Planetary (Rossby) waves and inertia–gravity (Poincaré) waves in a barotropic ocean over a sphere

2013 ◽  
Vol 726 ◽  
pp. 123-136 ◽  
Author(s):  
Nathan Paldor ◽  
Yair De-Leon ◽  
Ofer Shamir
Keyword(s):  
Gravity Waves ◽  
Rossby Waves ◽  
Phase Speed ◽  
Mode Number ◽  
Rotating Sphere ◽  
Zonal Wavenumber ◽  
Speed Of Gravity ◽  
Meridional Mode ◽  
Poincare Waves ◽  
The Waves

AbstractThe construction of approximate Schrödinger eigenvalue equations for planetary (Rossby) waves and for inertia–gravity (Poincaré) waves on an ocean-covered rotating sphere yields highly accurate estimates of the phase speeds and meridional variation of these waves. The results are applicable to fast rotating spheres such as Earth where the speed of barotropic gravity waves is smaller than twice the tangential speed on the equator of the rotating sphere. The implication of these new results is that the phase speed of Rossby waves in a barotropic ocean that covers an Earth-like planet is independent of the speed of gravity waves for sufficiently large zonal wavenumber and (meridional) mode number. For Poincaré waves our results demonstrate that the dispersion relation is linear, (so the waves are non-dispersive and the phase speed is independent of the wavenumber), except when the zonal wavenumber and the (meridional) mode number are both near 1.

Atmospheric Subseasonal Variability and Circulation Regimes: Spectra, Trends, and Uncertainties

2020 ◽  
Vol 33 (21) ◽  
pp. 9375-9390
Author(s):  
Nedjeljka Žagar ◽  
Žiga Zaplotnik ◽  
Khalil Karami
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Rossby Waves ◽  
Wave Activity ◽  
Subseasonal Variability ◽  
Zonal Wavenumber ◽  
Equatorial Wave ◽  
Wave Patterns ◽  
Meridional Mode ◽  
The One

AbstractThe globally integrated subseasonal variability associated with the two main atmospheric circulation regimes, the balanced (or Rossby) and unbalanced (or inertia–gravity) regimes, is evaluated for the four reanalysis datasets: ERA-Interim, JRA-55, MERRA, and ERA5. The results quantify amplitudes and trends in midlatitude traveling and quasi-stationary Rossby wave patterns as well as in the equatorial wave activity across scales. A statistically significant reduction of subseasonal variability is found in Rossby waves with zonal wavenumber k = 6 along with an increase in variability in wavenumbers k = 3–5 in the summer seasons of both hemispheres. The four reanalyses also agree regarding increased variability in the large-scale Kelvin waves, mixed Rossby–gravity waves, and westward-propagating inertio-gravity waves with the lowest meridional mode. The amplitude and sign of trends in inertia–gravity modes with smaller zonal scales and greater meridional modes differ between the ERA-Interim and JRA-55 datasets on the one hand and the ERA5 and MERRA data on the other. An increased variability in the ERA-Interim and JRA-55 accounts for positive trends in their total subseasonal variability.

scholarly journals Equatorial Waves in Opposite QBO Phases

2011 ◽  
Vol 68 (4) ◽  
pp. 839-862 ◽  
Author(s):  
Gui-Ying Yang ◽  
Brian J. Hoskins ◽  
Julia M. Slingo
Keyword(s):  
Group Velocity ◽  
Lower Stratosphere ◽  
Phase Speed ◽  
Kelvin Waves ◽  
Western Hemisphere ◽  
Equatorial Waves ◽  
Vertical Wavelength ◽  
Quasi Biennial Oscillation ◽  
Zonal Wavenumber ◽  
The Waves

Abstract A methodology for identifying equatorial waves is used to analyze the multilevel 40-yr ECMWF Re-Analysis (ERA-40) data for two different years (1992 and 1993) to investigate the behavior of the equatorial waves under opposite phases of the quasi-biennial oscillation (QBO). A comprehensive view of 3D structures and of zonal and vertical propagation of equatorial Kelvin, westward-moving mixed Rossby–gravity (WMRG), and n = 1 Rossby (R1) waves in different QBO phases is presented. Consistent with expectation based on theory, upward-propagating Kelvin waves occur more frequently during the easterly QBO phase than during the westerly QBO phase. However, the westward-moving WMRG and R1 waves show the opposite behavior. The presence of vertically propagating equatorial waves in the stratosphere also depends on the upper tropospheric winds and tropospheric forcing. Typical propagation parameters such as the zonal wavenumber, zonal phase speed, period, vertical wavelength, and vertical group velocity are found. In general, waves in the lower stratosphere have a smaller zonal wavenumber, shorter period, faster phase speed, and shorter vertical wavelength than those in the upper troposphere. All of the waves in the lower stratosphere show an upward group velocity and downward phase speed. When the phase of the QBO is not favorable for waves to propagate, their phase speed in the lower stratosphere is larger and their period is shorter than in the favorable phase, suggesting Doppler shifting by the ambient flow and a filtering of the slow waves. Tropospheric WMRG and R1 waves in the Western Hemisphere also show upward phase speed and downward group velocity, with an indication of their forcing from middle latitudes. Although the waves observed in the lower stratosphere are dominated by “free” waves, there is evidence of some connection with previous tropical convection in the favorable year for the Kelvin waves in the warm water hemisphere and WMRG and R1 waves in the Western Hemisphere, which is suggestive of the importance of convective forcing for the existence of propagating coupled Kelvin waves and midlatitude forcing for the existence of coupled WMRG and R1 waves.

scholarly journals Evidence for tropospheric wind shear excitation of high-phase-speed gravity waves reaching the mesosphere using the ray-tracing technique

2015 ◽  
Vol 15 (5) ◽  
pp. 2709-2721 ◽  
Author(s):  
M. Pramitha ◽  
M. Venkat Ratnam ◽  
A. Taori ◽  
B. V. Krishna Murthy ◽  
D. Pallamraju ◽  
...  
Keyword(s):  
Ray Tracing ◽  
Gravity Waves ◽  
High Frequency ◽  
Phase Speed ◽  
Horizontal Wind ◽  
Climatological Model ◽  
Background Temperature ◽  
The Waves ◽  
High Phase ◽  
Mf Radar

Abstract. Sources and propagation characteristics of high-frequency gravity waves observed in the mesosphere using airglow emissions from Gadanki (13.5° N, 79.2° E) and Hyderabad (17.5° N, 78.5° E) are investigated using reverse ray tracing. Wave amplitudes are also traced back, including both radiative and diffusive damping. The ray tracing is performed using background temperature and wind data obtained from the MSISE-90 and HWM-07 models, respectively. For the Gadanki region, the suitability of these models is tested. Further, a climatological model of the background atmosphere for the Gadanki region has been developed using nearly 30 years of observations available from a variety of ground-based (MST radar, radiosondes, MF radar) and rocket- and satellite-borne measurements. ERA-Interim products are utilized for constructing background parameters corresponding to the meteorological conditions of the observations. With the reverse ray-tracing method, the source locations for nine wave events could be identified to be in the upper troposphere, whereas for five other events the waves terminated in the mesosphere itself. Uncertainty in locating the terminal points of wave events in the horizontal direction is estimated to be within 50–100 km and 150–300 km for Gadanki and Hyderabad wave events, respectively. This uncertainty arises mainly due to non-consideration of the day-to-day variability in the tidal amplitudes. Prevailing conditions at the terminal points for each of the 14 events are provided. As no convection in and around the terminal points is noticed, convection is unlikely to be the source. Interestingly, large (~9 m s−1km−1) vertical shears in the horizontal wind are noticed near the ray terminal points (at 10–12 km altitude) and are thus identified to be the source for generating the observed high-phase-speed, high-frequency gravity waves.

scholarly journals The Superposition of Eastward and Westward Rossby Waves in Response to Localized Forcing

2016 ◽  
Vol 29 (20) ◽  
pp. 7547-7557 ◽  
Author(s):  
Jeffrey Shaman ◽  
Eli Tziperman
Keyword(s):  
El Niño ◽  
Rossby Waves ◽  
El Nino ◽  
Phase Speed ◽  
Planetary Waves ◽  
Stationary Waves ◽  
Zonal Wavenumber ◽  
Wide Range ◽  
Localized Forcing ◽  
Diabatic Forcing

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.

scholarly journals Investigation of sources of gravity waves observed in the Brazilian Equatorial region on 08 April 2005

2019 ◽  
Author(s):  
Oluwakemi Dare-Idowu ◽  
Igo Paulino ◽  
Cosme A. O. B. Figueiredo ◽  
Amauri F. Medeiros ◽  
Ricardo A. Buriti ◽  
...  
Keyword(s):  
Ray Tracing ◽  
Gravity Waves ◽  
Spectral Characteristics ◽  
Phase Speed ◽  
Radar Data ◽  
Equatorial Region ◽  
Inter Tropical Convergence Zone ◽  
Wind Profiles ◽  
Ray Path ◽  
The Waves

Abstract. On 08 April 2005, a strong gravity wave activity (more than 3 hours) was observed in São João do Cariri (7.4° S, 36.5° W). These waves propagated to the southeast and presented different spectral characteristics (wavelength, period and phase speed). Using OH airglow images, the parameters of 5 observed gravity waves were calculated; the wavelengths ranged from ~ 90 to 150 km, the periods from ~ 26 to 67 min and the phase speeds from 32 to 71 m/s. A reserve ray-tracing analysis was performed to investigate the likely sources of these waves. The ray-tracing database was composed of temperature profiles from NRLMSISE-00 model and SABER measurements and wind profiles from HWM-14 model and meteor radar data. According to the ray path, the likely source of these gravity waves was the Inter Tropical Convergence Zone with intense convective processes taking place in the northern part of the observatory. Also, the observed preferential propagation direction of the waves to the southeast could be explained using blocking diagrams, i.e., due to the wind filtering process.

Modification of Long Equatorial Rossby Wave Phase Speeds by Zonal Currents

2011 ◽  
Vol 41 (6) ◽  
pp. 1077-1101 ◽  
Author(s):  
Theodore S. Durland ◽  
Roger M. Samelson ◽  
Dudley B. Chelton ◽  
Roland A. de Szoeke
Keyword(s):  
Rossby Wave ◽  
Rossby Waves ◽  
Current System ◽  
Phase Speed ◽  
Meridional Velocity ◽  
Zonal Velocity ◽  
The Mean ◽  
Meridional Mode ◽  
Mean Current ◽  
Pv Gradient

Abstract Previously unaddressed aspects of how equatorial currents affect long Rossby wave phase speeds are investigated using solutions of the shallow-water equations linearized about quasi-realistic currents. Modification of the background potential vorticity (PV) gradient by curvature in the narrow equatorial currents is shown to play a role comparable to the Doppler shift emphasized by previous authors. The important variables are the meridional projections of mean-current features onto relevant aspects of the wave field. As previously shown, Doppler shifting of long Rossby waves is determined by the projection of the mean currents onto the wave’s squared zonal-velocity and pressure fields. PV-gradient modification matters only to the extent that it projects onto the wave field’s squared meridional velocity. Because the zeros of an equatorial wave’s meridional velocity are staggered relative to those of the zonal velocity and pressure, and because the meridional scales of the equatorial currents are similar to those of the low-mode Rossby waves, different parts of the current system dominate the advective and PV-gradient modification effects on a single mode. Since the equatorial symmetry of classical equatorial waves alternates between symmetric and antisymmetric with increasing meridional mode number, the currents produce opposite effects on adjacent modes. Meridional mode 1 is slowed primarily by a combination of eastward advection by the Equatorial Undercurrent (EUC) and the PV-gradient decrease at the peaks of the South Equatorial Current (SEC). The mode-2 phase speed, in contrast, is increased primarily by a combination of westward advection by the SEC and the PV-gradient increase at the core of the EUC. Perturbation solutions are carried to second order in ε, the Rossby number of the mean current, and it is shown that this is necessary to capture the full effect of quasi-realistic current systems, which are asymmetric about the equator. Equatorially symmetric components of the current system affect the phase speed at O(ε), but antisymmetric components of the currents and distortions of the wave structures by the currents do not influence the phase speed until O(ε2).

Interactions of Gravity Waves Generated by a Moving Source With the Shelf: Laboratory Experiment

2003 ◽  
Author(s):  
Yakov Afanasyev ◽  
Vasily Korabel
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Laboratory Experiments ◽  
Phase Speed ◽  
Critical Value ◽  
Total Reflection ◽  
Supercritical Regime ◽  
Subcritical Regime ◽  
Moving Storm ◽  
The Waves

Rapidly moving storm crossing the shelf from shallow water to deep water can generate tsunami-like waves which can cause local flooding and damage to docks when the waves hit the coast. We report on laboratory experiments to examine the reflection of waves generated by a moving disturbance from the shelf. Experiments are performed in a two-layer fluid consisting of a layer of oil based ferrofluid lying on top of a layer of water with step bottom. The disturbance is generated by a permanent magnet moving above the surface of ferrofluid. Digital images of the flow are analyzed to obtain the evolution of the wave field. The experimental flows demonstrate two distinct regimes, namely subcritical when the speed of the magnet is less than the phase speed of the wave, and supercritical when the speed of the magnet is greater than the phase speed of the wave. In subcritical regime the disturbance is localized and its size is determined by the spatial extent of the forcing. In supercritical regime the waves form two beams extending at “Mach angle” with respect to the direction of motion. Oblique wave incident on the shelf can experience total reflection if the angle between the wave front and the shelf is greater than a critical value.

scholarly journals Mesospheric gravity waves observed near equatorial and low–middle latitude stations: wave characteristics and reverse ray tracing results

2006 ◽  
Vol 24 (12) ◽  
pp. 3229-3240 ◽  
Author(s):  
C. M. Wrasse ◽  
T. Nakamura ◽  
H. Takahashi ◽  
A. F. Medeiros ◽  
M. J. Taylor ◽  
...  
Keyword(s):  
Ray Tracing ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Source Region ◽  
Phase Speed ◽  
Middle Latitude ◽  
Wave Source ◽  
Middle Latitudes ◽  
Summer Time ◽  
The Waves

Abstract. Gravity wave signatures were extracted from OH airglow observations using all-sky CCD imagers at four different stations: Cachoeira Paulista (CP) (22.7° S, 45° W) and São João do Cariri (7.4° S, 36.5° W), Brazil; Tanjungsari (TJS) (6.9° S, 107.9° E), Indonesia and Shigaraki (34.9° N, 136° E), Japan. The gravity wave parameters are used as an input in a reverse ray tracing model to study the gravity wave vertical propagation trajectory and to estimate the wave source region. Gravity waves observed near the equator showed a shorter period and a larger phase velocity than those waves observed at low-middle latitudes. The waves ray traced down into the troposphere showed the largest horizontal wavelength and phase speed. The ray tracing results also showed that at CP, Cariri and Shigaraki the majority of the ray paths stopped in the mesosphere due to the condition of m2<0, while at TJS most of the waves are traced back into the troposphere. In summer time, most of the back traced waves have their final position stopped in the mesosphere due to m2<0 or critical level interactions (|m|→∞), which suggests the presence of ducting waves and/or waves generated in-situ. In the troposphere, the possible gravity wave sources are related to meteorological front activities and cloud convections at CP, while at Cariri and TJS tropical cloud convections near the equator are the most probable gravity wave sources. The tropospheric jet stream and the orography are thought to be the major responsible sources for the waves observed at Shigaraki.

Rossby-Kelvin instability: a new type of ageostrophic instability caused by a resonance between Rossby waves and gravity waves

1989 ◽  
Vol 202 ◽  
pp. 149-176 ◽  
Author(s):  
Satoshi Sakai
Keyword(s):  
Gravity Waves ◽  
Rossby Waves ◽  
Baroclinic Instability ◽  
Phase Speed ◽  
Kelvin Wave ◽  
Layer System ◽  
Geostrophic Balance ◽  
New Type ◽  
Frontal Instability ◽  
Zero Phase

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.

Latitudinal Variations of the Convective Source and Propagation Condition of Inertio-Gravity Waves in the Tropics

2007 ◽  
Vol 64 (5) ◽  
pp. 1603-1618 ◽  
Author(s):  
Hye-Yeong Chun ◽  
Jung-Suk Goh ◽  
In-Sun Song ◽  
Lucrezia Ricciardulli
Keyword(s):  
Wave Propagation ◽  
Gravity Waves ◽  
Low Frequency ◽  
Phase Speed ◽  
Simple Relationship ◽  
Propagation Condition ◽  
Zonal Wavenumber ◽  
Vertical Propagation ◽  
Latitudinal Variations ◽  
The Tropics

Abstract Latitudinal variations of the convective source and vertical propagation condition of inertio-gravity waves (IGWs) in the tropical region (30°S–30°N) are examined using high-resolution Global Cloud Imagery (GCI) and 6-hourly NCEP–NCAR reanalysis data, respectively, for 1 yr (March 1985–February 1986). The convective source is estimated by calculating the deep convective heating (DCH) rate using the brightness temperature of the GCI data. The latitudinal variation of DCH is found to be significant throughout the year. The ratio of the maximum to minimum values of DCH in the annual mean is 3.2 and it is much larger in the June–August (JJA) and December–February (DJF) means. Spectral analyses show that DCH has a dominant period of 1 day, a zonal wavelength of about 1600 km, and a Gaussian-type phase-speed spectrum with a peak at the zero phase speed. The vertical propagation condition of IGWs is determined, in the zonal wavenumber and frequency domain, by two factors: (i) latitude, which determines the Coriolis parameter, and (ii) the basic-state wind structure in the target height range of wave propagation. It was found that the basic-state wind significantly influences the wave propagation condition in the lower stratosphere between 150 and 30 hPa, and accordingly a large portion of the source spectrum is filtered out. This is prominent not only in the latitudes higher than 15° where strong negative shear exists, but also near the equator where strong positive shear associated with the westerly phase of the quasi-biennial oscillation (QBO) filters out large portions of the low-frequency components of the convective source. There is no simple relationship between the ground-based frequency and latitude; lower latitudes are not always favorable for low-frequency IGWs to be observed in the stratosphere. The basic-state wind in the Tropics, which has seasonal, annual, and interannual variations, plays a major role not only in determining the wave propagation condition in the stratosphere but also in producing convective sources in the troposphere.

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