Yanai Waves Research Articles

A study of the dynamics of the equatorial lower stratosphere by use of ultra‐long‐duration balloons: 1. Planetary scales

In the late southern winter of 1998, Centre National d'Études Spatiales (CNES), the French Space Agency, released six 10‐m‐diameter, superpressure balloons from a location near Quito, Ecuador. Three balloons collapsed soon after launching, but the remaining three drifted westward for a few weeks at altitudes between 19 and 20 km. Two of those balloons crossed the Pacific Ocean before falling above the “maritime continent,” while the other completed a revolution around the Earth and crossed the Pacific for a second time before its final fall. Despite the small number and the relatively short duration of the flights, the balloons provided a unique in situ data set for the lower equatorial stratosphere. This part 1 of a two‐part paper describes this data set and analyzes outstanding features in the planetary scales. Part 2 focuses on gravity‐wave scale. It is argued that balloon trajectories over the Pacific are primarily determined by the westward drift during the easterly phase of the equatorial quasi‐biennial oscillation (QBO) and the meridional velocity field of a mixed Rossby‐gravity (Yanai) wave with an apparent period of 4 days and zonal wave number 4. This wave appears to have two episodes of amplification during the balloon flights. It is also argued that the balloons show evidence of oscillations with periods between 2 and 4 days and of a Kelvin wave with an apparent period close to 10 days and zonal wave number 1. In this way, the balloon behavior provided a pictorial view of air parcel trajectory in the equatorial lower stratosphere. It is stated that larger balloon campaigns can provide excellent in situ data sets for studies on the dynamics and composition of the middle atmosphere.

Mode conversion in the Gulf of Guinea

Linear mode conversion is the partial transfer of wave energy from one wave type (a) to another (b) in a weakly non-uniform background state. For propagation in one dimension (x), the local wavenumber kjx of each wave (j = a, b) varies with x; if these are equal at some xR, the waves are locally in phase, and resonant energy transfer can occur. We model wave propagation in the Gulf of Guinea, where wave a is an equatorially trapped Rossby–gravity (Yanai) wave, and wave b is a coastal Kelvin wave along the (zonal) north coast of the Gulf, both propagating in zonal coordinate x. The coupling of the waves is due to the overlap of their eigenfunctions (normal modes in y, the meridional coordinate). We derive coupled mode equations from a variational principle, and obtain an analytic expression for the wave-energy conversion coefficient, in terms of the wave frequency and the scale length of the thermocline depth.

Mixing induced by the Atlantic equatorial wave activity in an eddy‐resolving OGCM

The variability of equatorial circulation in the middepth Atlantic Ocean from an eddy‐resolving ocean general circulation model (OGCM) was analyzed. Four types of equatorially trapped waves were identified which dominate the variability of the circulation: an annual Rossby wave, a semiannual Rossby wave, a group of 40‐ to 60‐day short Rossby waves, and a group of 30‐day Yanai waves. In particular, the 40‐ to 60‐day short Rossby waves were found near the western boundary to the north of the equator, which may be related to nonlinear instability processes associated with the north Brazil current (NBC) retroflection. The wave‐induced stirring and transport along the equator was investigated by calculating the trajectories of a large ensemble of particles in the middepth equatorial Atlantic Ocean from the eddy‐resolving, model‐simulated velocity field. The distribution of finite‐time Lyapunov exponents derived from the simulated velocity at a depth of ∼2000 m bears a close resemblence to the observed CFC tongue, suggesting that the wave‐induced chaotic stirring and transport may contribute to the formation of the observed CFC tongue in the middepth equatorial Atlantic Ocean along the equator.

A wave-induced stirring mechanism in the mid-depth equatorial ocean

A wave-induced stirring and transport mechanism for the mid-depth equatorial ocean is proposed and examined using both analytic linear equatorial wave solutions and a fully nonlinear reduced-gravity model. The study of kinematic stirring using the linear solutions suggests that a superimposition of a few simple equatorial waves can lead to strong Lagrangian stirring and transport along the equator. In particular, a combination of an annual long Rossby wave and a high-frequency Yanai wave appears to be most effective in producing strong stirring in the interior equatorial region. Further investigations of stirring properties using an inverted, fully nonlinear reduced gravity shallow-water model support the results of the kinematic stirring study. By evaluating the finite-time estimates of Lyapunov exponents, we identified two regions where chaotic stirring is most active. One is the western boundary region where short Rossby waves likely play a dominant role in producing the strong chaotic stirring. The other is the equatorial waveguide where a low-frequency Rossby wave prescribes the pattern of the stirring geometry, and a high-frequency Yanai wave plays a role of stirring the fluid. The proposed stirring mechanism provides a plausible explanation of the observed chlorofluorocarbon distribution found in the mid-depth equatorial Atlantic Ocean.

Low-Frequency Equatorial Waves in Vertically Sheared Zonal Flow. Part I: Stable Waves

Abstract The mechanism by which a vertically sheared zonal flow affects large-scale, low-frequency equatorial waves is investigated with two-level equatorial,β-plane and spherical coordinates models. Vertical shears couple barolinic and barotropic components of equatorial wave motion, affecting significantly the Rossby wave and westward propagating Yanai wave but not the Kelvin wave. This difference results from the fact that the barotropic component is a modified Rossby mode and can be resonantly excited only by westward propagating internal waves. The barotropic components emanate poleward into the extratropics with a pronounced amplitude, while the baroclinic components remain equatorially trapped. A westerly vertical shear favors the trapping of Rossby and Yanai waves in the upper troposphere, whereas an easterly shear tends to confine them in the lower troposphere. As such, their westward propagation is slowed down by both westerly and easterly shears. When the strength of the vertical shear varies w...

On a generating mechanism for Yanai waves and the 25‐day oscillation

A spectral Chebyshev‐collocation method applied to the linear, 1.5 layer reduced‐gravity ocean model equations is used to study the dynamics of Yanai (or mixed Rossby‐gravity) wave packets. These are of interest because of the observations of equatorial instability waves (which have the characteristics of Yanai waves) and their role in the momentum and heat budgets in the tropics. A series of experiments is performed to investigate the generation of the waves by simple cross‐equatorial wind stress forcings in various configurations and the influence of a western boundary on the waves. They may be generated in the interior ocean as well as from a western boundary. The observations from all the oceans indicate that the waves have a preferential period and wavelength of around 25 days and 1000 km respectively. These properties are also seen in the model results and a plausible explanation is provided as being due to the dispersive properties of Yanai waves.

An Introduction to Wavelet Analysis in Oceanography and Meteorology: With Application to the Dispersion of Yanai Waves

Wavelet analysis is a relatively new technique that is an important addition to standard signal analysis methods. Unlike Fourier analysis that yields an average amplitude and phase for each harmonic in a dataset, the wavelet transform produces an “instantaneous” estimate or local value for the amplitude and phase of each harmonic. This allows detailed study of nonstationary spatial or time-dependent signal characteristics. The wavelet transform is discussed, examples are given, and some methods for preprocessing data for wavelet analysis are compared. By studying the dispersion of Yanai waves in a reduced gravity equatorial model, the usefulness of the transform is demonstrated. The group velocity is measured directly over a finite range of wavenumbers by examining the time evolution of the transform. The results agree well with linear theory at higher wavenumber but the measured group velocity is reduced at lower wavenumber, possibly due to interaction with the basin boundaries.

Nonlinear and dissipative dynamics in the connection region between western boundary currents and equatorial currents

The roles of nonlinearity and dissipation in connecting a western boundary current to an equatorial current are explored with a 1½ ‐layer numerical model. A permanent western boundary current ‐ equatorial current system is maintained between a mass source located near the western boundary several deformation radii from the equator and a sponge layer located along the eastern boundary. When a no‐slip boundary condition is used, the western boundary current separates within two deformation radii after crossing the equator to feed the eastward equatorial current. Because of equatorial scalings, flow within the connection region between these two currents is nearly nondivergent, and similarities with barotropic models of western boundary current extensions are emphasized by potential vorticity analysis. A series of experiments explores the relative importance of inertia to dissipation, measured by the Reynolds number, by varying the forcing strength. For small Reynolds numbers advection of relative vorticity out of the western boundary layer eastward results in a meandering equatorial current, which is interpreted as a damped, stationary Rossby wave. At higher Reynolds numbers, the boundary current is susceptible to horizontal shear instability, resulting in eddies which translate along the western boundary. At yet higher Reynolds numbers, eddy variability is not confined to the western boundary. Disturbances are advected out of the boundary layer, producing large (300 km diameter) eddies in the connection region. Variability also radiates eastward along the equator as free Yanai wave packets with periods between 30 and 70 days. Even in the presence of energetic eddies, net flow across the equator is due mostly to vorticity dissipation in the western boundary current. The effect of different boundary conditions is also examined. When a free‐slip rather than no‐slip boundary condition is used, the boundary current overshoots well outside the equatorial waveguide, but all flow returns to the equatorial region in an offshore countercurrent, and the solution is otherwise similar to solutions with a no‐slip boundary condition.

The 26‐day oscillation observed in the satellite sea surface temperature measurements in the equatorial western Indian Ocean

A 26‐day oscillation in sea surface temperature (SST) data is observed in the western Indian Ocean, from 52° to 60°E and in the vicinity of the equator. The SST data used in this study are obtained from the NOAA 9 satellite and are for the years 1987 and 1988. This fluctuation of SST at a period near 26 days is found to be antisymmetric about the equator and is trapped within the equatorial waveguide (equator ±6°). The variance associated with this oscillation has a maximum located at about 3° latitude; furthermore, the variance decreases at a faster rate toward the equator than poleward. These characteristics are consistent with the latitudinal structure for the mixed Rossby‐gravity (or Yanai) waves as predicted from linear wave theory. The temporal variation of this 26‐day oscillation is most energetic during the summer season (July to September), with maximum values of 0.4°C and 0.8°C found during August of 1987 and 1988 respectively. This observation agrees with the temporal variation of Yanai waves inferred from drifting buoy observations and numerical studies of the Indian Ocean. Thus we conclude that the Yanai wave is responsible for the 26‐day fluctuation observed in the SST data in this region.

Propagation of Equatorially Trapped Waves on a Sloping Thermocline

Abstract The WKBJ method and a multiple-scale expansion technique are used to study equatorially trapped waves propagating on a zonally sloping themocline. Assuming that variations of the main thermocline depth (MTD) are slow (the change of the MTD over one wavelength is smaller than the wave amplitude), wave reflections can be neglected and the amplitudes of equatorially trapped waves can be derived by using the energy conservation law. It is found that the wavelengths and amplitudes of free waves are significantly modified by the MTD variations. While propagating eastward in an ocean basin (where the MTD is shallower), Kelvin waves shrink meridionally and zonally but their amplitudes increase to preserve wave energy; short Rossby waves behave in the opposite way. The wavelength of westward-propagating long Rossby waves becomes longer when they propagate into the deeper western ocean. The response of a Yanai wave to the changing thermocline depends on the sign of phase speed. A simple numerical method is...

Equatorial waves in the stratosphere of Uranus

We have identified and characterized an equatorial wave in the stratosphere of Uranus through analysis of radio occultation data from Voyager 2. Our methodology relies on two physical phenomena: (1) atmospheric waves modulate the ambient background structure of a planetary atmosphere, producing a distinctive pattern of spatial variations in temperature and density; and (2) this type of spatial modulation in turn causes fluctuations in the phase and amplitude of radio signals received from an occulted spacecraft. We compared predictions of the linear theory for equatorial waves on a β-plane with observations of the stratosphere at both immersion (2.0°N, 342.2°E) and emersion (6.3°N, 197.5°E). (Note that the latitude system used here is the reverse of the IAU convention.) The observed quasi-periodic vertical variations in atmospheric density agree closely with theoretical predictions for a wave propagating vertically through the observed background structure of the stratosphere, providing compelling evidence for the presence of an atmospheric wave. The wave has an equivalent depth of 53 ± 12 m, a vertical wavelength of about one-third of a pressure scale height, and an amplitude at the 1-mbar pressure level at immersion (emersion) of 1.1 ± 0.4 K (0.5 ± 0.2 K). Within the framework of the linear wave theory, quantitative comparisons between the measurements at immersion and emersion yielded constraints on the meridional and zonal structure of the wave. The ratio of amplitudes at the two locations, 2.1 ± 0.3, is consistent with a wave confined in latitude near the equator. Moreover, the observations at immersion and emersion are correlated, suggesting a wave of planetary scale. These constraints allowed us to identify two equatorial wave modes as equally likely alternatives for explaining the observations; each retains a relatively simple spatial structure while accounting for the principal features of the data. The first is an inertia-gravity wave with westward zonal phase speed (relative to the mean zonal winds), a meridional index j = 1, and a zonal wavenumber n = 6. The second is an eastward inertia-gravity wave with j = 2 and n = 14. All Kelvin, Yanai, and Rossby wave modes are inconsistent with the observations. We expect the wave to begin breaking near the 200-μbar pressure level, resulting in an eddy diffusion coefficient of about 0.6 to 1.0 × 10 4 cm 2 sec −1, consistent with independent estimates of this parameter. Vertical transfer of momentum by the wave could accelerate the mean zonal wind at pressures less than 200 μbar by about ±10–20 cm sec −1 per planet rotation.

On the approximation of equatorially-trapped waves in the numerical models of ocean dynanics

Finite-differential schemes (continous in time) are studied for the shallow water equations on the equatorial β-plane on the grids B and C. The B-grid spectrum is shown to be symmetrical about fourgrid interval waves. It results in the wrong sign of the group velocity in the ddomain of wavelengths less than four intervals of the grid. An analytical solution is given for the differential analogues of Kelving and Yanai waves on grid C. A conclusion is drawn on the advantage of grid, C and the necessary filtration of the high-frequency band of the spectrum for grid B, if the grid intervals are 100 km or less.

Excitation of intermediate‐frequency equatorial waves at a western ocean boundary: With application to observations from the Indian Ocean

A linear, continuously stratified model is used to study the equatorial waves that are generated at the western boundary of the ocean by wind fields oscillating at periods of 30 and 60 days. Solutions are found in ocean basins with a western boundary oriented meridionally or slanted at a 45° angle, like the one in the Indian Ocean. They are evaluated analytically when the boundary is meridional but must be found numerically when the boundary is slanted. The possible equatorial waves are Kelvin and Yanai waves, and at the 60‐day period there are a few Rossby waves. Because Yanai and Rossby waves typically have short wavelengths, they are not directly forced by the wind; however, they can be strongly excited at the western boundary and in that case are highly visible in the interior ocean. When the western boundary is slanted, zonal winds also excite antisymmetric equatorial waves, resulting in considerable meridional flow on the equator. At the 30‐day period, energy associated with Kelvin and Yanai waves propagates eastward and downward from the western boundary along ray paths, producing an equatorial shadow zone in the western ocean. At the 60‐day period the presence of Rossby waves complicates the radiation pattern. Solutions compare favorably with several aspects of the observed equatorial wave field in the western Indian Ocean.

Linear Equatorial Wave Mode Initialization in a Model of the Tropical Pacific Ocean: An Initialization Scheme for Tropical Ocean Models

Data assimilation in models of the tropical oceans can generate spurious equatorial wave modes which are potentially harmful to the model background fields. The amplitudes of these spurious wave modes can often be large and, in general, depend upon the nature and size of the imbalances introduced into the model by the data assimilation process. Spurious equatorial Kelvin waves are likely to give rise to the most detrimental effects since they are dynamically very important in the real ocean, and am responsible for a variety of phenomena in the equatorial and coastal regions of the ocean. In this paper, an initialization scheme based on the technique of normal mode initialization (used for many years by meteorologists) is developed, which can be used to suppress spurious equatorial wave modes during data assimilation experiments. The initialization scheme maps information from observational data onto the linear planetary wave solutions of the discretized model equations of motion. In addition, equatorial Kelvin waves and Yanai waves driven by sea surface forcing in the model are retained. Using this method, the rate of growth of the assimilation errors between one assimilation time and the next can be reduced considerably. It is shown that the model need only he initialized in a narrow channel spanning the equator, and that the initialization method also works well in a fully nonlinear model.

The wind‐driven seasonal circulation in the southern tropical Indian Ocean

A numerical model of the Indian Ocean, driven by climatological monthly mean winds, realistically simulates the major features of the large scale upper ocean circulation observed in the southern hemisphere and equatorial regions. The principal feature in the tropical Indian Ocean is a basin‐wide clockwise southern hemisphere (cyclonic) gyre comprised of the South Equatorial Current to the south, the South Equatorial Countercurrent to the north, and the East African Coastal Current in the west. Rossby waves propagate westward in the shear zone between the South Equatorial Current and the South Equatorial Countercurrent, and are obstructed and partially reflected by the banks along the Seychelles‐Mauritius Ridge (60°E). A region of high eddy activity northwest of Madagascar is an extension of the tropical gyre and is a tropical analog to the Gulf Stream recirculation region. Oscillations in meridional transport at the equator have westward phase speed and eastward group velocity and are the result of mixed Rossby‐gravity (Yanai) waves forced by oscillations in the highly nonlinear western boundary current region. Oscillations with 40‐ to 50‐day periods are seen in most currents. These oscillations cannot be atmospherically forced, as the shortest period in the mean monthly wind forcing is 60 days. Mean transports in the western basin agree with observations. Small (2 Sv) mean throughflow from the Pacific to the Indian Ocean at the eastern open boundary is due to wind‐forced Indian Ocean dynamics alone and is within the range of observations of throughflow from the Pacific.

The 26‐ and 50‐day oscillations in the western Indian Ocean: Model results

The circulation of the western Indian Ocean is examined using a reduced‐gravity model with one active layer and realistic basin geometry for the entire Indian Ocean north of 30°S. The Hellerman and Rosenstein monthly mean wind stress climatology is used to force the model. The numerical simulations reproduce the observed (Luyten and Roemmich, 1982) 26‐day waves along the equator and the 50‐day oscillations (Mysak and Mertz, 1984; Schott et al. 1988) between the equator and Madagascar. The 25‐ to 28‐day oscillations of the model meridional velocity component agree with observed values of period, amplitude, wavelength, group velocity, and phase of the seasonal modulation. The model oscillations, which are excited in August and persist into February–March, are shown to be the result of Yanai waves generated between the western boundary and 50°E. During the southwest monsoon, the Yanai waves are initiated by a complex barotropic instability associated with the southern gyre. During the early stages of the northeast monsoon, the 26‐day Yanai waves are generated by resonant forcing due to the intrusion into the equatorial waveguide of a standing, 800‐ to 900‐km‐wavelength meander of the eastward flow fed by the East African Coastal Current. Hence the simulation reveals that the 26‐day oscillations in the equatorial Indian Ocean are excited by mechanisms significantly different than that believed to be responsible for the 20‐ to 30‐day oscillations in the equatorial Atlantic and Pacific oceans. The numerical simulation also shows a 50‐day oscillation between the equator and Madagascar west of 50°E. This periodicity is due to Rossby waves generated by a barotropic instability associated with the East African Coastal Current beginning about April each year. No evidence of the 50‐day period oscillation is found in a corresponding linear simulation. Hence the barotropic instability of the oceanic currents in this region is offered as an alternative to direct wind forcing as the generating mechanism for the observed 40‐ to 60‐day oscillations in the western Indian Ocean.

Aspects of Geostrophic Adjustment during Tropical Ocean Data Assimilation

Abstract Subsurface temperature data from the ship-of-opportunity network in the tropical Pacific Ocean was assimilated into a simple reduced-gravity model. A large initialization shock was found to occur in the model which takes the form of equatorially trapped waves. Observations in the western tropical Pacific are found to generate a more severe case of initialization shock than observations in the eastern half of the basin. In addition, the magnitude of the initialization shock was found to be dependent upon the strength of the sea surface forcing. Attempts to suppress the large amplitude equatorial Kelvin waves and Yanai waves excited as part of the initialization shock are partially successful, but the damage inflicted on the model first-guess fields by this procedure is greater than that which ensues if the Kelvin waves and Yanai waves are left unchecked. Despite the initialization shock, the model is able to predict the large-wale structure and variability of the major near surface currents in the...

The Generation Mechanism of Mixed Rossby-Gravity Waves in the Equatorial Troposphere

Numerical experiments are performed to clarify the excitation mechanism of mixed Rossby-gravity waves (Yanai waves) in the tropical troposphere, as well as the selection of zonal wavenumbers 4–5 and of the five-day period. The model used is governed by the primitive equations on an equatorial β-plane. Moisture budgets are calculated explicitly. A nonlinear wave-CISK mechanism produces Yanai waves with the same spectral peaks in wavenumber and frequency as observed. In the absence of antisymmetric lateral forcing, these peaks do not appear distinctly, because the symmetric equatorially trapped modes, i.e., Kelvin-like waves having different spectral peaks, are dominant. It is the lateral antisymmetric forcing which puts the peaks characterizing the antisymmetric Yanai waves in evidence. It appears that Yanai waves of very small wavenumbers (1–3) cannot have large amplitudes because their frequencies are too large for moisture to be effectively supplied for the convection associated with these waves. Symmetric Kelvin modes are dominant in the absence of forcing asymmetries due at least in part to the difference in the nature of heating between symmetric and antisymmetric modes: precipitation, and hence heating, is not normally distributed. Given a strongly skewed distribution of heating, it can be shown that symmetric modes are excited more effectively. Finally, our results indicate that the vertical wavenumber, and hence the period of Yanai waves are selected by the height of cumulus convection, while the lateral forcing selects the horizontal wavenumber within a certain band provided by the nonlinear wave-CISK mechanism.

The equatorial source of propagating variability along the Peru coast During the 1982–1983 El Niño

Using data obtained from tide gages in South America, current meters along the equator and the Peru coast, and an array of pressure gages and inverted echo sounders within and around the Galapagos archipelago, we have analyzed the equatorial origin of coastal trapped waves observed by Cornejo‐Rodriquez and Enfield (this issue) along the Peru coast during the intense 1982–1983 El Niño. The propagating fluctuations along the coast were much stronger at that time than either before or after the El Niño, and the variability was not locally forced by coastal winds. We find that the coastal variability was also more energetic during previous El Niño occurrences. At periods of 1–2 weeks the meridional component of currents on the equator is up to an order of magnitude more energetic than the zonal fluctuations and is consistently associated with sea level that fluctuates antisymmetrically between hemispheres. At periods longer than 2 weeks the zonal velocity component is more energetic, and the cross‐equatorial sea level variability is symmetric. The meridional and zonal phase structures of cross spectra involving the currents and sea level establish the 1‐ to 2‐week equatorial fluctuations as mixed Rossby‐gravity (Yanai) waves of low wave number with infinite phase speed (standing oscillations) in the middle of the band (10 days); the corresponding structures for longer periods are consistent with nondispersive Kelvin waves. Frequency domain EOF modes of the sea level and current data establish the mixed Rossby‐gravity waves as the principal source of the strong trapped wave variability in the 1‐ to 2‐week band along the Ecuador‐Peru coast during the 1982–1983 El Niño episode.

The Reflection of Equatorial Waves from Oceanic Boundaries

Abstract Theory is developed to discuss the reflection of long equatorial waves from ocean boundaries. The main results are as follows: 1) Energy flux reflection coefficients for the reflection of equatorial waves from meridional eastern and western ocean boundaries have been plotted as a function of frequency. The coefficients enable one to determine, for example, how much energy of an incoming equatorial wave of frequency ω is transmitted along an eastern oceanic boundary as poleward propagating Kelvin waves. The coefficients are useful for, both modal and vertically propagating descriptions of equatorial waves. As an example, the reflection of the Yanai wave observed in the equatorial Pacific is discussed in connection with poleward propagating sea levels along the South American coast. 2) Moore (1968) showed that the reflection of an incoming equatorial wave to an eastern meridional boundary consists, in part, of poleward propagating Kelvin waves. Here the same result is generalized to non-meridional ...