scholarly journals Instability of combined gravity-inertial-Rossby waves in atmospheres and oceans

2011 ◽  
Vol 29 (6) ◽  
pp. 997-1003 ◽  
Author(s):  
J. F. McKenzie
Keyword(s):  
Energy Exchange ◽  
Wave Speed ◽  
Rossby Waves ◽  
Low Frequency ◽  
Phase Speed ◽  
Ocean Dynamics ◽  
Stratified Medium ◽  
Instability Condition ◽  
Long Wavelength ◽  
Critical Latitude

Abstract. The properties of the instability of combined gravity-inertial-Rossby waves on a β-plane are investigated. The wave-energy exchange equation shows that there is an exchange of energy with the background stratified medium. The energy source driving the instability lies in the background enthalpy released by the gravitational buoyancy force. It is shown that if the phase speed of the westward propagating low frequency-long wavelength Rossby wave exceeds the Poincaré-Kelvin (or "equivalent" shallow water) wave speed, instability arises from the merging of Rossby and Poincaré modes. There are two key parameters in this instability condition; namely, the equatorial/rotational Mach (or Froude) number M and the latitude θ0 of the β-plane. In general waves equatorward of a critical latitude for given M can be driven unstable, with corresponding growth rates of the order of a day or so. Although these conclusions may only be safely drawn for short wavelengths corresponding to a JWKB wave packet propagating internally and located far from boundaries, nevertheless such a local instability may play a significant role in atmosphere-ocean dynamics.

scholarly journals On the unstable mode merging of gravity-inertial waves with Rossby waves

2011 ◽  
Vol 29 (8) ◽  
pp. 1377-1381 ◽  
Author(s):  
J. F. McKenzie
Keyword(s):  
High Frequency ◽  
Buoyancy Force ◽  
Rossby Waves ◽  
Unstable Mode ◽  
Low Frequency ◽  
Phase Speed ◽  
Intermediate Band ◽  
Long Wavelength ◽  
Wave Numbers ◽  
Inertial Wave

Abstract. We recapitulate the results of the combined theory of gravity-inertial-Rossby waves in a rotating, stratified atmosphere. The system is shown to exhibit a "local" (JWKB) instability whenever the phase speed of the low-frequency-long wavelength westward propagating Rossby wave exceeds the phase speed ("Kelvin" speed) of the high frequency-short wavelength gravity-inertial wave. This condition ensures that mode merging, leading to instability, takes place in some intermediate band of frequencies and wave numbers. The contention that such an instability is "spurious" is not convincing. The energy source of the instability resides in the background enthalpy which can be released by the action of the gravitational buoyancy force, through the combined wave modes.

Shear Alfvén Wave with Quantum Exchange-Correlation Effects in Plasmas

2017 ◽  
Vol 72 (10) ◽  
pp. 891-898 ◽  
Author(s):  
Zahid Mir ◽  
M. Jamil ◽  
A. Rasheed ◽  
M. Asif
Keyword(s):  
Low Frequency ◽  
Phase Speed ◽  
Alfven Wave ◽  
Exchange Potential ◽  
Correlation Effects ◽  
Long Wavelength ◽  
Exchange Correlation ◽  
Exchange Correlation Potential ◽  
Dust Charge ◽  
Correlation Potential

AbstractThe dust shear Alfvén wave is studied in three species dusty quantum plasmas. The quantum effects are incorporated through the Fermi degenerate pressure, tunneling potential, and in particular the exchange-correlation potential. The significance of exchange-correlation potential is pointed out by a graphical description of the dispersion relation, which shows that the exchange potential magnifies the phase speed. The low-frequency shear Alfvén wave is studied while considering many variables. The shear Alfvén wave gains higher phase speed at the range of small angles for the upper end of the wave vector spectrum. The increasing dust charge and the external magnetic field reflect the increasing tendency of phase speed. This study may explain many natural mechanisms associated with long wavelength radiations given in the summary.

scholarly journals The Low-Frequency Array (LOFAR): Opening a New Window on the Universe

2002 ◽  
Vol 199 ◽  
pp. 474-483
Author(s):  
Namir E. Kassim ◽  
T. Joseph W. Lazio ◽  
William C. Erickson ◽  
Patrick C. Crane ◽  
R. A. Perley ◽  
...  
Keyword(s):  
Angular Resolution ◽  
Broad Band ◽  
Low Frequency ◽  
Electromagnetic Spectrum ◽  
Interferometric Imaging ◽  
Very Large Array ◽  
Long Wavelength ◽  
Calibration Techniques ◽  
Long Baselines ◽  
The Universe

Decametric wavelength imaging has been largely neglected in the quest for higher angular resolution because ionospheric structure limited interferometric imaging to short (< 5 km) baselines. The long wavelength (LW, 2—20 m or 15—150 MHz) portion of the electromagnetic spectrum thus remains poorly explored. The NRL-NRAO 74 MHz Very Large Array has demonstrated that self-calibration techniques can remove ionospheric distortions over arbitrarily long baselines. This has inspired the Low Frequency Array (LOFAR)—-a fully electronic, broad-band (15—150 MHz)antenna array which will provide an improvement of 2—3 orders of magnitude in resolution and sensitivity over the state of the art.

scholarly journals On the Relationship between Regional Ocean Heat Content and Sea Surface Height

2017 ◽  
Vol 30 (22) ◽  
pp. 9195-9211 ◽  
Author(s):  
John T. Fasullo ◽  
Peter R. Gent
Keyword(s):  
Time Scales ◽  
Low Frequency ◽  
Heat Content ◽  
Sea Surface Height ◽  
Ocean Heat Content ◽  
Ocean Dynamics ◽  
Sea Surface ◽  
Altimeter Data ◽  
Model Control ◽  
The Relationship

Abstract An accurate diagnosis of ocean heat content (OHC) is essential for interpreting climate variability and change, as evidenced for example by the broad range of hypotheses that exists for explaining the recent hiatus in global mean surface warming. Potential insights are explored here by examining relationships between OHC and sea surface height (SSH) in observations and two recently available large ensembles of climate model simulations from the mid-twentieth century to 2100. It is found that in decadal-length observations and a model control simulation with constant forcing, strong ties between OHC and SSH exist, with little temporal or spatial complexity. Agreement is particularly strong on monthly to interannual time scales. In contrast, in forced transient warming simulations, important dependencies in the relationship exist as a function of region and time scale. Near Antarctica, low-frequency SSH variability is driven mainly by changes in the circumpolar current associated with intensified surface winds, leading to correlations between OHC and SSH that are weak and sometimes negative. In subtropical regions, and near other coastal boundaries, negative correlations are also evident on long time scales and are associated with the accumulated effects of changes in the water cycle and ocean dynamics that underlie complexity in the OHC relationship to SSH. Low-frequency variability in observations is found to exhibit similar negative correlations. Combined with altimeter data, these results provide evidence that SSH increases in the Indian and western Pacific Oceans during the hiatus are suggestive of substantial OHC increases. Methods for developing the applicability of altimetry as a constraint on OHC more generally are also discussed.

The role of the Pacific Decadal Oscillation and ocean-atmosphere interactions in driving United States heatwaves

2021 ◽  
Author(s):  
Sem Vijverberg ◽  
Dim Coumou
Keyword(s):  
Rossby Wave ◽  
Rossby Waves ◽  
Low Frequency ◽  
Causal Link ◽  
Causal Mechanism ◽  
Temperature Forecast ◽  
The Pacific ◽  
Ocean Atmosphere ◽  
The Waves

&lt;p&gt;Heatwaves can have devastating impact on society and reliable early warnings at several weeks lead time are needed. Heatwaves are often associated with quasi-stationary Rossby waves, which interact with sea surface temperature (SST). Previous studies showed that north-Pacific SST can provide long-lead predictability for eastern U.S. temperature, moderated by an atmospheric Rossby wave. The exact mechanisms, however, are not well understood. Here we analyze Rossby waves associated with heatwaves in western and eastern US. Causal inference analyses reveal that both waves are characterized by positive ocean-atmosphere feedbacks at synoptic timescales, amplifying the waves. However, this positive feedback on short timescales is not the causal mechanism that leads to a long-lead SST signal. Only the eastern US shows a long-lead causal link from SSTs to the Rossby wave. We show that the long-lead SST signal derives from low-frequency PDO variability, providing the source of eastern US temperature predictability. We use this improved physical understanding to identify more reliable long-lead predictions. When, at the onset of summer, the Pacific is in a pronounced PDO phase, the SST signal is expected to persist throughout summer. These summers are characterized by a stronger ocean-boundary forcing, thereby more than doubling the eastern US temperature forecast skill, providing a temporary window of enhanced predictability.&lt;/p&gt;

Waves, jets and vortices: Regime transitions in shallow water turbulence

2021 ◽  
Author(s):  
Nikos Bakas
Keyword(s):  
Shallow Water ◽  
Large Scale ◽  
Rossby Waves ◽  
Phase Speed ◽  
Critical Value ◽  
Turbulent Regime ◽  
Wave Regime ◽  
Frequency Spectra ◽  
Spectra Analysis ◽  
Zonal Jets

&lt;p&gt;Forced-dissipative beta-plane turbulence in a single-layer shallow-water fluid has been widely considered as a simplified model of planetary turbulence as it exhibits turbulence self-organization into large-scale structures such as robust zonal jets and strong vortices. In this study we perform a series of numerical simulations to analyze the characteristics of the emerging structures as a function of the planetary vorticity gradient and the deformation radius. We report four regimes that appear as the energy input rate &amp;#949; of the random stirring that supports turbulence in the flow increases. A homogeneous turbulent regime for low values of &amp;#949;, a regime in which large scale Rossby waves form abruptly when &amp;#949; passes a critical value, a regime in which robust zonal jets coexist with weaker Rossby waves when &amp;#949; passes a second critical value and a regime of strong materially coherent propagating vortices for large values of &amp;#949;. The wave regime which is not predicted by standard cascade theories of turbulence anisotropization and the vortex regime are studied thoroughly. Wavenumber-frequency spectra analysis shows that the Rossby waves in the second regime remain phase coherent over long times. The coherent vortices are identified using the Lagrangian Averaged Deviation (LAVD) method. The statistics of the vortices (lifetime, radius, strength and speed) are reported as a function of the large scale parameters. We find that the strong vortices propagate zonally with a phase speed that is equal or larger than the long Rossby wave speed and advect the background turbulence leading to a non-dispersive line in the wavenumber-frequency spectra.&lt;/p&gt;

scholarly journals Instability of coupled gravity-inertial-Rossby waves on a β-plane in solar system atmospheres

2009 ◽  
Vol 27 (11) ◽  
pp. 4221-4227 ◽  
Author(s):  
J. F. McKenzie
Keyword(s):  
Rossby Waves ◽  
Narrow Band ◽  
Boussinesq Approximation ◽  
The Other ◽  
The Earth ◽  
Propagating Waves ◽  
Inertial Wave ◽  
The One ◽  
Fifth Order ◽  
Critical Latitude

Abstract. This paper provides an analysis of the combined theory of gravity-inertial-Rossby waves on a β-plane in the Boussinesq approximation. The wave equation for the system is fifth order in space and time and demonstrates how gravity-inertial waves on the one hand are coupled to Rossby waves on the other through the combined effects of β, the stratification characterized by the Väisälä-Brunt frequency N, the Coriolis frequency f at a given latitude, and vertical propagation which permits buoyancy modes to interact with westward propagating Rossby waves. The corresponding dispersion equation shows that the frequency of a westward propagating gravity-inertial wave is reduced by the coupling, whereas the frequency of a Rossby wave is increased. If the coupling is sufficiently strong these two modes coalesce giving rise to an instability. The instability condition translates into a curve of critical latitude Θc versus effective equatorial rotational Mach number M, with the region below this curve exhibiting instability. "Supersonic" fast rotators are unstable in a narrow band of latitudes around the equator. For example Θc~12° for Jupiter. On the other hand slow "subsonic" rotators (e.g. Mercury, Venus and the Sun's Corona) are unstable at all latitudes except very close to the poles where the β effect vanishes. "Transonic" rotators, such as the Earth and Mars, exhibit instability within latitudes of 34° and 39°, respectively, around the Equator. Similar results pertain to Oceans. In the case of an Earth's Ocean of depth 4km say, purely westward propagating waves are unstable up to 26° about the Equator. The nonlinear evolution of this instability which feeds off rotational energy and gravitational buoyancy may play an important role in atmospheric dynamics.

scholarly journals Trapped Planetary (Rossby) Waves Observed in the Indian Ocean by Satellite Borne Altimeters

2017 ◽  
Author(s):  
Yair De-Leon ◽  
Nathan Paldor
Keyword(s):  
Indian Ocean ◽  
Rossby Waves ◽  
Low Frequency ◽  
Propagation Speed ◽  
Wave Theory ◽  
Planetary Waves ◽  
Sea Surface ◽  
Trapped Wave ◽  
The Indian Ocean ◽  
Frequency Variations

Abstract. Using 20 years of accurately calibrated, high resolution, observations of Sea Surface Height Anomalies (SSHA) by satellite ‎borne altimeters we show that in the Indian Ocean south of the Australian coast the low frequency variations of SSHA are ‎dominated by westward propagating, trapped, i.e. non-harmonic, planetary waves. Our results demonstrate that the ‎meridional-dependent amplitudes of the SSHA are large only within a few degrees of latitude next to the South-Australian ‎coast while farther in the ocean they are uniformly small. This meridional variation of the SSHA signal is typical of the ‎amplitude structure in the trapped wave theory. The westward propagation speed of the SSHA signals is analyzed by ‎employing three different methods of estimation. Each one of these methods yields speed estimates that can vary widely ‎between adjacent latitudes but the combination of at least two of the three methods yields much smoother variation. The ‎estimates obtained in this manner show that the observed phase speeds at different latitudes exceed the phase speeds of ‎harmonic Rossby (Planetary) waves by 140 % to 200 %. In contrast, the theory of trapped Rossby (Planetary) waves in a ‎domain bounded by a wall on its equatorward side yields phase speeds that approximate more closely the observed phase ‎speeds.‎

scholarly journals Kinetic extraordinary-mode eigenvalue equation for relativistic nonneutral electron flow in planar geometry

1989 ◽  
Vol 7 (1) ◽  
pp. 55-84 ◽  
Author(s):  
Ronald C. Davidson ◽  
Han S. Uhm
Keyword(s):  
Electron Flow ◽  
Low Frequency ◽  
Companion Paper ◽  
Field Configuration ◽  
Outer Edge ◽  
Eigenvalue Equation ◽  
Planar Geometry ◽  
Canonical Momentum ◽  
Stability Properties ◽  
Long Wavelength

Use is made of the Vlasov–Maxwell equations to derive an eigenvalue equation describing the extraordinary–mode stability properties of relativistic, non-neutral electron flow in high-voltage diodes. The analysis is based on well-established theoretical techniques developed in basic studies of the kinetic equilibrium and stability properties of nonneutral plasmas characterized by intense self fields. The formal eigenvalue equation is derived for extraordinary-mode flute perturbations in a planar diode. As a specific example, perturbations are considered about the choice of self-consistent Vlasov equilibrium , where . is the electron density at the cathode (x = 0), H is the energy, and Py is the canonical momentum in the Y-direction (the direction of the equilibrium electron flow). As a limiting case, the planar eigenvalue equation is further simplified for low-frequency long-wavelength perturbations with |ω − kvd, ≪ ωυ where and and ⋯c = eB0/mc, and B0ệz is the applied magnetic field in the vacuum region xb < x ≤ d. Here, the outer edge of the electron layer is located at x = xb; ω is complex oscillation frequency; k is the wavenumber in the y-direction; ωυ is the characteristic betatron frequency for oscillations in the x′-orbit about the equilibrium value x′ = x0 = xb/2; and Vd is the average electron flow velocity in the y-direction at x = x0. In simplifying the orbit integrals, a model is adopted in which the eigenfunction approximated by , where x′(t′) is the x′-orbit in the equilibrium field configuration. A detailed analysis of the resulting eigenvalue equation for , derived for low-frequency long-wavelength perturbations, is the subject of a companion paper.

Effect of Coriolis force on edge waves (I) Investigation of the normal modes

2020 ◽  
Vol 78 (4) ◽  
pp. 229-261
Author(s):  
Robert O. Reid
Keyword(s):  
Coriolis Force ◽  
Wind Stress ◽  
Formal Solution ◽  
Wave Length ◽  
Normal Modes ◽  
Low Frequency ◽  
Phase Speed ◽  
Free Edge ◽  
Edge Wave ◽  
Edge Waves

Essentially two classes of free edge waves can exist on a sloping continental shelf in the presence of Coriolis force. For small longshore wave length, fundamental waves of the first class behave like Stokes edge waves. However, for great wave lengths (of several hundred kilometers or more) the characteristics of the first class are significantly altered. In the northern hemisphere the phase speed for waves moving to the right (facing shore from the sea) exceeds the speed for waves which move to the left. Also, the group velocity for a given edge wave mode has a finite upper limit. Waves of the second class are essentially quasigeostrophic boundary waves with very low frequency and, like Kelvin waves, move only to the left (again facing shore from the sea). Unlike Stokes edge waves, those of the quasigeostrophic class are associated with large vorticity. Examination of the formal solution for forced edge waves indicates that those of the second class may be excited significantly by a wind stress vortex. Also, in contrast to the conclusion of Greenspan (1956), it is proposed that a hurricane can effectively excite the higher order edge wave modes in addition to the fundamental if wind stress is considered.

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