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1

Knessl, Charles, and Joseph B. Keller. "Rossby Waves." Studies in Applied Mathematics 94, no. 4 (May 1995): 359–76. http://dx.doi.org/10.1002/sapm1995944359.

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2

Müller, Detlev. "Trapped Rossby waves." Physical Review E 61, no. 2 (February 2000): 1468–85. http://dx.doi.org/10.1103/physreve.61.1468.

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3

Cheverry, Christophe, Isabelle Gallagher, Thierry Paul, and Laure Saint-Raymond. "Trapping Rossby waves." Comptes Rendus Mathematique 347, no. 15-16 (August 2009): 879–84. http://dx.doi.org/10.1016/j.crma.2009.05.007.

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4

McKenzie, J. F., and K. Naidu. "Rossby-type electrostatic electron plasma waves." Journal of Plasma Physics 41, no. 2 (April 1989): 395–404. http://dx.doi.org/10.1017/s0022377800013945.

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This paper explores the properties of Rossby-type electrostatic electron plasma waves at frequencies very much less than the electron gyrofrequency but very much greater than the ion gyrofrequency. Such waves represent the electron counterpart of ion Rossby waves, which propagate at frequencies very much less than the ion gyrofrequency in a plasma in which the ambient magnetic field possesses a spatial gradient perpendicular to its line of action. This feature simulates the ‘β-effect’ that operates in the classical atmospheric Rossby wave: the wave dynamics associated with both ion and electron Rossby waves are structurally similar to those associated with wave perturbations in a rotating fluid, where the β-effect arises from a spatial gradient in the Coriolis acceleration. It is shown that this plasma β-effect gives rise to a ‘new’ mode of the Rossby type, and in addition considerably modifies the conical wave propagation properties characteristic of the electron cyclotron mode. The highly dispersive and anisotropic nature of these waves is described in terms of the topology of the wavenumber surfaces concomitant with plane-wave solutions of the wave equation for the system as a whole.
5

Zhang, Yu, and Joseph Pedlosky. "Triad Instability of Planetary Rossby Waves." Journal of Physical Oceanography 37, no. 8 (August 2007): 2158–71. http://dx.doi.org/10.1175/jpo3100.1.

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Abstract The triad instability of the large-scale, first-mode, baroclinic Rossby waves is studied in the context of the planetary scale when the Coriolis parameter is to its lowest order varying with latitude. Accordingly, rather than remain constant as in quasigeostrophic theory, the deformation radius also changes with latitude, yielding new and interesting features to the propagation and triad instability processes. On the planetary scale, baroclinic waves vary their meridional wavenumbers along group velocity rays while they conserve both frequencies and zonal wavenumbers. The amplitudes of both barotropic and baroclinic waves would change with latitude along a ray path in the same way that the Coriolis parameter does if effects of the nonlinear interaction are ignored. The triad interaction for a specific triad is localized within a small latitudinal band where the resonance conditions are satisfied and quasigeostrophic theory is applicable locally. Using the growth rate from that theory as a measure, at each latitude along the ray path of the basic wave, a barotropic wave and a secondary baroclinic wave are picked up to form the most unstable triad and the distribution of this maximum growth rate is examined. It is found to increase southward under the assumption that triad interactions do not cause a noticeable decrease in the quantity of the basic wave’s amplitude divided by the Coriolis parameter. Different barotropic waves that maximize the growth rate at different latitudes have almost the same meridional length scale, on the order of the deformation radius. With many rays starting from different latitudes on the eastern boundary and with wavenumbers on each of them satisfying the no-normal-flow condition, the resulting two-dimensional distribution of the growth rate is a complicated function of the relative relations of zonal wavenumbers or frequencies on different rays and the orientation of the eastern boundary. In general, the growth rate is largest on rays originating to the north.
6

KALADZE, T. D., D. J. WU, O. A. POKHOTELOV, R. Z. SAGDEEV, L. STENFLO, and P. K. SHUKLA. "Rossby-wave driven zonal flows in the ionospheric E-layer." Journal of Plasma Physics 73, no. 1 (February 2007): 131–40. http://dx.doi.org/10.1017/s0022377806004351.

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Abstract.A novel mechanism for the generation of large-scale zonal flows by small-scale Rossby waves in the Earth's ionospheric E-layer is considered. The generation mechanism is based on the parametric excitation of convective cells by finite amplitude magnetized Rossby waves. To describe this process a generalized Charney equation containing both vector and scalar (Korteweg–de Vries type) nonlinearities is used. The magnetized Rossby waves are supposed to have arbitrary wavelengths (as compared with the Rossby radius). A set of coupled equations describing the nonlinear interaction of magnetized Rossby waves and zonal flows is obtained. The generation of zonal flows is due to the Reynolds stresses produced by finite amplitude magnetized Rossby waves. It is found that the wave vector of the fastest growing mode is perpendicular to that of the magnetized Rossby pump wave. Explicit expression for the maximum growth rate as well as for the optimal spatial dimensions of the zonal flows are obtained. A comparison with existing results is carried out. The present theory can be used for the interpretation of the observations of Rossby-type waves in the Earth's ionosphere.
7

Schecter, David A., and Michael T. Montgomery. "Waves in a Cloudy Vortex." Journal of the Atmospheric Sciences 64, no. 2 (February 2007): 314–37. http://dx.doi.org/10.1175/jas3849.1.

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Abstract This paper derives a system of equations that approximately govern small-amplitude perturbations in a nonprecipitating cloudy vortex. The cloud coverage can be partial or complete. The model is used to examine moist vortex Rossby wave dynamics analytically and computationally. One example shows that clouds can slow the growth of phase-locked counter-propagating vortex Rossby waves in the eyewall of a hurricane-like vortex. Another example shows that clouds can (indirectly) damp discrete vortex Rossby waves that would otherwise grow and excite spiral inertia–gravity wave radiation from a monotonic cyclone at high Rossby number.
8

Onishchenko, O. G., O. A. Pokhotelov, R. Z. Sagdeev, P. K. Shukla, and L. Stenflo. "Generation of zonal flows by Rossby waves in the atmosphere." Nonlinear Processes in Geophysics 11, no. 2 (April 2004): 241–44. http://dx.doi.org/10.5194/npg-11-241-2004.

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Abstract. A novel mechanism for the short-scale Rossby waves interacting with long-scale zonal flows in the Earth's atmosphere is studied. The model is based on the parametric excitation of convective cells by finite amplitude Rossby waves. We use a set of coupled equations describing the nonlinear interaction of Rossby waves and zonal flows which admits the excitation of zonal flows. The generation of such flows is due to the Reynolds stresses of the finite amplitude Rossby waves. It is found that the wave vector of the fastest growing mode is perpendicular to that of the pump Rossby wave. We calculate the maximum instability growth rate and deduce the optimal spatial dimensions of the zonal flows as well as their azimuthal propagation speed. A comparison with previous results is made. The present theory can be used for the interpretation of existing observations of Rossby type waves in the Earth's atmosphere.
9

Biancofiore, L., and F. Gallaire. "Counterpropagating Rossby waves in confined plane wakes." Physics of Fluids 24, no. 7 (July 2012): 074102. http://dx.doi.org/10.1063/1.4729617.

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10

Zülicke, Christoph, and Dieter Peters. "Parameterization of Strong Stratospheric Inertia–Gravity Waves Forced by Poleward-Breaking Rossby Waves." Monthly Weather Review 136, no. 1 (January 2008): 98–119. http://dx.doi.org/10.1175/2007mwr2060.1.

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Abstract The link between poleward-breaking Rossby waves and stratospheric inertia–gravity waves is examined. With a visual inspection of Ertel’s potential vorticity maps based on ECMWF analyses it was found that Rossby wave–breaking events occurred over northern Europe in about 40% of the winter days in 1999–2003. The majority of them were breaking poleward downstream. A total of 10 field campaigns were performed in the winters of 1999–2002 at Kühlungsborn, Germany (54°N, 12°E). They are related to such events and can be considered as representative for poleward-breaking Rossby waves. Inertia–gravity wave properties are diagnosed from radiosonde observations. They appeared to be shallower, slower, and stronger than the climatological mean for the north German lowlands. Hence, Rossby wave–breaking events are linked with strong stratospheric inertia–gravity wave activity. A novel parameterization of inertia–gravity wave generation and propagation is proposed. The stratospheric inertia–gravity wave action in the 16–20-km height range was parameterized with the synoptic-scale cross-stream ageostrophic wind, which accounts for imbalances in the upper-tropospheric jet streak. This empirical relationship is supported with quasigeostrophic theory. Effects of damping and critical level absorption are taken into account with Wentzel–Kramers–Brillouin theory. For verification of the parameterization with homogeneous meteorological fields in space and time, the 10 field campaigns were hindcasted with the nonhydrostatic fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model. About 80% of the variance in inertia–gravity wave action was found to be explained. For the 10 campaigns a close link was found between the poleward-breaking Rossby waves and the strong stratospheric inertia–gravity waves. The role of the polar vortex was twofold: first, it forced the poleward-oriented Rossby waves to break downstream and to form strong tropospheric jet streaks generating inertia–gravity waves. Second, the strong winds in the stratosphere favored the upward propagation of the inertia–gravity waves. The proposed new parameterization of inertia–gravity wave generation and propagation was validated and can be used to deduce mesoscale wave intensity from synoptic flow characteristics during poleward Rossby wave–breaking events.
11

Farneti, Riccardo. "Coupled Interannual Rossby Waves in a Quasigeostrophic Ocean–Atmosphere Model." Journal of Physical Oceanography 37, no. 5 (May 2007): 1192–214. http://dx.doi.org/10.1175/jpo3061.1.

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Abstract Rossby wave propagation is investigated in the framework of an idealized middle-latitude quasigeostrophic coupled ocean–atmosphere model. The Rossby waves are observed to propagate faster than both the classical linear theory (unperturbed solution) and the phase speed estimates when the effect of the zonal mean flow is added (perturbed solution). Moreover, using statistical eigentechniques, a clear coupled Rossby wave mode is identified between a baroclinic oceanic Rossby wave and an equivalent barotropic atmospheric wave. The spatial phase relationship of the coupled wave is similar to the one predicted by Goodman and Marshall, suggesting a positive ocean–atmosphere feedback. It is argued that oceanic Rossby waves can be efficiently coupled to the overlying atmosphere and that the atmospheric coupling is capable of adding an extra speedup to the wave; in fact, when the ocean is simply forced, the Rossby wave propagation speed approaches the perturbed solution.
12

Avalos-Zuniga, R., F. Plunian та K. H. Rädler. "Rossby waves andα-effect". Geophysical & Astrophysical Fluid Dynamics 103, № 5 (жовтень 2009): 375–96. http://dx.doi.org/10.1080/03091920903006099.

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13

Miles, John. "Resonantly Forced Rossby Waves." Journal of Physical Oceanography 15, no. 4 (April 1985): 467–74. http://dx.doi.org/10.1175/1520-0485(1985)015<0467:rfrw>2.0.co;2.

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14

Kang, Min-Jee, Hye-Yeong Chun, and Rolando R. Garcia. "Role of equatorial waves and convective gravity waves in the 2015/16 quasi-biennial oscillation disruption." Atmospheric Chemistry and Physics 20, no. 23 (December 2020): 14669–93. http://dx.doi.org/10.5194/acp-20-14669-2020.

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Abstract. In February 2016, the descent of the westerly phase of the quasi-biennial oscillation (QBO) was unprecedentedly disrupted by the development of easterly winds. Previous studies have shown that extratropical Rossby waves propagating into the deep tropics were the major cause of the 2015/16 QBO disruption. However, a large portion of the negative momentum forcing associated with the disruption still stems from equatorial planetary and small-scale gravity waves, which calls for detailed analyses by separating each wave mode compared with climatological QBO cases. Here, the contributions of resolved equatorial planetary waves (Kelvin, Rossby, mixed Rossby–gravity (MRG), and inertia–gravity (IG) waves) and small-scale convective gravity waves (CGWs) obtained from an offline CGW parameterization to the 2015/16 QBO disruption are investigated using MERRA-2 global reanalysis data from October 2015 to February 2016. In October and November 2015, anomalously strong negative forcing by MRG and IG waves weakened the QBO jet at 0–5∘ S near 40 hPa, leading to Rossby wave breaking at the QBO jet core in the Southern Hemisphere. From December 2015 to January 2016, exceptionally strong Rossby waves propagating horizontally (vertically) continuously decelerated the southern (northern) flank of the jet. In February 2016, when the westward CGW momentum flux at the source level was much stronger than its climatology, CGWs began to exert considerable negative forcing at 40–50 hPa near the Equator, in addition to the Rossby waves. The enhancement of the negative wave forcing in the tropics stems mostly from strong wave activity in the troposphere associated with increased convective activity and the strong westerlies (or weaker easterlies) in the troposphere, except that the MRG wave forcing is more likely associated with increased barotropic instability in the lower stratosphere.
15

Kang, Min-Jee, and Hye-Yeong Chun. "Contributions of equatorial waves and small-scale convective gravity waves to the 2019/20 quasi-biennial oscillation (QBO) disruption." Atmospheric Chemistry and Physics 21, no. 12 (July 2021): 9839–57. http://dx.doi.org/10.5194/acp-21-9839-2021.

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Abstract. In January 2020, unexpected easterly winds developed in the downward-propagating westerly quasi-biennial oscillation (QBO) phase. This event corresponds to the second QBO disruption in history, and it occurred 4 years after the first disruption of 2015/16. According to several previous studies, strong midlatitude Rossby waves propagating from the Southern Hemisphere (SH) during the SH winter likely initiated the disruption; nevertheless, the wave forcing that finally led to the disruption has not been investigated. In this study, we examine the role of equatorial waves and small-scale convective gravity waves (CGWs) in the 2019/20 QBO disruption using Modern-Era Retrospective Analysis for Research and Applications version 2 (MERRA-2) global reanalysis data. In June–September 2019, unusually strong Rossby wave forcing originating from the SH decelerated the westerly QBO at 0–5∘ N at ∼50 hPa. In October–November 2019, vertically (horizontally) propagating Rossby waves and mixed Rossby–gravity (MRG) waves began to increase (decrease). From December 2019, the contribution of the MRG wave forcing to the zonal wind deceleration was the largest, followed by the Rossby wave forcing originating from the Northern Hemisphere and the equatorial troposphere. In January 2020, CGWs provided 11 % of the total negative wave forcing at ∼43 hPa. Inertia–gravity (IG) waves exhibited a moderate contribution to the negative forcing throughout. Although the zonal mean precipitation was not significantly larger than the climatology, convectively coupled equatorial wave activities were increased during the 2019/20 disruption. As in the 2015/16 QBO disruption, the increased barotropic instability at the QBO edges generated more MRG waves at 70–90 hPa, and westerly anomalies in the upper troposphere allowed more westward IG waves and CGWs to propagate to the stratosphere. Combining the 2015/16 and 2019/20 disruption cases, Rossby waves and MRG waves can be considered the key factors inducing QBO disruption.
16

Gorman, Arthur D. "On caustics associated with Rossby waves." Applications of Mathematics 41, no. 5 (1996): 321–28. http://dx.doi.org/10.21136/am.1996.134329.

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17

Egger, Joseph. "Counterpropagating Rossby waves and barotropic instability." Meteorologische Zeitschrift 16, no. 5 (October 2007): 581–85. http://dx.doi.org/10.1127/0941-2948/2007/0239.

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18

Poulin, F. J. "Can Long Meridional Length Scales Yield Faster Rossby Waves?" Journal of Physical Oceanography 39, no. 2 (February 2009): 472–78. http://dx.doi.org/10.1175/2008jpo4099.1.

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Abstract There is much interest in better understanding the westward-propagating subinertial signal in the ocean basins because it influences many aspects of the ocean’s circulation. One explanation for the origin of this signal is that it is predominantly composed of Rossby waves. Chelton and Schlax assumed the observations were Rossby waves and compared their phase speeds with those predicted from nondispersive linear quasigeostrophic wave speeds. They concluded that the theory underestimated the observed wave speeds. Recently, in the context of the shallow-water model, Paldor, Rubin, and Mariano found that by including the full meridional variation of the Coriolis parameter, the Rossby waves have faster phase speeds. Here, their analysis is extended to derive a general dispersion relation for stratified Rossby waves that is suitable for both mesoscale and synoptic length scales. Then, realistic profiles of the buoyancy frequency are used to compare the phase speeds from the Ocean Topography Experiment (TOPEX)/Poseidon data with the new theory. It is found that the new theory does not yield any significant increase in Rossby wave speeds.
19

Zhang, Jiaqi, Liangui Yang, and Ruigang Zhang. "Solitary waves under curved topography and beta approximation." Modern Physics Letters B 34, no. 17 (April 2020): 2050196. http://dx.doi.org/10.1142/s0217984920501961.

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In this paper, the mechanisms of excitation and propagation of nonlinear Rossby waves are investigated by the approach of topographic balance under the beta approximation for the first time. Using time-space elongation transformation and perturbation expansion method, a Korteweg–de Vries model equation for topographic Rossby wave amplitude is derived. The influences of topography parameters on Rossby solitary waves are discussed through qualitative and quantitative analysis.
20

Rhines, P. B. "Jets and Orography: Idealized Experiments with Tip Jets and Lighthill Blocking." Journal of the Atmospheric Sciences 64, no. 10 (October 2007): 3627–39. http://dx.doi.org/10.1175/jas4008.1.

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Abstract This paper describes qualitative features of the generation of jetlike concentrated circulations, wakes, and blocks by simple mountainlike orography, both from idealized laboratory experiments and shallow-water numerical simulations on a sphere. The experiments are unstratified with barotropic lee Rossby waves, and jets induced by mountain orography. A persistent pattern of lee jet formation and lee cyclogenesis owes its origins to arrested topographic Rossby waves above the mountain and potential vorticity (PV) advection through them. The wake jet occurs on the equatorward, eastern flank of the topography. A strong upstream blocking of the westerly flow occurs in a Lighthill mode of long Rossby wave propagation, which depends on βa2/U, the ratio of Rossby wave speed based on the scale of the mountain, to zonal advection speed, U (β is the meridional potential vorticity gradient, f is the Coriolis frequency, and a is the diameter of the mountain). Mountains wider (north–south) than the east–west length scale of stationary Rossby waves will tend to block the oncoming westerly flow. These blocks are essentially β plumes, which are illustrated by their linear Green function. For large βa2/U, upwind blocking is strong; the mountain wake can be unstable, filling the fluid with transient Rossby waves as in the numerical simulations of Polvani et al. For small values, βa2/U ≪ 1 classic lee Rossby waves with large wavelength compared to the mountain diameter are the dominant process. The mountain height, δh, relative to the mean fluid depth, H, affects these transitions as well. Simple lee Rossby waves occur only for such small heights, δh/h ≪ aβ/f, that the f/h contours are not greatly distorted by the mountain. Nongeostrophic dynamics are seen in inertial waves generated by geostrophic shear, and ducted by it, and also in a texture of finescale, inadvertent convection. Weakly damped circulations induced in a shallow-water numerical model on a sphere by a lone mountain in an initially simple westerly wind are also described. Here, with βa2/U ∼1, potential vorticity stirring and transient Rossby waves dominate, and drive zonal flow acceleration. Low-latitude critical layers, when present, exert strong control on the high-latitude waves, and with no restorative damping of the mean zonal flow, they migrate poleward toward the source of waves. While these experiments with homogeneous fluid are very simplified, the baroclinic atmosphere and ocean have many tall or equivalent barotropic eddy structures owing to the barotropization process of geostrophic turbulence.
21

Niranjan Kumar, K., D. V. Phanikumar, T. B. M. J. Ouarda, M. Rajeevan, M. Naja, and K. K. Shukla. "Modulation of surface meteorological parameters by extratropical planetary-scale Rossby waves." Annales Geophysicae 34, no. 1 (January 2016): 123–32. http://dx.doi.org/10.5194/angeo-34-123-2016.

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Abstract. This study examines the link between upper-tropospheric planetary-scale Rossby waves and surface meteorological parameters based on the observations made in association with the Ganges Valley Aerosol Experiment (GVAX) campaign at an extratropical site at Aryabhatta Research Institute of Observational Sciences, Nainital (29.45° N, 79.5° E) during November–December 2011. The spectral analysis of the tropospheric wind field from radiosonde measurements indicates a predominance power of around 8 days in the upper troposphere during the observational period. An analysis of the 200 hPa meridional wind (v200 hPa) anomalies from the Modern-Era Retrospective Analysis for Research and Applications (MERRA) reanalysis shows distinct Rossby-wave-like structures over a high-altitude site in the central Himalayan region. Furthermore, the spectral analysis of global v200 hPa anomalies indicates the Rossby waves are characterized by zonal wave number 6. The amplification of the Rossby wave packets over the site leads to persistent subtropical jet stream (STJ) patterns, which further affects the surface weather conditions. The propagating Rossby waves in the upper troposphere along with the undulations in the STJ create convergence and divergence regions in the mid-troposphere. Therefore, the surface meteorological parameters such as the relative humidity, wind speeds, and temperature are synchronized with the phase of the propagating Rossby waves. Moreover, the present study finds important implications for medium-range forecasting through the upper-level Rossby waves over the study region.
22

Shaman, Jeffrey, and Eli Tziperman. "The Superposition of Eastward and Westward Rossby Waves in Response to Localized Forcing." Journal of Climate 29, no. 20 (October 2016): 7547–57. http://dx.doi.org/10.1175/jcli-d-16-0119.1.

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Abstract Rossby waves are a principal form of atmospheric communication between disparate parts of the climate system. These planetary waves are typically excited by diabatic or orographic forcing and can be subject to considerable downstream modification. Because of differences in wave properties, including vertical structure, phase speed, and group velocity, Rossby waves exhibit a wide range of behaviors. This study demonstrates the combined effects of eastward-propagating stationary barotropic Rossby waves and westward-propagating very-low-zonal-wavenumber stationary barotropic Rossby waves on the atmospheric response to wintertime El Niño convective forcing over the tropical Pacific. Experiments are conducted using the Community Atmosphere Model, version 4.0, in which both diabatic forcing over the Pacific and localized relaxation outside the forcing region are applied. The localized relaxation is used to dampen Rossby wave propagation to either the west or east of the forcing region and isolate the alternate direction signal. The experiments reveal that El Niño forcing produces both eastward- and westward-propagating stationary waves in the upper troposphere. Over North Africa and Asia the aggregate undamped upper-tropospheric response is due to the superposition and interaction of these oppositely directed planetary waves that emanate from the forcing region and encircle the planet.
23

Dias Pinto, João Rafael, and Jonathan Lloyd Mitchell. "Wave–Mean Flow Interactions and the Maintenance of Superrotation in a Terrestrial Atmosphere." Journal of the Atmospheric Sciences 73, no. 8 (July 2016): 3181–96. http://dx.doi.org/10.1175/jas-d-15-0208.1.

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Abstract The interplay between mean meridional circulation and transient eddies through wave–mean flow interaction processes defines the general behavior of any planetary atmospheric circulation. Under a higher-Rossby-number regime, equatorward momentum transports provided by large-scale disturbances generate a strong zonal flow at the equatorial region. At intermediate Rossby numbers, equatorial Kelvin waves play a leading role in maintaining a superrotating jet over the equator. However, at high Rossby numbers, the Kelvin wave only provides equatorward momentum fluxes during spinup, and the wave–mean flow process that maintains this strongly superrotating state has yet to be identified. This study presents a comprehensive analysis of the tridimensional structure and life cycle of atmospheric waves and their interaction with the mean flow, which maintains the strong, long-lived superrotating state in a higher-Rossby-number-regime atmosphere. The results show that the mean zonal superrotating circulation is maintained by the dynamical interaction between mixed baroclinic–barotropic Rossby wave modes via low-frequency variations of the zonal-mean state in short and sporadic periods of stronger instability. The modulation of amplitude of the equatorial and extratropical Rossby waves suggests a nonlinear mechanism of eddy–eddy interaction between these modes.
24

Shi, Yunlong, Baoshu Yin, Hongwei Yang, Dezhou Yang, and Zhenhua Xu. "Dissipative Nonlinear Schrödinger Equation for Envelope Solitary Rossby Waves with Dissipation Effect in Stratified Fluids and Its Solution." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/643652.

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We solve the so-called dissipative nonlinear Schrödinger equation by means of multiple scales analysis and perturbation method to describe envelope solitary Rossby waves with dissipation effect in stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt-Vaisala frequency, andβeffect are important factors to form the envelope solitary Rossby waves. By employing trial function method, the asymptotic solution of dissipative nonlinear Schrödinger equation is derived. Based on the solution, the effect of dissipation on the evolution of envelope solitary Rossby wave is also discussed. The results show that the dissipation causes a slow decrease of amplitude of envelope solitary Rossby waves and a slow increase of width, while it has no effect on the propagation velocity. That is quite different from the KdV-type solitary waves. It is notable that dissipation has certain influence on the carrier frequency.
25

McKenzie, J. F., and M. K. Dougherty. "Electrostatic Rossby-type ion plasma waves." Journal of Plasma Physics 39, no. 1 (February 1988): 103–14. http://dx.doi.org/10.1017/s0022377800012885.

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It is shown that a plasma in which the background magnetic field varies in a direction perpendicular to its line of action can support ‘Rossby-type’ electrostatic waves at frequencies very much less than the ion gyrofrequency. The intrinsic wave propagation mechanism at work is structurally similar to that in the atmospheric Rossby wave, which comes about from fluid perturbations being in quasi-geostrophic equilibrium (i.e. the Coriolis force nearly balances the pressure gradient) and the latitudinal variation of the vertical component of rotational frequency vector (the β-effect) so that the time rate of change of the vertical component of the fluid vorticity is equal to the northward transport of the planetary vorticity. In a plasma this ‘geostrophic balance’ arises from the near-vanishing of the Lorentz force on the ion motion while the β-effect is provided by the transverse spatial variation of the ambient magnetic field. Unlike the atmosphere, however, such a magnetized plasma is capable of supporting two distinct types of Rossby wave. The interesting dispersive and anisotropic features of these waves are revealed by the properties of their wave operators and described in terms of the geometry of their wavenumber surfaces. Since these surfaces intersect, inhomogeneity or nonlinearity will give rise to strong mode-mode coupling in regions where the phases of both modes nearly match.
26

Charria, G., I. Dadou, P. Cipollini, M. Drévillon, and V. Garçon. "Influence of Rossby waves on primary production from a coupled physical-biogeochemical model in the North Atlantic Ocean." Ocean Science Discussions 4, no. 6 (November 2007): 933–67. http://dx.doi.org/10.5194/osd-4-933-2007.

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Abstract. How do Rossby waves influence primary production in the North Atlantic Ocean? Rossby waves have a clear signature on surface chlorophyll concentrations which can be explained by a combination of vertical and horizontal mechanisms (reviewed in Killworth et al., 2004). In this study, we aim to investigate the role of the different physical processes to explain the surface chlorophyll signatures and the consequences on primary production using a 3-D coupled physical/biogeochemical model for the year 1998. The analysis at 20 given latitudes, mainly located in the subtropical gyre, where Rossby waves are strongly correlated with a surface chlorophyll signature, shows that vertical and horizontal processes are involved in the surface chlorophyll anomalies. Furthermore, the ecosystem response is, as expected, stronger when vertical input of dissolved inorganic nitrogen is observed. The surface chlorophyll anomalies, induced by these physical mechanisms, have an impact on primary production. We then estimate that Rossby waves induce, locally in space and time, increases (generally associated with the wave crest) and decreases (generally associated with the wave trough) in primary production (~±20% of the estimated primary production). This symmetrical situation suggests a net weak effect of Rossby waves on primary production.
27

Castanheira, J. M., M. L. R. Liberato, L. de la Torre, H.-F. Graf, and C. C. DaCamara. "Baroclinic Rossby Wave Forcing and Barotropic Rossby Wave Response to Stratospheric Vortex Variability." Journal of the Atmospheric Sciences 66, no. 4 (April 2009): 902–14. http://dx.doi.org/10.1175/2008jas2862.1.

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Abstract An analysis is performed on the dynamical coupling between the variability of the extratropical stratospheric and tropospheric circulations during the Northern Hemisphere winter. Obtained results provide evidence that in addition to the well-known Charney and Drazin mechanism by which vertical propagation of baroclinic Rossby waves is nonlinearly influenced by the zonal mean zonal wind, topographic forcing constitutes another important mechanism by which nonlinearity is introduced in the troposphere–stratosphere wave-driven coupled variability. On the one hand, vortex variability is forced by baroclinic Rossby wave bursts, with positive (negative) peaks of baroclinic Rossby wave energy occurring during rapid vortex decelerations (accelerations). On the other hand, barotropic Rossby waves of zonal wavenumbers s = 1 and 3 respond to the vortex state, and strong evidence is presented that such a response is mediated by changes of the topographic forcing due to zonal mean zonal wind anomalies progressing downward from the stratosphere. It is shown that wavenumbers s = 1 and 3 are the dominant Fourier components of the topography in the high-latitude belt where the zonal mean zonal wind anomalies are stronger; moreover, obtained results are in qualitative agreement with the analytical solution provided by the simple topographic wave model of Charney and Eliassen. Finally, evidence is provided that changes of barotropic long (s ≤ 3) Rossby waves associated with vortex variability reproduce a NAO-like dipole over the Atlantic Ocean but no dipole is formed over the Pacific Ocean. Moreover, results suggest that the nonlinear wave response to topographic forcing may explain the spatial changes of the NAO correlation patterns that have been found in previous studies.
28

Zhang, Ruigang, Quansheng Liu, and Liangui Yang. "New model and dynamics of higher-dimensional nonlinear Rossby waves." Modern Physics Letters B 33, no. 28 (October 2019): 1950342. http://dx.doi.org/10.1142/s0217984919503421.

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In this work, the propagation of higher-dimensional nonlinear Rossby waves under the generalized beta effect is considered. Using the methods of weak nonlinear perturbation expansions and the multiple scales, we obtain a new (2 + 1)-dimensional generalized Boussinesq equation from the barotropic potential vorticity equation for the first time. Furthermore, a new dispersion relation for the linear Rossby waves is given corresponding to the linearized Boussinesq equation. More importantly, based on the methods of the traveling wave setting and the Jacobi elliptic function expansions, several kinds of exact traveling wave solutions for the higher-dimensional nonlinear Rossby waves, including the periodic solutions, solitary solutions and others are obtained. Finally, we simulate the solitary solutions obtained by using the method of the Jacobi elliptic function. The numerical results show that the amplitude of the Rossby solitary waves is decreasing with the increase of generalized beta effect.
29

VANNESTE, JACQUES. "A nonlinear critical layer generated by the interaction of free Rossby waves." Journal of Fluid Mechanics 371 (September 1998): 319–44. http://dx.doi.org/10.1017/s0022112098002237.

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Two free waves propagating in a parallel shear flow generate a critical layer when their nonlinear interaction induces a perturbation whose phase velocity matches the basic-state velocity somewhere in the flow domain. The condition necessary for this to occur may be interpreted as a resonance condition for a triad formed by the two waves and a (singular) mode of the continuous spectrum associated with the shear. The formation of the critical layer is investigated in the case of freely propagating Rossby waves in a two-dimensional inviscid flow in a β-channel.A weakly nonlinear analysis based on a normal-mode expansion in terms of Rossby waves and modes of the continuous spectrum is developed; it leads to a system of amplitude equations describing the evolution of the two Rossby waves and of the modes of the continuous spectrum excited during the interaction. The assumption of weak nonlinearity is not however self-consistent: it breaks down because nonlinearity always becomes strong within the critical layer, however small the initial amplitudes of the Rossby waves. This demonstrates the relevance of nonlinear critical layers to monotonic, stable, unforced shear flows which sustain wave propagation.A nonlinear critical-layer theory is developed that is analogous to the well-known theory for forced critical layers. Differences arise because of the presence of the Rossby waves: the vorticity in the critical layer is advected in the cross-stream direction by the oscillatory velocity field due to the Rossby waves. An equation is derived which governs the modification of the Rossby waves that results from their interaction; it indicates that the two Rossby waves are undisturbed at leading order. An analogue of the Stewartson–Warn–Warn analytical solution is also considered.
30

Reshetnyak, M. Yu. "Rossby waves and cascade phenomena." Izvestiya, Physics of the Solid Earth 48, no. 9-10 (September 2012): 693–97. http://dx.doi.org/10.1134/s1069351312080034.

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31

Quartly, Graham D., Paolo Cipollini, David Cromwell, and Peter G. Challenor. "Rossby waves: synergy in action." Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 361, no. 1802 (November 2002): 57–63. http://dx.doi.org/10.1098/rsta.2002.1108.

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32

EGGER, JOSEPH, and KLAUS FRAEDRICH. "Topographic Rossby waves over Antarctica." Tellus A 39A, no. 2 (March 1987): 110–15. http://dx.doi.org/10.1111/j.1600-0870.1987.tb00293.x.

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33

Ivanov, L. M., C. A. Collins, T. M. Margolina, and V. N. Eremeev. "Nonlinear Rossby waves off California." Geophysical Research Letters 37, no. 13 (July 2010): n/a. http://dx.doi.org/10.1029/2010gl043708.

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34

Kloosterziel, R. C., and L. R. M. Maas. "Green’s functions for Rossby waves." Journal of Fluid Mechanics 830 (October 2017): 387–407. http://dx.doi.org/10.1017/jfm.2017.601.

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Compact solutions are presented for planetary, non-divergent, barotropic Rossby waves generated by (i) an impulsive point source and (ii) a sustained point source of curl of wind stress. Previously, only cumbersome integral expressions were known, rendering them practically useless. Our simple expressions allow for immediate numerical visualization/animation and further mathematical analysis.
35

Egger, Joseph, and Klaus Fraedrich. "Topographic Rossby waves over Antarctica." Tellus A: Dynamic Meteorology and Oceanography 39, no. 2 (January 1987): 110–15. http://dx.doi.org/10.3402/tellusa.v39i2.11745.

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36

Jury, Mark R. "South Indian Ocean Rossby Waves." Atmosphere-Ocean 56, no. 5 (October 2018): 322–31. http://dx.doi.org/10.1080/07055900.2018.1544882.

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37

Dukowicz, John K. "Mesh Effects for Rossby Waves." Journal of Computational Physics 119, no. 1 (June 1995): 188–94. http://dx.doi.org/10.1006/jcph.1995.1126.

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38

Bénard, P. "Stability of Rossby–Haurwitz waves." Quarterly Journal of the Royal Meteorological Society 146, no. 727 (December 2019): 613–28. http://dx.doi.org/10.1002/qj.3696.

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39

Persson, Anders. "Rossby waves - do they exist?" Weather 70, no. 12 (December 2015): 344–45. http://dx.doi.org/10.1002/wea.2588.

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40

Farrell, Brian, and Ian Watterson. "Rossby Waves in Opposing Currents." Journal of the Atmospheric Sciences 42, no. 16 (August 1985): 1746–56. http://dx.doi.org/10.1175/1520-0469(1985)042<1746:rwioc>2.0.co;2.

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41

Li, Haiyan, Robin Pilch Kedzierski, and Katja Matthes. "On the forcings of the unusual Quasi-Biennial Oscillation structure in February 2016." Atmospheric Chemistry and Physics 20, no. 11 (June 2020): 6541–61. http://dx.doi.org/10.5194/acp-20-6541-2020.

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Abstract. The westerly phase of the stratospheric Quasi-Biennial Oscillation (QBO) was reversed during Northern Hemisphere winter 2015/2016 for the first time since records began in 1953. Recent studies proposed that Rossby waves propagating from the extratropics played an important role during the reversal event in 2015/2016. Building upon these studies, we separated the extratropical Rossby waves into different wavenumbers and timescales by analyzing the combined ERA-40 and ERA-Interim reanalysis zonal wind, meridional wind, vertical velocity, and potential vorticity daily mean data from 1958 to 2017. We find that both synoptic and quasi-stationary Rossby waves are dominant contributors to the reversal event in 2015/2016 in the tropical lower stratosphere. By comparing the results for 2015/2016 with two additional events (1959/1960 and 2010/2011), we find that the largest differences in Rossby wave momentum fluxes are related to synoptic-scale Rossby waves of periods from 5 to 20 d. We demonstrate for the first time, that these enhanced synoptic Rossby waves at 40 hPa in the tropics in February 2016 originate from the extratropics as well as from local wave generation. The strong Rossby wave activity in 2016 in the tropics happened at a time with weak westerly zonal winds. This coincidence of anomalous factors did not happen in any of the previous events. In addition to the anomalous behavior in the tropical lower stratosphere in 2015/2016, we explored the forcing of the unusually long-lasting westerly zonal wind phase in the middle stratosphere (at 20 hPa). Our results reveal that mainly enhanced Kelvin wave activity contributed to this feature. This was in close relation with the strong El Niño event in 2015/2016, which forced more Kelvin waves in the equatorial troposphere. The easterly or very weak westerly zonal winds present around 30–70 hPa allowed these Kelvin waves to propagate vertically and deposit their momentum around 20 hPa, maintaining the westerlies there.
42

Lu, Chungu, and John P. Boyd. "Rossby Wave Ray Tracing in a Barotropic Divergent Atmosphere." Journal of the Atmospheric Sciences 65, no. 5 (May 2008): 1679–91. http://dx.doi.org/10.1175/2007jas2537.1.

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Abstract The effects of divergence on low-frequency Rossby wave propagation are examined by using the two-dimensional Wentzel–Kramers–Brillouin (WKB) method and ray tracing in the framework of a linear barotropic dynamic system. The WKB analysis shows that the divergent wind decreases Rossby wave frequency (for wave propagation northward in the Northern Hemisphere). Ray tracing shows that the divergent wind increases the zonal group velocity and thus accelerates the zonal propagation of Rossby waves. It also appears that divergence tends to feed energy into relatively high wavenumber waves, so that these waves can propagate farther downstream. The present theory also provides an estimate of a phase angle between the vorticity and divergence centers. In a fully developed Rossby wave, vorticity and divergence display a π/2 phase difference, which is consistent with the observed upper-level structure of a mature extratropical cyclone. It is shown that these theoretical results compare well with observations.
43

Mizuta, Genta. "Upgradient and Downgradient Potential Vorticity Fluxes Produced by Forced Rossby Waves. Part II: Parameter Sensitivity and Physical Interpretation." Journal of Physical Oceanography 48, no. 5 (May 2018): 1211–30. http://dx.doi.org/10.1175/jpo-d-17-0198.1.

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AbstractWe examine the potential vorticity (PV) flux produced by forced Rossby waves in a two-layer quasigeostrophic model, using a perturbation analysis. Rossby waves are excited by external forcing applied to the upper layer. The southward PV flux is produced in the lower layer by the higher-order Rossby waves that are excited by nonlinear wave–wave interactions, whereas the northward PV flux is produced in the upper layer. The direction of the PV flux is consistent with that obtained by an eddy-resolving model of the wind-driven circulation in previous studies. The southward PV flux is produced in a wide parameter range comparable to the eddy-resolving model. The basic features of the PV flux remain unchanged even in the limit of weak stratification. In this limit, stratification has nearly no effect on the flow, except that it isolates the lower layer from the direct effects of external forcing. The mechanism of the southward PV flux is explained using basic features of the barotropic Rossby waves and does not depend on details of the model. Furthermore, the resonant triad interaction of Rossby waves does not affect the PV flux. Stratification weakens or strengthens the PV flux depending on the horizontal scale of the external forcing.
44

Kandaswamy, Palani G., B. Tamil Selvi, and Lokenath Debnath. "Propagation of Rossby waves in stratified shear flows." International Journal of Mathematics and Mathematical Sciences 12, no. 3 (1989): 547–57. http://dx.doi.org/10.1155/s0161171289000682.

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A study is made of the propagation of Rossby waves in a stably stratified shear flows. The wave equation for the Rossby waves is derived in an isothermal atmosphere on a beta plane in the presence of a latitudinally sheared zonal flow. It is shown that the wave equation is singular at five critical levels, but the wave absorption takes place only at the two levels where the local relative frequency equals in magnitude to the Brunt Vaisala frequency. This analysis also reveals that these two levels exhibit valve effect by allowing the waves to penetrate them from one side only. The absorption coefficient exp(2πμ)is determined at these levels. Both the group velocity approach and single wave treatment are employed for the investigation of the problem.
45

Farrar, J. Thomas. "Observations of the Dispersion Characteristics and Meridional Sea Level Structure of Equatorial Waves in the Pacific Ocean." Journal of Physical Oceanography 38, no. 8 (August 2008): 1669–89. http://dx.doi.org/10.1175/2007jpo3890.1.

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Abstract Spectral techniques applied to altimetry data are used to examine the dispersion relation and meridional sea level structure of wavelike variability with periods of about 20 to 200 days in the equatorial Pacific Ocean. Zonal wavenumber–frequency power spectra of sea surface height, when averaged over about 7°S–7°N, exhibit spectral peaks near the theoretical dispersion curves of first baroclinic-mode equatorial Kelvin and Rossby waves. There are distinct, statistically significant ridges of power near the first and second meridional-mode Rossby wave dispersion curves. Sea level variability near the theoretical Kelvin wave and first meridional-mode Rossby wave dispersion curves is dominantly (but not perfectly) symmetric about the equator, while variability near the theoretical second meridional-mode Rossby wave dispersion curve is dominantly antisymmetric. These results are qualitatively consistent with expectations from classical or shear-modified theories of equatorial waves. The meridional structures of these modes resemble the meridional modes of equatorial wave theory, but there are some robust features of the meridional profiles that were not anticipated. The meridional sea level structure in the intraseasonal Kelvin wave band closely resembles the theoretically expected Gaussian profile, but sea level variability coherent with that at the equator is detected as far away as 11.75°S, possibly as a result of the forced nature of these Kelvin waves. Both first and second meridional-mode Rossby waves have larger amplitude in the Northern Hemisphere. The meridional sea level structure of tropical instability waves closely resembles that predicted by Lyman et al. using a model linearized about a realistic equatorial zonal current system.
46

Gnevyshev, V. G., A. V. Frolova, A. A. Kubryakov, Yu V. Sobko, and T. V. Belonenko. "Interaction of Rossbi waves with a jet flow: basic equations and verification for Antarctic circumpolar current." Известия Российской академии наук. Физика атмосферы и океана 55, no. 5 (November 2019): 39–50. http://dx.doi.org/10.31857/s0002-351555539-50.

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The article focuses on the interaction of Rossby waves in the ocean with zonal jet flows. A new approach is proposed to show that nonlinearity in the long-wave approximation exactly compensates the Doppler shift. A new dispersion relation for the Rossby waves interacting with the jets is deduced from the nonlinear theory. The conclusion is verified using satellite altimetry data of the Antarctic Circumpolar Current (ACC). For the ACC area, we compare empirical velocities obtained from the altimetry data with theoretical phase velocities of Rossby waves calculated from nonlinear dispersion relation using the equivalent beta effect. The comparison shows that the new dispersion relation based on the nonlinear approach is capable of describing both the westward and the eastward propagation of mesoscale eddies in the field of sea level anomalies that can be identified as manifestation of Rossby waves in the ocean.
47

Sakai, Satoshi. "Rossby-Kelvin instability: a new type of ageostrophic instability caused by a resonance between Rossby waves and gravity waves." Journal of Fluid Mechanics 202 (May 1989): 149–76. http://dx.doi.org/10.1017/s0022112089001138.

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An ageostrophic version of Phillips’ model is studied. All instabilities found are systematically interpreted in terms of resonance of wave components. The instability occurs if there is a pair of wave components which propagate in the opposite direction to the basic flow and these wave components have almost the same Doppler-shifted frequency. A new instability, identified as a resonance between the Kelvin wave and the Rossby waves, is found at Froude number F ≈ 0.7. The Rossby waves are almost completely in geostrophic balance while the ageostrophic Kelvin wave is the same as in a one-layer system. Doppler shifting matches frequencies which would otherwise be very different. This instability is presumably the mechanism of the frontal instability observed by Griffiths & Linden (1982) in a laboratory experiment. Ageostrophic, baroclinic instability with non-zero phase speed is also observed in the numerical calculation. This instability is caused by resonance between different geostrophic modes.
48

Schecter, David A. "The Spontaneous Imbalance of an Atmospheric Vortex at High Rossby Number." Journal of the Atmospheric Sciences 65, no. 8 (August 2008): 2498–521. http://dx.doi.org/10.1175/2007jas2490.1.

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Abstract This paper discusses recent progress toward understanding the instability of a monotonic vortex at high Rossby number, due to the radiation of spiral inertia–gravity (IG) waves. The outward-propagating IG waves are excited by inner undulations of potential vorticity that consist of one or more vortex Rossby waves. An individual vortex Rossby wave and its IG wave emission have angular pseudomomenta of opposite sign, positive and negative, respectively. The Rossby wave therefore grows in response to producing radiation. Such growth is potentially suppressed by the resonant absorption of angular pseudomomentum in a critical layer, where the angular phase velocity of the Rossby wave matches the angular velocity of the mean flow. Suppression requires a sufficiently steep radial gradient of potential vorticity in the critical layer. Both linear and nonlinear steepness requirements are reviewed. The formal theory of radiation-driven instability, or “spontaneous imbalance,” is generalized in isentropic coordinates to baroclinic vortices that possess active critical layers. Furthermore, the rate of angular momentum loss by IG wave radiation is reexamined in the hurricane parameter regime. Numerical results suggest that the negative radiation torque on a hurricane has a smaller impact than surface drag, despite recent estimates of its large magnitude.
49

Lott, François, Jayanarayanan Kuttippurath, and François Vial. "A Climatology of the Gravest Waves in the Equatorial Lower and Middle Stratosphere: Method and Results for the ERA-40 Re-Analysis and the LMDz GCM." Journal of the Atmospheric Sciences 66, no. 5 (May 2009): 1327–46. http://dx.doi.org/10.1175/2008jas2880.1.

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Abstract A climatology of the three-dimensional life cycle of the gravest waves in the tropical lower and middle stratosphere is presented. It shows that at periods around 10 days the gravest waves correspond to Kelvin and Rossby–gravity wave packets that substantially affect specific regions in the lower stratosphere. It also shows that the planetary-scale Kelvin waves with zonal wavenumber s = 1 and periods between 10 and 20 days produce a substantial signal. Still at the planetary scales, the climatology also shows that the global planetary Rossby waves with s = 1 and periods around 5 and 16 days have a substantial equatorial signature. This climatology is for all the dynamical fields (horizontal wind, temperature, and geopotential height) and relates the equatorial waves to the equatorial zonal mean flow evolution associated with the quasi-biennial oscillation. The method used to extract the climatology is a composite analysis of the dynamical fields keyed on simple indexes measuring when the waves enter in the stratosphere. For the Kelvin waves, the Rossby–gravity waves, and the 5- and 16-day Rossby planetary waves, these indexes are related to the latitudinal means over the equatorial band of the temperature, the meridional wind, the geopotential height, and the zonal wind respectively. The method is applied first to ERA-40 and then to a simulation done with the LMDz GCM. When compared to the results from ERA-40, this reveals that the LMDz GCM underestimates the Rossby–gravity wave packets and a fraction of the Kelvin wave packets. This deficit is attributed to the fact that the model has a too coarse vertical resolution and an insufficient tropospheric forcing for the horizontal wavenumbers s &gt; 3.
50

Iga, Keita. "Transition modes of rotating shallow water waves in a channel." Journal of Fluid Mechanics 294 (July 1995): 367–90. http://dx.doi.org/10.1017/s002211209500293x.

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Normal modes of shallow water waves in a channel wherein the Coriolis parameter and the depth vary in the spanwise direction are investigated based on the conservation of the number of zeros in an eigenfunction. As a result, it is generally shown that the condition for transition modes (Kelvin modes and mixed Rossby-gravity modes) to exist, besides Rossby and Poincaré modes, is determined only by boundary conditions. A Kelvin mode is interpreted as a modification of a Kelvin wave or a boundary wave along a closed boundary, and a mixed Rossby-gravity mode as a modification of an inertial oscillation or a boundary wave along an open boundary. Transition modes appearing in edge and continental-shelf waves, equatorial waves and free oscillations over a sphere are systematically understood by applying the theory in this paper.

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