scholarly journals Baroclinic Stationary Waves in Aquaplanet Models

2011 ◽  
Vol 68 (5) ◽  
pp. 1023-1040 ◽  
Author(s):  
Giuseppe Zappa ◽  
Valerio Lucarini ◽  
Antonio Navarra
Keyword(s):  
Dispersion Relation ◽  
Baroclinic Instability ◽  
Surface Wind ◽  
Low Frequency ◽  
Phase Speed ◽  
Stationary Wave ◽  
Instability Wave ◽  
Stationary Waves ◽  
Frequency Wave ◽  
Inverse Energy Cascade

Abstract An aquaplanet model is used to study the nature of the highly persistent low-frequency waves that have been observed in models forced by zonally symmetric boundary conditions. Using the Hayashi spectral analysis of the extratropical waves, the authors find that a quasi-stationary wave 5 belongs to a wave packet obeying a well-defined dispersion relation with eastward group velocity. The components of the dispersion relation with k ≥ 5 baroclinically convert eddy available potential energy into eddy kinetic energy, whereas those with k < 5 are baroclinically neutral. In agreement with Green’s model of baroclinic instability, wave 5 is weakly unstable, and the inverse energy cascade, which had been previously proposed as a main forcing for this type of wave, only acts as a positive feedback on its predominantly baroclinic energetics. The quasi-stationary wave is reinforced by a phase lock to an analogous pattern in the tropical convection, which provides further amplification to the wave. It is also found that the Pedlosky bounds on the phase speed of unstable waves provide guidance in explaining the latitudinal structure of the energy conversion, which is shown to be more enhanced where the zonal westerly surface wind is weaker. The wave’s energy is then trapped in the waveguide created by the upper tropospheric jet stream. In agreement with Green’s theory, as the equator-to-pole SST difference is reduced, the stationary marginally stable component shifts toward higher wavenumbers, while wave 5 becomes neutral and westward propagating. Some properties of the aquaplanet quasi-stationary waves are found to be in interesting agreement with a low frequency wave observed by Salby during December–February in the Southern Hemisphere so that this perspective on low frequency variability, apart from its value in terms of basic geophysical fluid dynamics, might be of specific interest for studying the earth’s atmosphere.

scholarly journals Dynamics of Eddy-Driven Low-Frequency Dipole Modes. Part III: Meridional Displacement of Westerly Jet Anomalies during Two Phases of NAO

2007 ◽  
Vol 64 (9) ◽  
pp. 3232-3248 ◽  
Author(s):  
Dehai Luo ◽  
Tingting Gong ◽  
Yina Diao
Keyword(s):  
Theoretical Model ◽  
Storm Track ◽  
Low Frequency ◽  
Stationary Wave ◽  
Negative Phase ◽  
Stationary Waves ◽  
The North ◽  
Westerly Jet ◽  
Two Phases ◽  
The North Atlantic Oscillation

Abstract In this paper, the north–south variability of westerly jet anomalies during the two phases of the North Atlantic Oscillation (NAO) is examined in a theoretical model. It is found that the north–south variability of the zonal mean westerly anomaly results from the interaction between the eddy-driven anomalous stationary waves with a dipole meridional structure (NAO anomalies) and topographically induced climatological stationary waves with a monopole structure, which is dependent upon the phase of the NAO. The westerly jet anomaly tends to shift northward during the positive NAO phase but southward during the negative phase. Synoptic-scale eddies tend to maintain westerly jet anomalies through the excitation of NAO anomalies, but the climatological stationary wave and its position relative to the eddy-driven anomalous stationary wave appear to dominate the north–south shift of westerly jet anomalies. On the other hand, it is shown that when the climatological stationary wave ridge is located downstream of the eddy-driven anomalous stationary wave, the storm track modulated by the NAO pattern splits into two branches for the negative phase, in which the northern branch is generally stronger than the southern one. However, the southern one can be dominant as the relative position between anomalous and climatological stationary waves is within a moderate range. The storm track for the positive phase tends to drift northeastward when there is a phase difference between the NAO anomaly and climatological stationary wave ridge downstream. Thus, it appears that the relationship between the NAO jets and storm tracks can be clearly seen from the present theoretical model.

Spatially amplifying modes of the Charney baroclinic-instability problem

1986 ◽  
Vol 170 ◽  
pp. 293-317 ◽  
Author(s):  
R. T. Pierrehumbert
Keyword(s):  
Broad Class ◽  
Baroclinic Instability ◽  
Surface Wind ◽  
Stationary Wave ◽  
Vertical Shear ◽  
Coriolis Parameter ◽  
Spatial Instability ◽  
Wide Range ◽  
Amplification Rate ◽  
Zero Frequency

We determine the circumstances under which baroclinic instability in the Charney model subjected to localized time-periodic forcing manifests itself as a wavetrain that oscillates at the source frequency and amplifies in space with distance from the source; analytical and numerical results describing the salient characteristics of such waves are presented. The spatially amplifying disturbance is a hitherto unsuspected part of the response to a pulsating source, and coexists with the more familiar neutral Rossby wavetrains; it is likely to play a role in a wide range of atmospheric and oceanic phenomena.The central results rely on a careful application of a causality criterion due to Briggs. These results illustrate a practical means of attacking spatial instability problems, which can be applied to a broad class of systems besides the one at hand. We have found that the Charney problem with positive vertical shear is not absolutely unstable, so long as the wind at the ground is non-negative. This implies that spatial instability and forced stationary-wave problems are well posed in an open domain under typical atmospheric circumstances.The amplifying waves appear on the downstream side of the source, have eastward (downstream) phase propagation and have wavelengths that increase monotonically with decreasing frequency, becoming infinite at zero frequency. When the surface wind is not too large, the spatial amplification rate has a single maximum near the frequency ωm= (f/N)Uz, wherefis the Coriolis parameter,Nis the stability frequency andUzis the vertical shear; the rate approaches zero at zero frequency and asymptotes algebraically to zero at large frequency for any positive surface wind. Distinct Charney and Green modes do not appear until the surface wind is made very large. The amplification rate at ωmbecomes infinite as surface wind approaches zero, suggesting a mechanism for the concentration of eddy activity.We also discuss the relationship of these results to the structure of low- and high-frequency atmospheric variability.

Modulational Instability and Stationary Waves for the Coupled Generalized Schrödinger-Boussinesq System

2011 ◽  
Vol 66 (3-4) ◽  
pp. 143-150 ◽  
Author(s):  
Zu-Feng Liang
Keyword(s):  
Modulational Instability ◽  
Low Frequency ◽  
Travelling Wave ◽  
Boussinesq System ◽  
Wave Number ◽  
Dispersive Media ◽  
Stationary Waves ◽  
Travelling Wave Solutions ◽  
Frequency Wave ◽  
General Dispersion

The coupled generalized Schr¨odinger-Boussinesq (SB) system, which can describe a highfrequency mode coupled to a low-frequency wave in dispersive media is investigated. First, we study the modulational instability (MI) of the SB system. As a result, the general dispersion relation between the frequency and the wave number of the modulating perturbations is derived, and thus a number of possible MI regions are identified. Then two classes of exact travelling wave solutions are obtained expressed in the general forms. Several explicit examples are presented.

scholarly journals Slow flow of a Bingham fluid in a shallow channel of finite width

2001 ◽  
Vol 431 ◽  
pp. 135-159 ◽  
Author(s):  
CHIANG C. MEI ◽  
MASATOSHI YUHI
Keyword(s):  
Transient Flow ◽  
Three Dimensional ◽  
Phase Speed ◽  
Stationary Wave ◽  
Channel Cross Section ◽  
Finite Width ◽  
Stationary Waves ◽  
Steady Flows ◽  
Bingham Plastic ◽  
Fluid Property

We present a theory for the three-dimensional flow of a Bingham-plastic fluid in a shallow and wide channel. Focusing attention on slow flows appropriate for gentle slopes, low discharge rates or the final stage of deposition, we ignore inertia and apply the long-wave approximation. For steady flows, the velocity distribution, total discharge, and section-averaged flux are obtained analytically in terms of the fluid property and the geometry of the channel cross-section. Nonlinear stationary waves, which connect a uniform depth upstream to another uniform depth downstream, are then investigated, for both wet and dry beds. A numerical scheme is applied to calculate the transient flow evolution. The final development of the stationary wave due to steady discharge upstream is obtained numerically and the relation between the tongue-like shape of the wave front and the fluid property is discussed. The phase speed of the stationary wave is also derived analytically. Finally, the transient spreading of a finite fluid mass released from a reservoir after a dam break is simulated numerically. The transient development of the front and the final extent of deposition are examined.

scholarly journals North Atlantic Multidecadal Variability Enhancing Decadal Extratropical Extremes in Boreal Late Summer in the Early Twenty-First Century

2020 ◽  
Vol 33 (14) ◽  
pp. 6047-6064 ◽  
Author(s):  
Jie Zhang ◽  
Zhiheng Chen ◽  
Haishan Chen ◽  
Qianrong Ma ◽  
Asaminew Teshome
Keyword(s):  
Energy Transfer ◽  
North Atlantic ◽  
Low Frequency ◽  
Late Summer ◽  
First Century ◽  
Stationary Waves ◽  
Frequency Wave ◽  
Multidecadal Variability ◽  
Longitudinal Temperature Gradient ◽  
Twenty First Century

AbstractIn the beginning of the twenty-first century, weather and climate extremes occurred more and more in extratropical summer, linked to the magnified amplitudes of quasi-stationary waves and external forcing. The study analyzes the relations between multidecadal extratropical extremes in boreal late summer and the North Atlantic (NA; 35°–65°N, 40°W–0°) multidecadal variability (NAMV) in the mid- to high latitudes. The results show that multidecadal extratropical extremes link with the intensified NAMV and the related positive–negative–positive (+ − +) zonal mode of sea surface temperature (SST). 1) The SST mode favors the eastward shift of the negative-phase NA oscillation (NNAO), with a latitudinal pattern of cyclone anomalies over the western European coast and anticyclones over Greenland; NNAO is helpful to baroclinic energy transfer and a longitudinal wavelike pattern. 2) The SST mode and the eddy-driven jet of NNAO are conducive to a southeast extension of the NA jet in close conjunction with the Afro-Asian jet, thereby enhancing the jet waveguide and barotropic energy transfer for the maintenance of a low-frequency wave. 3) The effect of the intensified NAMV on warming Europe contributes to the longitudinal temperature gradient–like “cooling ocean and warming land” pattern, which enhances the meridional wind and wave amplitude of the low-frequency wave. Based on these causes, the intensified NAMV and the + − + SST mode favor the enhancement of the low-frequency wave and quasi-resonant probability, which magnifies the amplitude of the quasi-stationary wave and enhances extratropical extremes on the decadal time scale.

scholarly journals Wave dispersion in pulsar plasma. Part 1. Plasma rest frame

2019 ◽  
Vol 85 (3) ◽  
Author(s):  
M. Z. Rafat ◽  
D. B. Melrose ◽  
A. Mastrano
Keyword(s):  
Dispersion Relation ◽  
Rest Frame ◽  
Resonance Condition ◽  
Low Frequency ◽  
Phase Speed ◽  
Wave Dispersion ◽  
Relativistic Plasma ◽  
Dispersion Function ◽  
One Dimensional ◽  
Mode Dispersion

Wave dispersion in a pulsar plasma (a one-dimensional, strongly magnetized, pair plasma streaming highly relativistically with a large spread in Lorentz factors in its rest frame) is discussed, motivated by interest in beam-driven wave turbulence and the pulsar radio emission mechanism. In the rest frame of the pulsar plasma there are three wave modes in the low-frequency, non-gyrotropic approximation. For parallel propagation (wave angle$\unicode[STIX]{x1D703}=0$) these are referred to as the X, A and L modes, with the X and A modes having dispersion relation$|z|=z_{\text{A}}\approx 1-1/2\unicode[STIX]{x1D6FD}_{\text{A}}^{2}$, where$z=\unicode[STIX]{x1D714}/k_{\Vert }c$is the phase speed and$\unicode[STIX]{x1D6FD}_{\text{A}}c$is the Alfvén speed. The L mode dispersion relation is determined by a relativistic plasma dispersion function,$z^{2}W(z)$, which is negative for$|z|<z_{0}$and has a sharp maximum at$|z|=z_{\text{m}}$, with$1-z_{\text{m}}<1-z_{0}\ll 1$. We give numerical estimates for the maximum of$z^{2}W(z)$and for$z_{\text{m}}$and$z_{0}$for a one-dimensional Jüttner distribution. The L and A modes reconnect, for$z_{\text{A}}>z_{0}$, to form the O and Alfvén modes for oblique propagation ($\unicode[STIX]{x1D703}\neq 0$). For$z_{\text{A}}<z_{0}$the Alfvén and O mode curves reconnect forming a new mode that exists only for$\tan ^{2}\unicode[STIX]{x1D703}\gtrsim z_{0}^{2}-z_{\text{A}}^{2}$. The L mode is the nearest counterpart to Langmuir waves in a non-relativistic plasma, but we argue that there are no ‘Langmuir-like’ waves in a pulsar plasma, identifying three features of the L mode (dispersion relation, ratio of electric to total energy and group speed) that are not Langmuir like. A beam-driven instability requires a beam speed equal to the phase speed of the wave. This resonance condition can be satisfied for the O mode, but only for an implausibly energetic beam and only for a tiny range of angles for the O mode around$\unicode[STIX]{x1D703}\approx 0$. The resonance is also possible for the Alfvén mode but only near a turnover frequency that has no counterpart for Alfvén waves in a non-relativistic plasma.

scholarly journals Planetary geostrophic Boussinesq dynamics: barotropic flow, baroclinic instability and forced stationary waves

2020 ◽  
Author(s):  
Stamen Dolaptchiev ◽  
Ulrich Achatz ◽  
Thomas Reitz
Keyword(s):  
Spatial Scales ◽  
Baroclinic Instability ◽  
Surface Wind ◽  
Temperature Fields ◽  
Stationary Waves ◽  
Barotropic Flow ◽  
Model Response ◽  
Flow Through ◽  
Baroclinic Flow ◽  
Boussinesq Fluid

&lt;p&gt;Motions on planetary spatial scales in the atmosphere are governed by&lt;br&gt;the planetary geostrophic equations. However, not much attention has&lt;br&gt;been paid to the interaction between the baroclinic and barotropic&lt;br&gt;flow within the planetary geostrophic scaling. This is the focus of&lt;br&gt;the present study by utilizing planetary geostrophic equations for a&lt;br&gt;Boussinesq fluid supplemented by an asymptotically derived evolution&lt;br&gt;equation for the barotropic flow. The latter is effected by meridional&lt;br&gt;momentum flux due to baroclinic flow and drag by the surface wind. The&lt;br&gt;barotropic wind on the other hand affects the baroclinic flow through&lt;br&gt;buoyancy advection. By relaxing towards a prescribed buoyancy profile&lt;br&gt;the model produces realistic major features of the zonally symmetric&lt;br&gt;wind and temperature fields. We show that there is considerable&lt;br&gt;cancelation between the barotropic and the baroclinic surface zonal&lt;br&gt;mean zonal wind. The linear and nonlinear model response to steady&lt;br&gt;diabatic zonally asymmetric forcing is investigated. The arising&lt;br&gt;stationary waves are interpreted in terms of analytical solutions. We&lt;br&gt;also study the problem of baroclinic instability on the sphere within&lt;br&gt;the present model.&lt;/p&gt;&lt;p&gt;Reference: Dolaptchiev, S. I., Achatz, U. and Th. Reitz, 2019: Planetary&lt;br&gt;geostrophic Boussinesq dynamics: barotropic flow, baroclinic&lt;br&gt;instability and forced stationary waves, Quart. J. Roy. Met. Soc., 145: 3751-3765.&lt;/p&gt;

Testing the Limits and Breakdown of the Nonacceleration Theorem for Orographic Stationary Waves

2020 ◽  
Vol 77 (5) ◽  
pp. 1513-1529
Author(s):  
Nicholas J. Lutsko
Keyword(s):  
General Circulation ◽  
Large Scale ◽  
Surface Wind ◽  
Circulation Model ◽  
Wave Model ◽  
Stationary Wave ◽  
Surface Wind Speed ◽  
Maximum Height ◽  
Stationary Waves ◽  
Mean Flow

Abstract The nonacceleration theorem states that the torque exerted on the atmosphere by orography is exactly balanced by the convergence of momentum by the stationary waves that the orography excites. This balance is tested in simulations with a stationary wave model and with a dry, idealized general circulation model (GCM), in which large-scale orography is placed at the latitude of maximum surface wind speed. For the smallest mountain considered (maximum height H = 0.5 m), the nonacceleration balance is nearly met, but the damping in the stationary wave model induces an offset between the stationary eddy momentum flux (EMF) convergence and the mountain torque, leading to residual mean flow changes. A stationary nonlinearity appears for larger mountains (H ≥ 10 m), driven by preferential deflection of the flow around the poleward flank of the orography, and causes further breakdown of the nonacceleration balance. The nonlinearity grows as H is increased, and is stronger in the GCM than in the stationary wave model, likely due to interactions with transient eddies. The midlatitude jet shifts poleward for H ≤ 2 km and equatorward for larger mountains, reflecting changes in the transient EMFs, which push the jet poleward for smaller mountains and equatorward for larger mountains. The stationary EMFs consistently force the jet poleward. These results add to our understanding of how orography affects the atmosphere’s momentum budget, providing insight into how the nonacceleration theorem breaks down; the roles of stationary nonlinearities and transients; and how orography affects the strength and latitude of eddy-driven jets.

scholarly journals A Diagnosis of the Seasonally and Longitudinally Varying Midlatitude Circulation Response to Global Warming*

2014 ◽  
Vol 71 (7) ◽  
pp. 2489-2515 ◽  
Author(s):  
Isla R. Simpson ◽  
Tiffany A. Shaw ◽  
Richard Seager
Keyword(s):  
Global Warming ◽  
Wind Stress ◽  
High Frequency ◽  
Surface Wind ◽  
Coupled Model ◽  
Stationary Flow ◽  
Stationary Wave ◽  
Stationary Waves ◽  
Surface Wind Stress ◽  
Poleward Shift

Abstract Zonal-mean or basin-mean analyses often conclude that the midlatitude circulation will undergo a poleward shift with global warming. In this study, the models from phase 5 of the Coupled Model Intercomparison Project are used to provide a detailed examination of midlatitude circulation change as a function of longitude and season. The two-dimensional vertically integrated momentum budget is used to identify the dominant terms that maintain the anomalous surface wind stress, thereby allowing a distinction between features that are maintained by high-frequency eddies and those that involve changes in the lower-frequency or stationary flow. In the zonal mean, in each season and hemisphere there is a poleward shifting of the midlatitude surface wind stress, primarily maintained by high-frequency transient eddies. This is not necessarily the case locally. In the Southern Hemisphere, for the most part, the interpretation of the response as being a high-frequency eddy-driven poleward shifting of the midlatitude westerlies holds true. The Northern Hemisphere is considerably more complex with only the fall months showing a robust poleward shift of both the Atlantic and Pacific jets. During the winter months the jet in the east Pacific actually shifts equatorward and the Atlantic jet strengthens over Europe. An important role for altered climatological stationary waves in these responses is found. This motivates future work that should focus on zonal asymmetries and stationary wave changes, as well as the changes in high-frequency transients that bring about the poleward shifting of the westerlies in the zonal mean.

Resonant interactions between topographic planetary waves in a continuously stratified fluid

1978 ◽  
Vol 84 (4) ◽  
pp. 769-793 ◽  
Author(s):  
Lawrence A. Mysak
Keyword(s):  
Low Frequency ◽  
Phase Speed ◽  
Stratified Fluid ◽  
Planetary Waves ◽  
Buoyancy Frequency ◽  
Frequency Wave ◽  
Resonant Interactions ◽  
Frequency Correction ◽  
Resonant Triads ◽  
The Waves

The resonant interactions between topographic planetary waves in a continuously stratified fluid are investigated theoretically. The interacting waves form a resonant triad and travel along a channel with a uniformly sloping bottom. The basic state stratification in the channel is characterized by a constant buoyancy frequency. The existence of solutions to the quadratic resonance conditions is established graphically. Each wave by itself is a bottom-intensified oscillation of the type discovered by Rhines (1970) except for the addition of a small positive frequency correction. This correction must be included to satisfy higher-order terms in the bottom boundary condition. For strong stratification (r2[Gt ]L2, wherer= internal deformation radius andL= channel width), the waves are strongly bottom-trapped and this frequency correction is negligible. For weak stratification (r2[Lt ]L2) the waves are barotropic and the frequency correction isO(δ), where δ = fractional change in depth across the channel. In many oceanic contexts, δ lies in the range 0·1-0·4 and therefore this correction can produce a significant change in the phase speed. The amplitudes of the waves in the triad obey the classical gyroscopic equations usually encountered in quadratic resonance problems. In particular, the amplitudes evolve on the slow time scale\[ t=O(1/f_0\delta^2), \]which for our scaling assumptions is alsoO(1/f0Ro), whereRois the Rossby number.The results are applied to the Norwegian continental slope region. It is shown that, in this vicinity, there may exist resonant triads consisting of two short, high-frequency waves (periods around 3-4 days) and one long, low-frequency wave (period around 9 days).

Sign in / Sign up

Export Citation Format

Share Document