Статті в журналах: "Rossby waves"

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 1, 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

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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5

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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6

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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7

Fedotova, Maria, Dmitry Klimachkov, and Arakel Petrosyan. "Resonant interactions of magneto-Poincaré and magneto-Rossby waves in quasi-two-dimensional rotating astrophysical plasma." Monthly Notices of the Royal Astronomical Society 509, no. 1 (October 14, 2021): 314–26. http://dx.doi.org/10.1093/mnras/stab2957.

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ABSTRACT Increased interest in research of non-linear resonant interactions of waves in rotating astrophysical plasma has taken place in recent years. This is due to the discovering solar magneto-Rossby waves and the emergence of new data on the effect of three-wave interactions of magneto-Rossby waves on solar activity. In context of large-scale magnetohydrodynamic flows in presence of rotation, magneto-Poincaré waves and magneto-Rossby waves are highlighted. The β-plane approximation is developed to simplify the theory of spherical Rossby waves. Nevertheless, the representation of the Coriolis force in this approximation contains a latitude-independent term that ensures the existence of magneto-Poincaré waves on β-plane along with magneto-Rossby waves. In this paper, it is shown that they satisfy the phase matching condition, which leads to emergence of new non-linear interactions mechanisms of waves: two magneto-Poincaré waves and one magneto-Rossby wave; two magneto-Rossby waves and one magneto-Poincaré. Complete dispersion equations on β-plane in quasi-two-dimensional magnetohydrodynamic approximation is analysed both for homogeneous and stratified astrophysical plasma with vertical magnetic field. New dispersion relations for magneto-Poincaré waves on β-plane are obtained. Detailed qualitative analysis of the phase matching condition is carried out, and new types of three-wave interactions of magneto-Poincaré waves and magneto-Rossby waves are found. Three-wave interactions are studied and instabilities of the decay and amplification type are investigated.

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8

Song, Jian, та ShaoXia Liu. "The barotropic Rossby waves with topography on the earth’s δ-surface". International Journal of Nonlinear Sciences and Numerical Simulation 21, № 7-8 (18 листопада 2020): 781–88. http://dx.doi.org/10.1515/ijnsns-2019-0178.

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AbstractThe Rossby solitary waves in the barotropic vorticity model which contains the topography on the earth’s δ-surface is investigated. First, applying scale analysis method, obtained the generalized quasi-geostrophic potential vorticity equation (QGPVE). Using The Wentzel–Kramers–Brillouin (WKB) theory, the evolution equation of Rossby waves is the variable-coefficient Korteweg–de Vries (KdV) equation for the barotropic atmospheric model. In order to study the Rossby waves structural change to exist in some basic flow and topography on the δ-surface approximation, the variable coefficient of KdV equation must be explicitly, Chebyshev polynomials is used to solve a Sturm-Liouville-type eigenvalue problem and the eigenvalue Rossby waves, these solutions show that the parameter δ usually plays the stable part in Rossby waves and slow down the growing or decaying of Rossby waves with the parameter β.

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9

Dikpati, Mausumi, Peter A. Gilman, Gustavo A. Guerrero, Alexander G. Kosovichev, Scott W. McIntosh, Katepalli R. Sreenivasan, Jörn Warnecke, and Teimuraz V. Zaqarashvili. "Simulating Solar Near-surface Rossby Waves by Inverse Cascade from Supergranule Energy." Astrophysical Journal 931, no. 2 (June 1, 2022): 117. http://dx.doi.org/10.3847/1538-4357/ac674b.

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Abstract Rossby waves are found at several levels in the Sun, most recently in its supergranule layer. We show that Rossby waves in the supergranule layer can be excited by an inverse cascade of kinetic energy from the nearly horizontal motions in supergranules. We illustrate how this excitation occurs using a hydrodynamic shallow-water model for a 3D thin rotating spherical shell. We find that initial kinetic energy at small spatial scales inverse cascades quickly to global scales, exciting Rossby waves whose phase velocities are similar to linear Rossby waves on the sphere originally derived by Haurwitz. Modest departures from the Haurwitz formula originate from nonlinear finite amplitude effects and/or the presence of differential rotation. Like supergranules, the initial small-scale motions in our model contain very little vorticity compared to their horizontal divergence, but the resulting Rossby waves are almost all vortical motions. Supergranule kinetic energy could have mainly gone into gravity waves, but we find that most energy inverse cascades to global Rossby waves. Since kinetic energy in supergranules is three or four orders of magnitude larger than that of the observed Rossby waves in the supergranule layer, there is plenty of energy available to drive the inverse-cascade mechanism. Tachocline Rossby waves have previously been shown to play crucial roles in causing seasons of space weather through their nonlinear interactions with global flows and magnetic fields. We briefly discuss how various Rossby waves in the tachocline, convection zone, supergranule layer, and corona can be reconciled in a unified framework.

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10

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.

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11

Rhines, P. B. "Jets and Orography: Idealized Experiments with Tip Jets and Lighthill Blocking." Journal of the Atmospheric Sciences 64, no. 10 (October 1, 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.

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12

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 14, 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.

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13

Hindman, Bradley W., and Rekha Jain. "Radial Trapping of Thermal Rossby Waves within the Convection Zones of Low-mass Stars." Astrophysical Journal 932, no. 1 (June 1, 2022): 68. http://dx.doi.org/10.3847/1538-4357/ac6d64.

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Abstract We explore how thermal Rossby waves propagate within the gravitationally stratified atmosphere of a low-mass star with an outer convective envelope. Under the conditions of slow, rotationally constrained dynamics, we derive a local dispersion relation for atmospheric waves in a fully compressible stratified fluid. This dispersion relation describes the zonal and radial propagation of acoustic waves and gravito-inertial waves. Thermal Rossby waves are just one class of prograde-propagating gravito-inertial wave that manifests when the buoyancy frequency is small compared to the rotation rate of the star. From this dispersion relation, we identify the radii at which waves naturally reflect and demonstrate how thermal Rossby waves can be trapped radially in a waveguide that permits free propagation in the longitudinal direction. We explore this trapping further by presenting analytic solutions for thermal Rossby waves within an isentropically stratified atmosphere that models a zone of efficient convective heat transport. We find that, within such an atmosphere, waves of short zonal wavelength have a wave cavity that is radially thin and confined within the outer reaches of the convection zone near the star’s equator. The same behavior is evinced by the thermal Rossby waves that appear at convective onset in numerical simulations of convection within rotating spheres. Finally, we suggest that stable thermal Rossby waves could exist in the lower portion of the Sun’s convection zone, despite that region’s unstable stratification. For long wavelengths, the Sun’s rotation rate is sufficiently rapid to stabilize convective motions, and the resulting overstable convective modes are identical to thermal Rossby waves.

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14

Waidele, M., and Junwei Zhao. "Observed Power and Frequency Variations of Solar Rossby Waves with Solar Cycles." Astrophysical Journal Letters 954, no. 1 (September 1, 2023): L26. http://dx.doi.org/10.3847/2041-8213/acefd0.

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Abstract Several recent studies utilizing different helioseismic methods have confirmed the presence of large-scale vorticity waves known as solar Rossby waves within the Sun. Rossby waves are distinct from acoustic waves, typically with longer periods and lifetimes, and their general properties, even if only measured at the surface, may be used to infer properties of the deeper convection zone, such as the turbulent viscosity and entropy gradients that are otherwise difficult to observe. In this study, we utilize 12 yr of inverted subsurface velocity fields derived from the Solar Dynamics Observatory/Helioseismic and Magnetic Imager’s time–distance and ring-diagram pipelines to investigate the properties of the solar equatorial Rossby waves. By covering the maximum and the decline phases of Solar Cycle 24, these data sets enable a systematic analysis of any potential cycle dependence of these waves. Our analysis provides evidence of a correlation between the average power of equatorial Rossby waves and the solar cycle, with stronger Rossby waves during the solar maximum and weaker waves during the minimum. Our result also shows that the frequency of the Rossby waves is lower during the magnetic active years, implying a larger retrograde drift relative to the solar rotation. Although the underlying mechanism that enhances the Rossby wave power and lowers its frequency during the cycle maximum is not immediately known, this observation has the potential to provide new insights into the interaction of large-scale flows with the solar cycle.

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15

Schecter, David A., and Michael T. Montgomery. "Waves in a Cloudy Vortex." Journal of the Atmospheric Sciences 64, no. 2 (February 1, 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.

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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 26, 2007): 581–85. http://dx.doi.org/10.1127/0941-2948/2007/0239.

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18

Pinault, Jean-Louis. "A Review of the Role of the Oceanic Rossby Waves in Climate Variability." Journal of Marine Science and Engineering 10, no. 4 (April 2, 2022): 493. http://dx.doi.org/10.3390/jmse10040493.

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In this paper, the role of oceanic Rossby waves in climate variability is reviewed, as well as their dynamics in tropical oceans and at mid-latitudes. For tropical oceans, both the interactions between equatorial Rossby and Kelvin waves, and off-equatorial Rossby waves are privileged. The difference in the size of the basins induces disparities both in the forcing modes and in the dynamics of the tropical waves, which form a single quasi-stationary wave system. For Rossby waves at mid-latitudes, a wide range of periods is considered, varying from a few days to several million years when very-long-period Rossby waves winding around the subtropical gyres are hypothesized. This review focuses on the resonant forcing of Rossby waves that seems ubiquitous: the quasi-geostrophic adjustment of the oceans favors natural periods close to the forcing period, while those far from it are damped because of friction. Prospective work concentrates on the resonant forcing of dynamical systems in subharmonic modes. According to this new concept, the development of ENSO depends on its date of occurrence. Opportunities arise to shed new light on open issues such as the Middle Pleistocene transition.

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19

Roundy, Paul. "Equatorial Rossby waves and their impacts on monsoon region deep convection." MAUSAM 74, no. 2 (March 29, 2023): 267–72. http://dx.doi.org/10.54302/mausam.v74i2.5992.

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Convectively coupled equatorial Rossby waves are the dominant mode of westward-moving subseasonal convection in the tropics. A portion of the variance in these waves has been shown to associate with the tropical intraseasonal oscillation, along with a process often mediated by the extratropical Rossby wave response to tropical convection that yields Rossby waves breaking back into the tropical atmosphere. The potential vorticity anomalies driven by Rossby wave breaking become the equatorial Rossby waves. This work creates an index of planetary scale equatorial Rossby waves and applies the method of seasonally varying regression slope coefficients to diagnose their preferred associations with tropical and extratropical circulation features. Results confirm the already known association between these waves and the extratropical atmosphere and they reveal a pattern of westward-and northward-moving anomalies of tropical convection over the Indian Ocean and Southern Asia during the Northern Hemisphere summer. These patterns are associated with a cycle of suppression and enhancement of convection in which negative anomalies of outgoing longwave radiation are found to be 3-times as likely during the wet than the dry phases of the waves.

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20

Blume, Catherine C., Bradley W. Hindman, and Loren I. Matilsky. "Inertial Waves in a Nonlinear Simulation of the Sun's Convection Zone and Radiative Interior." Astrophysical Journal 966, no. 1 (April 23, 2024): 29. http://dx.doi.org/10.3847/1538-4357/ad27d1.

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Abstract Recent observations of Rossby waves and other more exotic forms of inertial oscillations in the Sun’s convection zone have kindled the hope that such waves might be used as a seismic probe of the Sun's interior. Here, we present a 3D numerical simulation in spherical geometry that models the Sun’s convection zone and upper radiative interior. This model features a wide variety of inertial oscillations, including both sectoral and tesseral equatorial Rossby waves, retrograde mixed inertial modes, prograde thermal Rossby waves, the recently observed high-frequency retrograde (HFR) vorticity modes, and what may be latitudinal overtones of these HFR modes. With this model, we demonstrate that sectoral and tesseral Rossby waves are ubiquitous within the radiative interior as well as within the convection zone. We suggest that there are two different Rossby-wave families in this simulation that live in different wave cavities: one in the radiative interior and one in the convection zone. Finally, we suggest that many of the retrograde inertial waves that appear in the convection zone, including the HFR modes, are in fact all related, being latitudinal overtones that are mixed modes with the prograde thermal Rossby waves.

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21

VANNESTE, JACQUES. "A nonlinear critical layer generated by the interaction of free Rossby waves." Journal of Fluid Mechanics 371 (September 25, 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.

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22

Mizuta, Genta. "Role of the Rossby Waves in the Broadening of an Eastward Jet." Journal of Physical Oceanography 42, no. 3 (March 1, 2012): 476–94. http://dx.doi.org/10.1175/jpo-d-11-070.1.

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Abstract To investigate the effect of the Rossby waves on an eastward jet such as the Kuroshio or Gulf Stream Extensions, a series of numerical experiments is conducted using a primitive equation model. In these experiments, an inflow and an outflow imposed on the western and eastern boundaries drive an unstable narrow jet and a broad interior flow in the western and eastern regions of the model domain, respectively. The barotropic Rossby waves are radiated from the transient region between the two regions. The eddy potential vorticity flux by the waves tends to compensate for the difference in the mean potential vorticity along mean streamlines between both sides of the transient region. Instability of the jet is insufficient for this compensation and weakens the mean potential vorticity gradient too much. Moreover, as the potential vorticity of the outflow is increased, the Rossby waves are intensified in order to compensate for the increase in the difference in the mean potential vorticity. These features strongly suggest that the Rossby waves are substantial in matching a jet with an interior flow. The speed of the waves and properties of eddies in recirculations of the jet are consistent with a two-layer analytic model, which indicates that the Rossby waves are radiated from eddies in recirculations. These eddies as well as the Rossby waves increase in amplitude with the transport of the recirculation near the surface presumably because of mean advection. Therefore, the mean potential vorticity of the interior flow, the intensity of the Rossby waves, and the transport of the recirculation change consistently with one another.

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23

Lewis, Neil T., Nicholas A. Lombardo, Peter L. Read, and Juan M. Lora. "Equatorial Waves and Superrotation in the Stratosphere of a Titan General Circulation Model." Planetary Science Journal 4, no. 8 (August 1, 2023): 149. http://dx.doi.org/10.3847/psj/ace76f.

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

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24

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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25

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 19, 2002): 57–63. http://dx.doi.org/10.1098/rsta.2002.1108.

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26

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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27

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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28

Kloosterziel, R. C., and L. R. M. Maas. "Green’s functions for Rossby waves." Journal of Fluid Mechanics 830 (October 2, 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.

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29

Jury, Mark R. "South Indian Ocean Rossby Waves." Atmosphere-Ocean 56, no. 5 (October 20, 2018): 322–31. http://dx.doi.org/10.1080/07055900.2018.1544882.

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30

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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31

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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32

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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33

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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34

Bénard, P. "Stability of Rossby–Haurwitz waves." Quarterly Journal of the Royal Meteorological Society 146, no. 727 (December 22, 2019): 613–28. http://dx.doi.org/10.1002/qj.3696.

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35

Chen, Xin, Hongwei Yang, Min Guo, and Baoshu Yin. "(2 + 1)-Dimensional Coupled Model for Envelope Rossby Solitary Waves and Its Solutions as well as Chirp Effect." Mathematical Problems in Engineering 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/1378740.

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Using the method of multiple scales and perturbation method, a set of coupled models describing the envelope Rossby solitary waves in (2+1)-dimensional condition are obtained, also can be called coupled NLS (CNLS) equations. Following this, based on trial function method, the solutions of the NLS equation are deduced. Moreover, the modulation instability of coupled envelope Rossby waves is studied. We can find that the stable feature of coupled envelope Rossby waves is decided by the value of S. Finally, learning from the concept of chirp in the optical soliton communication field, we study the chirp effect caused by nonlinearity and dispersion in the propagation of Rossby waves.

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36

Zheng, Cheng, and Edmund Kar-Man Chang. "The Role of Extratropical Background Flow in Modulating the MJO Extratropical Response." Journal of Climate 33, no. 11 (June 1, 2020): 4513–36. http://dx.doi.org/10.1175/jcli-d-19-0708.1.

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AbstractThe Madden–Julian oscillation (MJO) is the dominant mode of tropical intraseasonal variability. Many studies have found that the MJO, which acts as a tropical heating source, can excite Rossby waves that propagate into the midlatitude and modulate midlatitude circulation. The extratropical mean flow can modulate the MJO extratropical response. Rossby waves can grow or decay in different extratropical background flows, and the propagation of the Rossby waves also varies as the background flow acts as a waveguide. In this study, how extratropical mean flow modulates the MJO extratropical response is explored by using a nonlinear baroclinic primitive equation model. MJO-associated heating, as an external forcing of the model, is imposed into scenarios with different extratropical background flows. Different background flow modulates the generation and advection of the vorticity anomalies induced by the MJO, which determines the initial location and strength of the Rossby waves. The midlatitude waveguides can be different as the background flow changes. As the propagation of Rossby waves follows the waveguides, the background flow determines whether the Rossby waves are trapped in the Pacific Ocean region or can propagate to the north and to the east into North America. The experiments also show that the anomalies associated with the Rossby waves can extract energy from the midlatitude jet over the jet exit region and the southern flank of the jet. This further modulates the strength, location, and duration of the MJO extratropical response.

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37

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.

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38

Gavrilov, Milivoj, Lazar Lazic, and Jasmina Djordjevic. "Weather conditions and weather forecast on the planets of the solar system based on the behavior of Rossby waves." Glasnik Srpskog geografskog drustva 90, no. 1 (2010): 135–44. http://dx.doi.org/10.2298/gsgd1001135g.

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Out of all atmospheric processes on the planets of the Solar System, special attention will be devoted here to leading circulation of planetary or global scales, known as Rossby waves. These waves occur in all rotating fluids that have relative movement to the rotation system. Rossby waves exert dominant influence on so-called global weather. Based on the knowledge of some properties of Rossby waves are made approximate analysis of weather conditions on the planets of the Solar System. Also, these considerations can serve as an introduction to weather forecasting on the planet. .

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39

Yin, Xiaojun, Liangui Yang, and Quansheng Liu. "The evolution equation of non-linear waves and its exact solutions by subsidiary ordinary differential equation method." Modern Physics Letters B 34, no. 34 (August 25, 2020): 2050390. http://dx.doi.org/10.1142/s021798492050390x.

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In this work, we investigate the dynamics of the equatorial Rossby waves by including the complete Coriolis force, external source and dissipation. The amplitude evolution of equatorial Rossby waves is described as an extended non-linear mKdV–Burgers equation from a potential vorticity equation and it is unlike the standard mKdV–Burgers equation. Built on the obtained model, the corresponding physical phenomena related to the non-linear Rossby waves are analyzed. Also, the subsidiary ordinary differential equation method is employed to solve the solitary solution of the mKdV equation. By analyzing the solution, we find that the horizontal component of Coriolis parameter works on the amplitude of the Rossby waves. Meanwhile, we use the Adomian decomposition method to obtain the approximate soliton solution of the model.

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40

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 1, 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.

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41

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.

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42

Rydbeck, Adam V., Tommy G. Jensen, and Matthew R. Igel. "Idealized Modeling of the Atmospheric Boundary Layer Response to SST Forcing in the Western Indian Ocean." Journal of the Atmospheric Sciences 76, no. 7 (June 26, 2019): 2023–42. http://dx.doi.org/10.1175/jas-d-18-0303.1.

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Abstract The atmospheric response to sea surface temperature (SST) variations forced by oceanic downwelling equatorial Rossby waves is investigated using an idealized convection-resolving model. Downwelling equatorial Rossby waves sharpen SST gradients in the western Indian Ocean. Changes in SST cause the atmosphere to hydrostatically adjust, subsequently modulating the low-level wind field. In an idealized cloud model, surface wind speeds, surface moisture fluxes, and low-level precipitable water maximize near regions of strongest SST gradients, not necessarily in regions of warmest SST. Simulations utilizing the steepened SST gradient representative of periods with oceanic downwelling equatorial Rossby waves show enhanced patterns of surface convergence and precipitation that are linked to a strengthened zonally overturning circulation. During these conditions, convection is highly organized, clustering near the maximum SST gradient and ascending branch of the SST-induced overturning circulation. When the SST gradient is reduced, as occurs during periods of weak or absent oceanic equatorial Rossby waves, convection is much less organized and total rainfall is decreased. This demonstrates the previously observed upscale organization of convection and rainfall associated with oceanic downwelling equatorial Rossby waves in the western Indian Ocean. These results suggest that the enhancement of surface fluxes that results from a steepening of the SST gradient is the leading mechanism by which oceanic equatorial Rossby waves prime the atmospheric boundary layer for rapid convective development.

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43

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 5, 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.

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44

Vanneste, Jacques, and Francois Vial. "Nonlinear wave propagation on a sphere: Interaction between Rossby waves and gravity waves; stability of the Rossby waves." Geophysical & Astrophysical Fluid Dynamics 76, no. 1-4 (November 1994): 121–44. http://dx.doi.org/10.1080/03091929408203662.

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45

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 25, 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.

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46

Zhang, Jiaqi, Liangui Yang, and Ruigang Zhang. "Solitary waves under curved topography and beta approximation." Modern Physics Letters B 34, no. 17 (April 1, 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.

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47

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 1, 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.

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48

Li, Yaokun. "On the Energy Dispersion of Magnetic Rossby Waves." Astrophysical Journal 934, no. 1 (July 1, 2022): 40. http://dx.doi.org/10.3847/1538-4357/ac778d.

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Abstract The energy dispersion of magnetic Rossby waves has been investigated by applying the two-dimensional incompressible magnetohydrodynamic (MHD) equations in both uniform basic flow and basic magnetic field. The dispersion relation suggests that the magnetic Rossby waves can be divided into fast- and slow-propagating modes, respectively. The fast-propagating mode propagates eastward and is similar to the fast Alfvén waves. The energy dispersion speed is faster than the phase speed, which means the perturbation energy can lead the perturbations themselves to arrive downstream. The slow-propagating waves with smaller (larger) horizontal scales are similar to those of the slow Alfvén waves (Rossby waves). The zonal group velocity is slower than the zonal phase speed for the slow-propagating magnetic Rossby waves. For the slow-propagating waves that propagate eastward, this means that the perturbation energy may trigger new perturbations that are located upstream of the perturbations themselves. The group velocity vector is basically same as (opposite of) the wavevector for the fast-propagating (slow-propagating) magnetic Rossby waves that propagate eastward. The endpoints of the group velocity vectors and the wavevector multiplying a factor are located on a cycle in the wavenumber space. Due to the uniform basic flow and the uniform basic magnetic field, the energy dispersion paths (called rays) are straight lines. Along the straight-line rays, the wave action, wave energy, and amplitude keep their initial values, and the wave neither develops nor decays.

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49

Yang, Hongwei, Shanshan Jin, and Baoshu Yin. "Benjamin-Ono-Burgers-MKdV Equation for Algebraic Rossby Solitary Waves in Stratified Fluids and Conservation Laws." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/175841.

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In the paper, by using multiple-scale method, the Benjamin-Ono-Burgers-MKdV (BO-B-MKdV) equation is obtained which governs algebraic Rossby solitary waves in stratified fluids. This equation is first derived for Rossby waves. By analysis and calculation, some conservation laws are derived from the BO-B-MKdV equation without dissipation. The results show that the mass, momentum, energy, and velocity of the center of gravity of algebraic Rossby waves are conserved and the presence of a small dissipation destroys these conservations.

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50

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 29, 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.

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