scholarly journals The Longitudinal Variation of Equatorial Waves due to Propagation on a Varying Zonal Flow

2016 ◽  
Vol 73 (2) ◽  
pp. 605-620 ◽  
Author(s):  
Brian J. Hoskins ◽  
Gui-Ying Yang
Keyword(s):  
Wave Theory ◽  
Zonal Flow ◽  
Equatorial Waves ◽  
Kelvin Wave ◽  
Property B ◽  
Wave Distribution ◽  
The Individual ◽  
The Waves ◽  
Zonal Propagation ◽  
Remarkable Agreement

Abstract The general 1D theory of waves propagating on a zonally varying flow is developed from basic wave theory, and equations are derived for the variation of wavenumber and energy along ray paths. Different categories of behavior are found, depending on the sign of the group velocity cg and a wave property B. For B positive, the wave energy and the wavenumber vary in the same sense, with maxima in relative easterlies or westerlies, depending on the sign of cg. Also the wave accumulation of Webster and Chang occurs where cg goes to zero. However, for B negative, they behave in opposite senses and wave accumulation does not occur. The zonal propagation of the gravest equatorial waves is analyzed in detail using the theory. For nondispersive Kelvin waves, B reduces to 2, and an analytic solution is possible. For all the waves considered, B is positive, except for the westward-moving mixed Rossby–gravity (WMRG) wave, which can have negative B as well as positive B. Comparison is made between the observed climatologies of the individual equatorial waves and the result of pure propagation on the climatological upper-tropospheric flow. The Kelvin wave distribution is in remarkable agreement, considering the approximations made. Some aspects of the WMRG and Rossby wave distributions are also in qualitative agreement. However, the observed maxima in these waves in the winter westerlies in the eastern Pacific and Atlantic Oceans are generally not in accord with the theory. This is consistent with the importance of the sources of equatorial waves in these westerly duct regions due to higher-latitude wave activity.

scholarly journals Convectively Coupled Equatorial Waves. Part I: Horizontal and Vertical Structures

2007 ◽  
Vol 64 (10) ◽  
pp. 3406-3423 ◽  
Author(s):  
Gui-Ying Yang ◽  
Brian Hoskins ◽  
Julia Slingo
Keyword(s):  
Composite Structures ◽  
Wave Structure ◽  
Wave Theory ◽  
Western Hemisphere ◽  
Equatorial Waves ◽  
Kelvin Wave ◽  
Ambient Flow ◽  
Convectively Coupled Equatorial Waves ◽  
Eastern Hemisphere ◽  
Equatorial Wave

Abstract Multilevel 15-yr ECMWF Re-Analysis (ERA-15) and satellite-observed brightness temperature (Tb) data for the period May–October 1992 are used to examine the horizontal and vertical structures of convectively coupled equatorial waves. Dynamical waves are isolated using a methodology developed previously. Composite structures of convectively coupled equatorial waves are obtained using linear regression/correlation between convection (Tb) and dynamical structures. It is found that the relationship depends on the ambient flow and the nature of the convective coupling, and varies between off-equatorial- and equatorial-centered convection, different hemispheres, and seasons. The Kelvin wave structure in the Western Hemisphere is generally consistent with classic equatorial wave theory and has its convection located in the region of low-level convergence. In the Eastern Hemisphere the Kelvin wave tends to have convection in the region of enhanced lower-tropospheric westerlies and a tilted vertical structure. The Kelvin wave also tends to have a third peak in zonal wind amplitude at 500 hPa and exhibits upward propagation into the lower stratosphere. Lower-tropospheric westward-moving mixed Rossby–gravity (WMRG) and n = 1 Rossby (R1) wave structures and their relationship with convection are consistent with classic equatorial wave theory and the implied lower-tropospheric convergences. In the Eastern Hemisphere the WMRG and R1 waves have first baroclinic mode structures in the vertical. However, in the Western Hemisphere, the R1 wave has a barotropic structure. In the Eastern Hemisphere the R1 wave, like the Kelvin wave, tends to have equatorial convection in the region of enhanced lower-level westerlies, suggesting that enhanced surface energy fluxes associated with these waves may play an important organizing role for equatorial convection in this warm-water hemisphere. In the upper troposphere, eastward-moving Rossby–gravity (EMRG) and n = 1 gravity waves are found in the Eastern Hemisphere, and eastward-moving WMRG and R1 waves are found in the Western Hemisphere, suggestive of Doppler shifting of waves by the ambient flow.

scholarly journals Individual Alpha Peak Frequency, an Important Biomarker for Live Z-Score Training Neurofeedback in Adolescents with Learning Disabilities

2021 ◽  
Vol 11 (2) ◽  
pp. 167
Author(s):  
Rubén Pérez-Elvira ◽  
Javier Oltra-Cucarella ◽  
José Antonio Carrobles ◽  
Minodora Teodoru ◽  
Ciprian Bacila ◽  
...  
Keyword(s):  
Learning Disabilities ◽  
Pediatric Population ◽  
Peak Frequency ◽  
Normative Values ◽  
Z Score ◽  
Absolute Power ◽  
The Individual ◽  
And Behavior ◽  
The Waves ◽  
Alpha Peak

Learning disabilities (LDs) have an estimated prevalence between 5% and 9% in the pediatric population and are associated with difficulties in reading, arithmetic, and writing. Previous electroencephalography (EEG) research has reported a lag in alpha-band development in specific LD phenotypes, which seems to offer a possible explanation for differences in EEG maturation. In this study, 40 adolescents aged 10–15 years with LDs underwent 10 sessions of Live Z-Score Training Neurofeedback (LZT-NF) Training to improve their cognition and behavior. Based on the individual alpha peak frequency (i-APF) values from the spectrogram, a group with normal i-APF (ni-APF) and a group with low i-APF (li-APF) were compared in a pre-and-post-LZT-NF intervention. There were no statistical differences in age, gender, or the distribution of LDs between the groups. The li-APF group showed a higher theta absolute power in P4 (p = 0.016) at baseline and higher Hi-Beta absolute power in F3 (p = 0.007) post-treatment compared with the ni-APF group. In both groups, extreme waves (absolute Z-score of ≥1.5) were more likely to move toward the normative values, with better results in the ni-APF group. Conversely, the waves within the normal range at baseline were more likely to move out of the range after treatment in the li-APF group. Our results provide evidence of a viable biomarker for identifying optimal responders for the LZT-NF technique based on the i-APF metric reflecting the patient’s neurophysiological individuality.

scholarly journals Propagation of Rossby waves in stratified shear flows

1989 ◽  
Vol 12 (3) ◽  
pp. 547-557
Author(s):  
Palani G. Kandaswamy ◽  
B. Tamil Selvi ◽  
Lokenath Debnath
Keyword(s):  
Wave Equation ◽  
Relative Frequency ◽  
Shear Flows ◽  
Rossby Waves ◽  
Zonal Flow ◽  
Single Wave ◽  
Beta Plane ◽  
Valve Effect ◽  
The Waves ◽  
Isothermal Atmosphere

A study is made of the propagation of Rossby waves in a stably stratified shear flows. The wave equation for the Rossby waves is derived in an isothermal atmosphere on a beta plane in the presence of a latitudinally sheared zonal flow. It is shown that the wave equation is singular at five critical levels, but the wave absorption takes place only at the two levels where the local relative frequency equals in magnitude to the Brunt Vaisala frequency. This analysis also reveals that these two levels exhibit valve effect by allowing the waves to penetrate them from one side only. The absorption coefficient exp(2πμ)is determined at these levels. Both the group velocity approach and single wave treatment are employed for the investigation of the problem.

scholarly journals A Transactional, Whole-School Approach to Resilience

2021 ◽  
pp. 220-231
Author(s):  
Carmel Cefai
Keyword(s):  
Research Evidence ◽  
Social Contexts ◽  
Ecological Perspective ◽  
Educational Systems ◽  
Multiple Systems ◽  
Whole School ◽  
Resilience Framework ◽  
Whole School Approach ◽  
The Individual ◽  
The Waves

In contrast to the earlier understandings of resilience for the select, invulnerable few, an ecological perspective provides the opportunity for all children to develop resilience given resilience-enhancing, protective social contexts. In this chapter, the author explores a transactional-ecological perspective of resilience in the context of educational systems, underlining the limitations of an overreliance on the individual in resilience building. The chapter presents a transactional, whole-school, resilience framework for educational systems informed by the research evidence, focusing on both curricular competence-building and contextual processes across multiple systems. The chapter concludes with an illustration of a recent resilience program, RESCUR Surfing the Waves, informed by this approach.

scholarly journals <i>Letter to the Editor</i>: Revision of the basic equations of wave distribution function analysis

1998 ◽  
Vol 16 (5) ◽  
pp. 651-653
Author(s):  
L. R. O. Storey
Keyword(s):  
Signal Processing ◽  
Distribution Function ◽  
Magnetic Fields ◽  
Function Analysis ◽  
Adaptive Antennas ◽  
Radio Science ◽  
Electric And Magnetic Fields ◽  
Wave Distribution ◽  
Basic Equations ◽  
The Waves

Abstract. The basic equations of wave distribution function analysis are rewritten in forms that treat the electric and magnetic fields of the waves in a more symmetrical way than the original equations do, and are slightly better for computing.Key words. Radio science (electromagnetic metrology) · Electromagnetics (plasmas; signal processing and adaptive antennas)

scholarly journals Response of the West African Monsoon to the Madden–Julian Oscillation

2009 ◽  
Vol 22 (15) ◽  
pp. 4097-4116 ◽  
Author(s):  
Sally L. Lavender ◽  
Adrian J. Matthews
Keyword(s):  
West Africa ◽  
Monsoon Season ◽  
West African Monsoon ◽  
Circulation Model ◽  
Negative Temperature ◽  
Equatorial Waves ◽  
Madden Julian Oscillation ◽  
Global Circulation Model ◽  
Kelvin Wave ◽  
Sst Anomalies

Abstract Observations show that rainfall over West Africa is influenced by the Madden–Julian oscillation (MJO). A number of mechanisms have been suggested: 1) forcing by equatorial waves; 2) enhanced monsoon moisture supply; and 3) increased African easterly wave (AEW) activity. However, previous observational studies are not able to unambiguously distinguish between cause and effect. Carefully designed model experiments are used to assess these mechanisms. Intraseasonal convective anomalies over West Africa during the summer monsoon season are simulated in an atmosphere-only global circulation model as a response to imposed sea surface temperature (SST) anomalies associated with the MJO over the equatorial warm pool region. 1) Negative SST anomalies stabilize the atmosphere leading to locally reduced convection. The reduced convection leads to negative midtropospheric latent heating anomalies that force dry equatorial waves. These waves propagate eastward (Kelvin wave) and westward (Rossby wave), reaching Africa approximately 10 days later. The associated negative temperature anomalies act to destabilize the atmosphere, resulting in enhanced monsoon convection over West and central Africa. The Rossby waves are found to be the most important component, with associated westward-propagating convective anomalies over West Africa. The eastward-propagating equatorial Kelvin wave also efficiently triggers convection over the eastern Pacific and Central America, consistent with observations. 2) An increase in boundary layer moisture is found to occur as a result of the forced convective anomalies over West Africa rather than a cause. 3) Increased shear on the African easterly jet, leading to increased AEW activity, is also found to occur as a result of the forced convective anomalies in the model.

Application of Ship-Wave Theory to the Hydrofoil of Finite Span

1957 ◽  
Vol 1 (02) ◽  
pp. 27-55
Author(s):  
John P. Breslin
Keyword(s):  
Wave Theory ◽  
Wave Pattern ◽  
Wave Drag ◽  
Test Results ◽  
Dimensional Theory ◽  
Ship Hydrodynamics ◽  
Finite Span ◽  
Induced Drag ◽  
Load Distributions ◽  
The Waves

It is demonstrated in this paper2 that the deepwater wave drag of a hydrofoil of finite span can be found directly from the theory developed largely for ship hydrodynamics by Havelock and others. The wave drag is then studied at high Froude numbers and from the observed behavior the induced drag of the hydrofoil can be deduced from existing aerodynamic formulas. Evaluation of the resulting formulas is effected for two arbitrary load distributions and a comparison with some model test results is made. A practical approximation which gives the influence of gravity over a range of high Froude numbers is found and from this one can deduce a Froude number beyond which the effects of gravity may be ignored. It is also shown that an expression for the waves at some distance aft of the hydrofoil can be deduced from the general formulas developed for ship hydrodynamics. A discussion of the wave pattern is given with particular emphasis on the centerline profile at high Froude numbers and a contrast is pointed out in regard to the results of the two-dimensional theory for the hydrofoil waves and wave resistance.

scholarly journals Multivariate analysis of Kelvin wave seasonal variability in ECMWF L91 analyses

2018 ◽  
Author(s):  
Marten Blaauw ◽  
Nedjeljka Žagar
Keyword(s):  
Seasonal Variability ◽  
Wave Theory ◽  
Fast Response ◽  
Linear Wave ◽  
Kelvin Wave ◽  
Vertical Projection ◽  
Northern Summer ◽  
Eastern Hemisphere ◽  
Function Decomposition ◽  
Vertically Propagating

Abstract. The paper presents the seasonal variability of Kelvin waves (KWs) in 2007–2013 ECMWF analyses on 91 model levels. The waves are filtered using the normal-mode function decomposition which simultaneously analyses wind and mass field based on their relationships from linear wave theory. Both spectral as well as spatiotemporal features of the KWs are examined in terms of their seasonal variability in comparison with background wind and stability. Furthermore, a differentiation is made using spectral bandpass filtering between the slow horizontal barotropic KW response and the fast vertical projection response observed as vertically-propagating KWs. Results show a clear seasonal cycle in KW activity which is predominantly at the largest zonal scales (wavenumber 1–2) where up to 50 % more energy is observed during the solstice seasons in comparison with spring and autumn. The spatiotemporal structure of the KW reveals the slow response as a robust Gill-type structure with its position determined by the location of the dominant convective outflow winds throughout the seasons. Its maximum strength occurs during northern summer when easterlies in the Eastern Hemisphere are strongest. The fast response in the form of free traveling KWs occur throughout the year with seasonal variability mostly found in the wave amplitudes being dependent on background easterly winds.

On kinematic waves I. Flood movement in long rivers

1955 ◽  
Vol 229 (1178) ◽  
pp. 281-316 ◽  
Keyword(s):  
Shock Waves ◽  
Equations Of Motion ◽  
Functional Relation ◽  
Wave Theory ◽  
Observation Point ◽  
Rate Of Change ◽  
Kinematic Wave ◽  
Unit Distance ◽  
Kinematic Waves ◽  
The Waves

In this paper and in part II, we give the theory of a distinctive type of wave motion, which arises in any one-dimensional flow problem when there is an approximate functional relation at each point between the flow q (quantity passing a given point in unit time) and concentration k (quantity per unit distance). The wave property then follows directly from the equation of continuity satisfied by q and k . In view of this, these waves are described as ‘kinematic’, as distinct from the classical wave motions, which depend also on Newton’s second law of motion and are therefore called ‘dynamic’. Kinematic waves travel with the velocity dq/dk , and the flow q remains constant on each kinematic wave. Since the velocity of propagation of each wave depends upon the value of q carried by it, successive waves may coalesce to form ‘kinematic shock waves ’. From the point of view of kinematic wave theory, there is a discontinuous increase in q at a shock, but in reality a shock wave is a relatively narrow region in which (owing to the rapid increase of q ) terms neglected by the flow concentration relation become important. The general properties of kinematic waves and shock waves are discussed in detail in §1. One example included in §1 is the interpretation of the group-velocity phenomenon in a dispersive medium as a particular case of the kinematic wave phenomenon. The remainder of part I is devoted to a detailed treatment of flood movement in long rivers, a problem in which kinematic waves play the leading role although dynamic waves (in this case, the long gravity waves) also appear. First (§2), we consider the variety of factors which can influence the approximate flow-concentration relation, and survey the various formulae which have been used in attempts to describe it. Then follows a more mathematical section (§3) in which the role of the dynamic waves is clarified. From the full equations of motion for an idealized problem it is shown that at the ‘Froude numbers’ appropriate to flood waves, the dynamic waves are rapidly attenuated and the main disturbance is carried downstream by the kinematic waves; some account is then given of the behaviour of the flow at higher Froude numbers. Also in §3, the full equations of motion are used to investigate the structure of the kinematic shock; for this problem, the shock is the ‘monoclinal flood wave’ which is well known in the literature of this subject. The final sections (§§4 and 5) contain the application of the theory of kinematic waves to the determination of flood movement. In §4 it is shown how the waves (including shock waves) travelling downstream from an observation point may be deduced from a knowledge of the variation with time of the flow at the observation point; this section then concludes with a brief account of the effect on the waves of tributaries and run-off. In §5, the modifications (similar to diffusion effects) which arise due to the slight dependence of the flow-concentration curve on the rate of change of flow or concentration, are described and methods for their inclusion in the theory are given.

Uncertainties of Estimates of Inertia–Gravity Energy in the Atmosphere. Part II: Large-Scale Equatorial Waves

2009 ◽  
Vol 137 (11) ◽  
pp. 3858-3873 ◽  
Author(s):  
N. Žagar ◽  
J. Tribbia ◽  
J. L. Anderson ◽  
K. Raeder
Keyword(s):  
Large Scale ◽  
Normal Modes ◽  
Lower Troposphere ◽  
Physical Space ◽  
Significant Degree ◽  
Hadley Cell ◽  
Equatorial Waves ◽  
Kelvin Wave ◽  
Energy Propagation ◽  
Zonal Wavenumber

Abstract This paper analyzes the spectra and spatiotemporal features of the large-scale inertia-gravity (IG) circulations in four analysis systems in the tropics. Of special interest is the Kelvin wave (KW), which represents between 7% and 25% of the total IG wave (zonal wavenumber k ≠ 0) energy. The mixed Rossby–gravity (MRG) mode comprises between 4% and 15% of the IG wave energy. At the longest scales, the KW spectra are fitted by a law while the MRG energy spectrum appears flat. At shorter scales both modes follow a −3 law. Energy spectra of the total IG wave motion at long zonal scales (zonal wavenumber smaller than 7) have slopes close to −1. The average circulation associated with KW is characterized by reverse flows in the upper and lower troposphere consistent with the ideas behind simple tropical models. The inverse projection is used to quantify the role of Kelvin and MRG waves in current analysis systems in the upper troposphere over the Indian Ocean. At these levels, easterlies between 10°S and 30°N are represented by the KW to a significant degree while the cross-equatorial flow toward the descending branch of the Hadley cell at 10°S is associated with the MRG waves. The transient structure of equatorial waves is presented in the space of normal modes defined by the zonal wavenumbers, meridional Hough functions, and the vertical eigenfunctions. The difference in the depth of the model domain in DART–CAM and NCEP–NCAR on one hand and ECMWF and NCEP on the other appears to be one reason for different wave propagation properties. In the latter case the vertical energy propagation is diagnosed by filtering the propagating KW modes back to physical space. The results agree with the linear theory of vertically propagating equatorial waves.

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