eddy heat transport arises. It is brought about by a westward eddy heat transport in the midlatitude jet, which results in a pressure drop across the basin and consequently in a modified mean meridional overturning. This compensation is discussed within the framework of wave–mean flow interaction. It is demonstrated that compensation results from eddy–mean flow interaction when the diabatic forcing is sufficiently weak; rings are recaptured before their SST anomaly is modified s...