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NASA NTRS1977

On the theory of solitary Rossby waves

The evolution of long, finite amplitude Rossby waves in a horizontally sheared zonal current is studied. The wave evolution is described by the Korteweg-de Vries equation or the modified Korteweg-de Vries equation depending on the atmospheric stratification. In either case, the cross-stream modal structure of these waves is given by the long-wave limit of the neutral eigensolutions of the barotropic stability equation. Both non-singular and singular eigensolutions are considered and the appropriate analysis is developed to yield a uniformly valid description of the motion in the critical-layer region where the wave speed matches the flow velocity. The analysis demonstrates that coherent, propagating, eddy structures can exist in stable shear flows and that these eddies have peculiar interaction properties quite distinct from the traditional views of turbulent motion.

Redekopp, L. G.↗
NASA NTRS1988

Nonlinear instability of a forced baroclinic Rossby wave

The nonlinear instability of forced baroclinic Rossby waves to finite-amplitude perturbations was investigated using a simple two-layer quasi-geostrophic weakly nonlinear model and a low-order spectral model, developed for this purpose. The results were applied to a study of the interaction of planetary-scale stationary eddies with synoptic-scale transient eddies. A comparison of the energetics of the weakly nonlinear solution with that seen in observational analysis and in GCM experiments indicate three basic properties of the interaction between the two types of eddies: (1) eddy available potential energy is transferred from the planetary-scale stationary eddies to the synoptic-scale transient eddies, (2) eddy kinetic energy is transferred in the opposite direction, and (3) the eddy available potential energy transfer dominates the transfer of eddy kinetic energy. It is concluded that the simple weakly nonlinear model used in these studies does indeed capture much of the fundamental behavior of wave-wave interactions seen in the atmosphere.

Feldstein, Steven B.↗
NASA NTRS2003

The Effect of Surface Topography on the Nonlinear Dynamics of Rossby Waves

Boussinesq convection in rotating systems attracts a sustained attention of the fluid dynamics community, because it has intricate non-linear dynamics (Cross & Hohenberg 1993) and plays an important role in geophysical and astrophysical applications, such as the motion of the liquid outer core of Earth, the Red Spot in Jupiter, the giant cells in the Sun etc. (Alridge et al. 1990). A fundamental distinction between the real geo- and astrophysical problems and the idealized laboratory studies is that natural systems are inhomogeneous (Alridge et al. 1990). Heterogeneities modulate the flow and influence significantly the dynamics of convective patterns (Alridge et al. 1990; Hide 1971). The effect of modulations on pattern formation and transition to turbulence in Boussinesq convection is far from being completely understood (Cross & Hohenberg 1993; Aranson & Kramer 2002). It is generally accepted that in the liquid outer core of the Earth the transport of the angular momentum and internal heat occurs via thermal Rossby waves (Zhang et al. 2001; Kuang & Bloxham 1999). These waves been visualized in laboratory experiments in rotating liquid-filled spheres and concentric spherical shells (Zhang et al. 2001; Kuang & Bloxham 1999). The basic dynamical features of Rossby waves have been reproduced in a cylindrical annulus, a system much simpler than the spherical ones (Busse & Or 1986; Or & Busse 1987). For convection in a cylindrical annulus, the fluid motion is two-dimensional, and gravity is replaced by a centrifugal force, (Busse & Or 1986; Or & Busse 1987). Hide (1971) has suggested that the momentum and heat transport in the core might be influenced significantly by so-called bumps, which are heterogeneities on the mantle-core boundary. To model the effect of surface topography on the transport of momentum and energy in the liquid outer core of the Earth, Bell & Soward (1996), Herrmann & Busse (1998) and Westerburg & Busse (2001) have studied the nonlinear dynamics of thermal Rossby waves in a cylindrical annulus with azimuthally modulated height.

Abarzhi, S. I.↗
NASA NTRS1991

Rossby waves in a fluctuating zonal mean flow

The effects of the zonal mean wind variability on the energy propagation of a stationary Rossby wave in a barotropic nondivergent atmosphere are studied. It is shown that the random nature of the zonal wind fluctuations do not allow Rossby wave energy to propagate from its energy source. The mechanism for this effect is strongly dependent on the spatial resolution at which the zonal mean flow is assumed to be known. Some speculations are offered on the relation between this mechanism and the systematic error of some low-resolution climate models.

Pandolfo, Lionel↗
NASA NTRS2007

Solar Rossby Wave 'Hills' Identified As Supergranules

We explore the nature of 'hills' observed on the solar surface which had previously been attributed to Rossby waves. We investigate the sol ar hills phenomenon by analyzing the output from a synthetic model ba sed solely on the observed solar photospheric convection spectrum. We show that the characteristics of these hills can be explained by the corrugation of the surface produced by the radial flows of the conve ction. The hills in our simulations are dominated by supergranules, a well-known component of solar convection. Rossby waves have been predicted to exist within the Sun and may play an important role in the d ynamics of the solar interior, including the Sun's differential rotat ion and magnetic dynamo. Our study suggests, however, that the hills observed at the solar limb do not confirm the existence of solar Ross by waves.

Williams, P. E.↗
NASA NTRS1990

Reflection of annual Rossby waves at the maritime western boundary of the tropical Pacific

Results are presented of an examination of altimetric sea level time series from the first 17 months of the Geosat Geodetic Mission. The examination provides the first direct evidence of the Rossby wave reflection process operating in both hemispheres at the maritime western boundary of the tropical Pacific, in regard to annual Rossby activity. It is demonstrated that the Philippines in the Northern Hemisphere and the Solomon, the Bismarck, and the New Guinea islands in the Southern Hemisphere reflected the incident baroclinic Rossby wave activity of the one-year period, generating equatorial Kelvin wave activity that emanated from the maritime western boundary of the tropical Pacific, conducting the annual baroclinic signal along the equator into the eastern equatorial Pacific.

White, Warren B.↗
NASA NTRS1982

A note on the limits of Rossby wave amplitudes

Quasi-geostrophic dynamics, as usually formulated, centers on the conservation of pseudopotential vorticity (PV) on isobaric surfaces. The present study has the objective to investigate some simple constraints which conservation of PV imposes on internal Rossby waves. Attention is given to some of the limitations that conservation of potential vorticity imposes on the dynamics of the stratosphere. Another possible constraint imposed by hydrodynamic stability is also discussed. The quantitative limitations these constraints put on the amplitudes of internal Rossby waves are assessed and compared with observations of the lower stratosphere.

Lindzen, R. S.↗
NASA NTRS1984

An observational study of large-scale atmospheric Rossby waves during FGGE

Analyzed global data from the European Center for Medium Range Weather Forecasts for the FGGE year are projected onto Hough functions at each synoptic time and the time series filtered to retain all westward propagating components on time scales less than seasonal. The evolution of Hough mode phase agrees closely with Rossby wave theory whenever the amplitudes are not small. The evolution of the wave amplitude is described as irregular vacillation. The first three zonal and meridional wavenumbers are studied. The total Rossby wave field can be as large as 130 m and can potentially explain a significant part of observed, persistent anomalies.

Lindzen, R. S.↗
NASA NTRS2012

Discovery Of A Rossby Wave In Jupiter's South Equatorial Region

A detailed study of the chevron-shaped dark spots on the strong southern equatorial wind jet near 7.5 deg S planetographic latitude shows variations in velocity with longitude and time. The chevrons move with velocities near the maximum wind jet velocity of approx.140 m/s, as deduced by the history of velocities at this latitude and the magnitude of the symmetric wind jet near 7 deg N latitude. Their repetitive nature is consistent with an inertia-gravity wave (n = 75-100) with phase speed up to 25 m/s, relative to the local flow, but the identity of this wave mode is not well constrained. However, high spatial resolution movies from Cassini images show that the chevrons oscillate in latitude with a approx.7-day period. This oscillating motion has a wavelength of approx.20 deg and a speed of approx.100 m/s, following a pattern similar to that seen in the Rossby wave plumes of the North Equatorial Zone, and possibly reinforced by it, though they are not perfectly in phase. The transient anticyclonic South Equatorial Disturbance (SED) may be a similar wave feature, but moves at slower velocity. All data show chevron latitude variability, but it is unclear if this Rossby wave is present during other epochs, without time series movies that fully delineate it. In the presence of multiple wave modes, the difference in dominant cloud appearance between 7 deg N and 7.5 deg S may be due to the presence of the Great Red Spot, either through changes in stratification and stability or by acting as a wave boundary.

Simon-Miller, Amy A.↗
NASA NTRS1984

The growth, propagation and decay of global scale Rossby waves during FGGE

A portrait of the evolution of global scale Rossby waves for the FGGE year is presented. Emphasis is placed on the temporal evolution of the amplitude and phase of Hough mode projections, rather than on characteristics of the time spectra of these waves. On the basis of previous work, it was felt that it would be adequate to consider the 500 mb level in isolation from the others, and that the Hough functions (which are vector functions of the horizontal wind components and the height field) were good approximations to the "true' eigenfunctions. Thus, the first steps of the analysis consisted of projecting the 500 mb height and wind data (obtained from the ECMWF analyses) onto Hough functions for each synoptic time. The seasonal cycle and time mean were removed separately for each season, and all remaining eastward propagating components removed on a seasonal basis; all remaining westward propagating components were retained.

Lindzen, R. S.↗
NASA NTRS1980

Solitary Rossby waves in the presence of vertical shear

The effects of vertical shear on regular neutral mode Rossby solitons driven by a horizontal shear are investigated in light of the proposition that certain features in the Jupiter atmosphere may be explained by solitary Rossby waves. Consideration is given to a two-layer quasi-geostrophic model in which the motion in each layer consists of a different zonal shear flow, with vertical shear concentrated at the interface between the layers. In the case of a strong vertical shear, it is found that only a very restricted set of flows will admit Rossby neutral model solitons. For the more realistic case of a weak vertical shear, results indicate similar, but latitudinally shifted, wave patterns in each layer. It is noted that no such slant has yet been detected in the Great Red Spot.

Weidman, P. D.↗
NASA NTRS2010

Warm Season Subseasonal Variability and Climate Extremes in the Northern Hemisphere: The Role of Stationary Rossby Waves

This study examines the nature of boreal summer subseasonal atmospheric variability based on the new NASA Modern-Era Retrospective analysis for Research and Applications (MERRA) for the period 1979-2010. An analysis of the June, July and August subseasonal 250hPa v-wind anomalies shows distinct Rossby wave-like structures that appear to be guided by the mean jets. On monthly subseasonal time scales, the leading waves (the first 10 rotated empirical orthogonal functions or REOFs of the 250hPa v-wind) explain about 50% of the Northern Hemisphere vwind variability, and account for more than 30% (60%) of the precipitation (surface temperature) variability over a number of regions of the northern middle and high latitudes, including the U.S. northern Great Plains, parts of Canada, Europe, and Russia. The first REOF in particular, consists of a Rossby wave that extends across northern Eurasia where it is a dominant contributor to monthly surface temperature and precipitation variability, and played an important role in the 2003 European and 2010 Russian heat waves. While primarily subseasonal in nature, the Rossby waves can at times have a substantial seasonal mean component. This is exemplified by REOF 4 which played a major role in the development of the most intense anomalies of the U.S. 1988 drought (during June) and the 1993 flooding (during July), though differed in the latter event by also making an important contribution to the seasonal mean anomalies. A stationary wave model (SWM) is used to reproduce some of the basic features of the observed waves and provide insight into the nature of the forcing. In particular, the responses to a set of idealized forcing functions are used to map the optimal forcing patterns of the leading waves. Also, experiments to reproduce the observed waves with the SWM using MERRA-based estimates of the forcing indicate that the wave forcing is dominated by sub-monthly vorticity transients.

Schubert, Siegfried↗
NASA NTRS2014

The East Atlantic - West Russia Teleconnection in the North Atlantic: Climate Impact and Relation to Rossby Wave Propagation

Large-scale winter teleconnection of the East Atlantic - West Russia (EA-WR) over the Atlantic and surrounding regions is examined in order to quantify its impacts on temperature and precipitation and identify the physical mechanisms responsible for its existence. A rotated empirical orthogonal function (REOF) analysis of the upper-tropospheric monthly height field captures successfully the EA-WR pattern and its interannual variation, with the North Atlantic Oscillation as the first mode. EA-WRs climate impact extends from eastern North America to Eurasia. The positive (negative) EA-WR produces positive (negative) temperature anomalies over the eastern US, western Europe and Russia east of Caspian Sea, with negative (positive) anomalies over eastern Canada, eastern Europe including Ural Mountains and the Middle East. These anomalies are largely explained by lower-tropospheric temperature advections. Positive (negative) precipitation anomalies are found over the mid-latitude Atlantic and central Russia around 60E, where lower-level cyclonic (anticyclonic) circulation anomaly is dominant. The eastern Canada and the western Europe are characterized by negative (positive) precipitation anomalies.The EA-WR is found to be closely associated with Rossby wave propagation. Wave activity fluxes show that it is strongly tied to large-scale stationary waves. Furthermore, a stationary wave model (SWM) forced with vorticity transients in the mid-latitude Atlantic (approximately 40N) or diabatic heat source over the subtropical Atlantic near the Caribbean Sea produces well-organized EA-WR-like wave patterns, respectively. Sensitivity tests with the SWM indicate improvement in the simulation of the EA-WR when the mean state is modified to have a positive NAO component that enhances upper-level westerlies between 40-60N.

EA/WR↗
NASA NTRS1994

Transport out of the lower stratospheric Arctic vortex by Rossby wave breaking

The fine-scale structure in lower stratospheric tracer transport during the period of the two Arctic Airborne Stratospheric Expeditions (January and February 1989; December 1991 to March 1992) is investigated using contour advection with surgery calculations. These calculations show that Rossby wave breaking is an ongoing occurrence during these periods and that air is ejected from the polar vortex in the form of long filamentary structures. There is good qualitative agreement between these filaments and measurements of chemical tracers taken aboard the NASA ER-2 aircraft. The ejected air generally remains filamentary and is stretched and mixed with midlatitude air as it is wrapped around the vortex. This process transfers vortex air into midlatitudes and also produces a narrow region of fine-scale filaments surrounding the polar vortex. Among other things, this makes it difficult to define a vortex edge. The calculations also show that strong stirring can occur inside as well as outside the vortex.

Waugh, D. W.↗
NASA NTRS1993

Global normal-mode Rossby waves observed in stratospheric ozone data

Westward-propagating Rossby normal-mode planetary waves are documented in stratospheric ozone data using Solar Backscatter Ultraviolet (SBUV) satellite measurements. These modes are evidenced by enhanced spectral power and near-global coherence for westward-traveling zonal wave 1 oscillations with periods of 5-10 days. The ozone waves have maxima in high latitudes of the middle stratosphere (due to transport) and over midlatitudes in the upper stratosphere (due to photochemistry). These modes are nearly continuous throughout the eight years of SBUV observations, with maximum global coherence during the equinoxes. The upper-stratospheric waves are symmetric (in phase) between hemispheres, even for modes previously identified as antisymmetric in geopotential height. This behavior is due to differing wave vertical structure in each hemisphere; the planetary temperature waves are nearly in phase in the upper stratosphere, even though the height waves are out of phase. The observed ozone waves are furthermore compared to calculations based on linear wave transport and photochemistry, incorporating derived wind and temperature fields. Good agreement is found, showing that normal modes provide an idealized context to study the linear wave behavior of trace constituents in the real atmosphere.

Randel, William J.↗