scholarly journals The Phase Speed of a Travelling Disturbance in the F Region of the Ionosphere and its Comparison with Group Velocity

1961 ◽  
Vol 14 (4) ◽  
pp. 481 ◽  
Author(s):  
LH Heisler ◽  
JD Whitehead
Keyword(s):  
Group Velocity ◽  
Phase Speed ◽  
Theoretical Explanation ◽  
F Region

Three methods of measuring the phase speed of a disturbance in the F region, that is, the speed of a peak or trough in the isoionic contours, are given using ionograms records from one station. The analysis has been applied to one such disturbance whose group velocity was known to be 10 km/min. All three methods gave the phase speed to be about half of this. The theoretical explanation of this observation is discussed.

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 Local Rossby Wave Packet Amplitude, Phase Speed, and Group Velocity: Seasonal Variability and Their Role in Temperature Extremes

2020 ◽  
Vol 33 (20) ◽  
pp. 8767-8787 ◽  
Author(s):  
Georgios Fragkoulidis ◽  
Volkmar Wirth
Keyword(s):  
Group Velocity ◽  
Rossby Wave ◽  
Model Simulation ◽  
Phase Speed ◽  
Meridional Wind ◽  
Reanalysis Data ◽  
Spatiotemporal Variability ◽  
Temperature Extremes ◽  
Time Period ◽  
Real Atmosphere

AbstractTransient Rossby wave packets (RWPs) are a prominent feature of the synoptic to planetary upper-tropospheric flow at the midlatitudes. Their demonstrated role in various aspects of weather and climate prompts the investigation of characteristic properties like their amplitude, phase speed, and group velocity. Traditional frameworks for the diagnosis of the two latter have so far remained nonlocal in space or time, thus preventing a detailed view on the spatiotemporal evolution of RWPs. The present work proposes a method for the diagnosis of horizontal Rossby wave phase speed and group velocity locally in space and time. The approach is based on the analytic signal of upper-tropospheric meridional wind velocity and RWP amplitude, respectively. The new diagnostics are first applied to illustrative examples from a barotropic model simulation and the real atmosphere. The main seasonal and interregional variability features of RWP amplitude, phase speed, and group velocity are then explored using ERA5 reanalysis data for the time period 1979–2018. Apparent differences and similarities in these respects between the Northern and Southern Hemispheres are also discussed. Finally, the role of RWP amplitude and phase speed during central European short-lived and persistent temperature extremes is investigated based on changes of their distribution compared to the climatology of the region. The proposed diagnostics offer insight into the spatiotemporal variability of RWP properties and allow the evaluation of their implications at low computational demands.

Group velocity dispersion of a multicore fibre with 5 × 5 coupled cores for in-phase and out-of-phase supermodes

2021 ◽  
Vol 18 (12) ◽  
pp. 125104
Author(s):  
A V Andrianov ◽  
N A Kalinin ◽  
E A Anashkina
Keyword(s):  
Group Velocity ◽  
Wavelength Range ◽  
Silica Glass ◽  
Spatial Light Modulator ◽  
Velocity Dispersion ◽  
Group Velocity Dispersion ◽  
Wavelength Dependence ◽  
Theoretical Explanation ◽  
Light Modulator ◽  
The Difference

Abstract In-phase and out-of-phase supermodes were selectively excited (with modal content >90%) in the wavelength range near 1030 nm in a silica multicore fibre with 5 × 5 coupled cores using a spatial light modulator. Group velocity dispersion (GVD) parameters of 21 ps2 km−1 and 14 ps2 km−1 at 1030 nm were measured for in-phase and out-of-phase supermodes, respectively, using an interferometric scheme. The numerically simulated GVD values agree with the experimental results. The calculated zero-dispersion wavelengths (ZDWs) of 1360 nm and 1180 nm for in-phase and out-of-phase supermodes are red-shifted and blue-shifted, respectively, compared to the ZDW of silica glass. The anomalous dispersion for the out-of-phase supermode is predicted in the telecommunication O-band near 1300 nm. The theoretical explanation of the difference in the wavelength-dependence of GVD for in-phase and out-of-phase supermodes is given.

Local diagnostics of Rossby wave packet properties – Seasonal variability and their role in temperature extremes

2020 ◽  
Author(s):  
Georgios Fragkoulidis ◽  
Volkmar Wirth
Keyword(s):  
Group Velocity ◽  
Rossby Wave ◽  
Phase Speed ◽  
Meridional Wind ◽  
Reanalysis Data ◽  
Diagnostic Methods ◽  
Temperature Extremes ◽  
Time Period ◽  
Tropospheric Circulation ◽  
Systematic Biases

<p>Transient Rossby wave packets (RWPs) are a prominent feature of the synoptic to planetary upper-tropospheric flow at the mid-latitudes. This prompts the development of diagnostic methods to identify and investigate the spatiotemporal evolution of key RWP properties. Such properties include the RWP phase speed and group velocity, the diagnosis of which has so far remained non-local in space and/or time. To this end, a novel diagnostic approach is presented here, which is based on the analytic signal of upper-tropospheric meridional wind velocity and thus allows the evaluation of RWP properties locally in space and time. The detailed insight into these properties can be utilized toward a better understanding of the upper-tropospheric circulation, its interplay with local weather features, and its model representation. In particular, climatologies of RWP amplitude, wavenumber, phase speed, and group velocity are investigated using reanalysis data for the time period 1979 – 2018. Pronounced features of seasonal and interregional variability are highlighted. Moreover, the role of RWP amplitude and phase speed in the occurrence and duration of temperature extremes in Europe is explored. Finally, indications of systematic biases in medium-range forecasts of these fields suggest that a correct representation of the RWP evolution is crucial for the predictability of temperature extreme events.</p>

scholarly journals Lagrangian transport by vertically confined internal gravity wavepackets

2019 ◽  
Vol 864 ◽  
pp. 348-380 ◽  
Author(s):  
T. S. van den Bremer ◽  
H. Yassin ◽  
B. R. Sutherland
Keyword(s):  
Group Velocity ◽  
Phase Speed ◽  
Stable Stratification ◽  
Stokes Drift ◽  
Near Surface ◽  
Lagrangian Transport ◽  
Special Cases ◽  
Induced Flow ◽  
Boussinesq Fluid ◽  
Exponential Stratification

We examine the flows induced by horizontally modulated, vertically confined (or guided), internal wavepackets in a stratified, Boussinesq fluid. The wavepacket induces both an Eulerian flow and a Stokes drift, which together determine the Lagrangian transport of passive tracers. We derive equations describing the wave-induced flows in arbitrary stable stratification and consider four special cases: a two-layer fluid, symmetric and asymmetric piecewise constant (‘top-hat’) stratification and, more representative of the ocean, exponential stratification. In a two-layer fluid, the Stokes drift is positive everywhere with the peak value at the interface, whereas the Eulerian flow is negative and uniform with depth for long groups. Combined, the net depth-integrated Lagrangian transport is zero. If one layer is shallower than the other, the wave-averaged interface displaces into that layer making the Eulerian flow in that layer more negative and the Eulerian flow in the opposite layer more positive so that the depth-integrated Eulerian transports are offset by the same amount in each layer. By contrast, in continuous stratification the depth-integrated transport due to the Stokes drift and Eulerian flow are each zero, but the Eulerian flow is singular if the horizontal phase speed of the induced flow equals the group velocity of the wavepacket, giving rise to a single resonance in uniform stratification (McIntyre, J. Fluid Mech., vol. 60, 1973, pp. 801–811). In top-hat stratification, this single resonance disappears, being replaced by multiple resonances occurring when the horizontal group velocity of the wavepacket matches the horizontal phase speed of higher-order modes. Furthermore, if the stratification is not vertically symmetric, then the Eulerian induced flow varies as the inverse squared horizontal wavenumber for shallow waves, the same as for the asymmetric two-layer case. This ‘infrared catastrophe’ also occurs in the case of exponential stratification suggesting significant backward near-surface transport by the Eulerian induced flow for modulated oceanic internal modes. Numerical simulations are performed confirming these theoretical predictions.

scholarly journals The MJO as a Dispersive, Convectively Coupled Moisture Wave: Theory and Observations

2016 ◽  
Vol 73 (3) ◽  
pp. 913-941 ◽  
Author(s):  
Ángel F. Adames ◽  
Daehyun Kim
Keyword(s):  
Group Velocity ◽  
Rossby Wave ◽  
Linear Regression Analysis ◽  
Phase Speed ◽  
Wave Theory ◽  
Reanalysis Data ◽  
Horizontal Wind ◽  
Model Parameters ◽  
Linear Wave ◽  
Zonal Wavenumber

Abstract A linear wave theory for the Madden–Julian oscillation (MJO), previously developed by Sobel and Maloney, is extended upon in this study. In this treatment, column moisture is the only prognostic variable and the horizontal wind is diagnosed as the forced Kelvin and Rossby wave responses to an equatorial heat source/sink. Unlike the original framework, the meridional and vertical structure of the basic equations is treated explicitly, and values of several key model parameters are adjusted, based on observations. A dispersion relation is derived that adequately describes the MJO’s signal in the wavenumber–frequency spectrum and defines the MJO as a dispersive equatorial moist wave with a westward group velocity. On the basis of linear regression analysis of satellite and reanalysis data, it is estimated that the MJO’s group velocity is ~40% as large as its phase speed. This dispersion is the result of the anomalous winds in the wave modulating the mean distribution of moisture such that the moisture anomaly propagates eastward while wave energy propagates westward. The moist wave grows through feedbacks involving moisture, clouds, and radiation and is damped by the advection of moisture associated with the Rossby wave. Additionally, a zonal wavenumber dependence is found in cloud–radiation feedbacks that cause growth to be strongest at planetary scales. These results suggest that this wavenumber dependence arises from the nonlocal nature of cloud–radiation feedbacks; that is, anomalous convection spreads upper-level clouds and reduces radiative cooling over an extensive area surrounding the anomalous precipitation.

scholarly journals Planetary wave characteristics of gravity wave modulation from 30–130 km

2012 ◽  
Vol 10 ◽  
pp. 271-277 ◽  
Author(s):  
P. Hoffmann ◽  
Ch. Jacobi
Keyword(s):  
Planetary Wave ◽  
Middle Atmosphere ◽  
Model Simulation ◽  
Phase Speed ◽  
Circulation Model ◽  
Wave Characteristics ◽  
F Region ◽  
Zonal Wavenumber ◽  
Momentum Fluxes ◽  
High Phase

Abstract. Fast gravity waves (GW) have an important impact on the momentum transfer between the middle and upper atmosphere. Experiments with a circulation model indicate a penetration of high phase speed GW into the thermosphere as well as an indirect propagation of planetary waves by the modulation GW of momentum fluxes into the thermosphere. Planetary wave characteristics derived from middle atmosphere SABER temperatures, GW potential energy and ionospheric GPS-TEC data at midlatitudes reveal a possible correspondence of PW signatures in the middle atmosphere and ionosphere in winter around solar maximum (2002–2005). In the case of the westward propagating 16-day wave with zonal wavenumber 1 a possible connection could be found in data analysis (November–December 2003) and model simulation. Accordingly, GW with high phase speeds might play an essential role in the transfer of PW and other meteorological disturbances up to the ionospheric F-region.

scholarly journals A Dissection of Energetics of the Geostrophic Flow: Reconciliation of Rossby Wave Energy Flux and Group Velocity

2013 ◽  
Vol 70 (7) ◽  
pp. 2179-2196 ◽  
Author(s):  
Ming Cai ◽  
Bohua Huang
Keyword(s):  
Potential Energy ◽  
Group Velocity ◽  
Energy Flux ◽  
Rossby Waves ◽  
Phase Speed ◽  
Energy Propagation ◽  
Pressure Work ◽  
Geostrophic Flow ◽  
Wave Energy Flux ◽  
The Difference

Abstract It is shown in this paper that there is no ambiguity in the final form of the governing equations of a quasigeostrophic (QG) model after partitioning the total flow into the geostrophic, balanced ageostrophic, and unbalanced ageostrophic components. The uniqueness of the QG model formulation ensures that the energetics of a QG model is the same as that derived from the QG potential vorticity equation. Particularly, the well-known but somewhat mysterious “missing term” in the energetics of Rossby waves, identified in the literature as the difference between the pressure work and the energy flux transported at the group velocity, can be easily recovered. The missing term is the pressure work on the convergence of the balanced ageostrophic flow, representing a “hidden” conversion between kinetic and potential energy of the geostrophic flow that excites the unbalanced flow. This energy conversion equals the convergence of a one-directional energy flux that always transports energy westward at the zonal phase speed of Rossby waves. The pressure work on the divergence of the unbalanced flow does the actual conversion between kinetic and potential energy of the geostrophic flow and the pressure work on the unbalanced flow causes energy propagation in other directions. Therefore, it is the pressure work on the unbalanced flow that causes Rossby waves to be dispersive, leading to the downstream development. The sum of the energy transported at the zonal phase speed of Rossby waves and the pressure work on the unbalanced flow exactly equals the energy transported at the group velocity of Rossby waves.

Stability of steep gravity–capillary solitary waves in deep water

2002 ◽  
Vol 452 ◽  
pp. 123-143 ◽  
Author(s):  
DAVID C. CALVO ◽  
T. R. AKYLAS
Keyword(s):  
Solitary Waves ◽  
Deep Water ◽  
Wave Solution ◽  
Wave Equations ◽  
Solitary Wave Solution ◽  
Phase Speed ◽  
Theoretical Explanation ◽  
Solution Branch ◽  
Viscous Effects ◽  
The Stability

The stability of steep gravity–capillary solitary waves in deep water is numerically investigated using the full nonlinear water-wave equations with surface tension. Out of the two solution branches that bifurcate at the minimum gravity–capillary phase speed, solitary waves of depression are found to be stable both in the small-amplitude limit when they are in the form of wavepackets and at finite steepness when they consist of a single trough, consistent with observations. The elevation-wave solution branch, on the other hand, is unstable close to the bifurcation point but becomes stable at finite steepness as a limit point is passed and the wave profile features two well-separated troughs. Motivated by the experiments of Longuet-Higgins & Zhang (1997), we also consider the forced problem of a localized pressure distribution applied to the free surface of a stream with speed below the minimum gravity–capillary phase speed. We find that the finite-amplitude forced solitary-wave solution branch computed by Vanden-Broeck & Dias (1992) is unstable but the branch corresponding to Rayleigh’s linearized solution is stable, in agreement also with a weakly nonlinear analysis based on a forced nonlinear Schrödinger equation. The significance of viscous effects is assessed using the approach proposed by Longuet-Higgins (1997): while for free elevation waves the instability predicted on the basis of potential-flow theory is relatively weak compared with viscous damping, the opposite turns out to be the case in the forced problem when the forcing is strong. In this régime, which is relevant to the experiments of Longuet-Higgins & Zhang (1997), the effects of instability can easily dominate viscous effects, and the results of the stability analysis are used to propose a theoretical explanation for the persistent unsteadiness of the forced wave profiles observed in the experiments.

Interferometric (Fourier-Spectroscopic) Measurement of Electron Energy Distributions

1990 ◽  
Vol 48 (2) ◽  
pp. 110-111 ◽  
Author(s):  
F. Hasselbach ◽  
A. Schäfer
Keyword(s):  
Group Velocity ◽  
Wave Packets ◽  
Index Of Refraction ◽  
Electron Wave ◽  
Fringe Contrast ◽  
Faraday Cage ◽  
Optical Index ◽  
Wien Filter ◽  
Coherent Wave ◽  
Electric And Magnetic Fields

Möllenstedt and Wohland proposed in 1980 two methods for measuring the coherence lengths of electron wave packets interferometrically by observing interference fringe contrast in dependence on the longitudinal shift of the wave packets. In both cases an electron beam is split by an electron optical biprism into two coherent wave packets, and subsequently both packets travel part of their way to the interference plane in regions of different electric potential, either in a Faraday cage (Fig. 1a) or in a Wien filter (crossed electric and magnetic fields, Fig. 1b). In the Faraday cage the phase and group velocity of the upper beam (Fig.1a) is retarded or accelerated according to the cage potential. In the Wien filter the group velocity of both beams varies with its excitation while the phase velocity remains unchanged. The phase of the electron wave is not affected at all in the compensated state of the Wien filter since the electron optical index of refraction in this state equals 1 inside and outside of the Wien filter.

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