Jet Interaction and the Influence of a Minimum Phase Speed Bound on the Propagation of Eddies

2013 ◽  
Vol 70 (8) ◽  
pp. 2614-2628 ◽  
Author(s):  
Amanda K. O'Rourke ◽  
Geoffrey K. Vallis
Keyword(s):  
Phase Speed ◽  
Zonal Flow ◽  
Separation Distance ◽  
Long Waves ◽  
Minimum Phase ◽  
Planetary Scale ◽  
Subtropical Jet ◽  
Zonal Wavenumber ◽  
Propagating Waves ◽  
Cospectral Analysis

Abstract The feedback between planetary-scale eddies and analogs of the midlatitude eddy-driven jet and the subtropical jet is investigated in a barotropic β-plane model. In the model the subtropical jet is generated by a relaxation process and the eddy-driven jet by an imposed wavemaker. A minimum zonal phase speed bound is proposed in addition to the established upper bound, where the zonal phase speed of waves must be less than that of the zonal mean zonal flow. Cospectral analysis of eddy momentum flux convergence shows that eddy activity is generally restricted by these phase speed bounds. The wavenumber-dependent minimum phase speed represents a turning line for meridionally propagating waves. By varying the separation distance between the relaxation and stirring regions, it is found that a sustained, double-jet state is achieved when either a critical or turning latitude forms in the interjet region. The interjet turning latitude filters eddies by zonal wavenumber such that shorter waves tend to be reflected off of the relaxed jet and are confined to the eddy-driven jet. The interjet region is transparent to long waves that act to blend the jets and may be associated with barotropic instability. The eddy-driven and relaxed jets tend to merge owing to the propagation of these long waves through the relaxed jet waveguide.

scholarly journals Meridional Propagation of Planetary-Scale Waves in Vertical Shear: Implication for the Venus Atmosphere

2006 ◽  
Vol 63 (6) ◽  
pp. 1623-1636 ◽  
Author(s):  
Takeshi Imamura
Keyword(s):  
Numerical Solutions ◽  
Middle Atmosphere ◽  
Phase Speed ◽  
Momentum Transport ◽  
Vertical Shear ◽  
Zonal Flows ◽  
Planetary Scale ◽  
Propagating Waves ◽  
Low Latitudes ◽  
Zonal Propagation

Abstract It is shown that planetary-scale waves are inherently accompanied by latitudinal momentum transport when they propagate vertically in vertically sheared zonal flows. Because of the dependence of the wave's latitudinal scale on the intrinsic phase speed, positive (negative) vertical shear should force prograde (retrograde) waves to focus equatorward and retrograde (prograde) waves to expand poleward in the course of upward propagation. Consequently, Eliassen–Palm (EP) flux vectors are tilted from the vertical and nonzero latitudinal momentum fluxes occur. The direction of momentum transport should always be equatorward (poleward) in positive (negative) vertical shear irrespective of the zonal propagation direction. The idea was applied to upwardly propagating waves in the Venusian middle atmosphere, where vertical shear of strong midlatitude jets and equatorial superrotation exist. Numerical solutions showed that Kelvin and prograde inertio-gravity waves focus equatorward and mixed Rossby–gravity and Rossby waves expand poleward below the cloud top. The former is attributed primarily to the vertical shear of the superrotation, while the latter to the vertical shear beneath the midlatitude jets. Such characteristics of planetary-scale waves will cause angular momentum separation between high and low latitudes and, at least partly, contribute to the maintenance of the superrotation.

Planetary (Rossby), Inertia-Gravity (Poincaré) and Kelvin waves on the f-plane and β-plane in the presence of a uniform zonal flow

2021 ◽  
Author(s):  
Yair De-Leon ◽  
Chaim I. Garfinkel ◽  
Nathan Paldor
Keyword(s):  
Numerical Solutions ◽  
Bottom Topography ◽  
Phase Speed ◽  
Zonal Flow ◽  
Dispersion Curves ◽  
Kelvin Waves ◽  
Linear Wave ◽  
Hermite Function ◽  
Mean Flow ◽  
Zonal Wavenumber

<p>A linear wave theory of the Rotating Shallow Water Equations (RSWE) is developed in a channel on either the mid-latitude f-plane/β-plane or on the equatorial β-plane in the presence of a uniform mean zonal flow that is balanced geostrophically by a meridional gradient of the fluid surface height. We show that this surface height gradient is a potential vorticity (PV) source that generates Rossby waves even on the f-plane similar to the generation of these waves by PV sources such as the β–effect, shear of the mean flow and bottom topography. Numerical solutions of the RSWE show that the resulting planetary (Rossby), Inertia-Gravity (Poincaré) and Kelvin-like waves differ from their counterparts without mean flow in both their phase speeds and meridional structures. Doppler shifting of the “no mean-flow” phase speeds does not account for the difference in phase speeds, and the meridional structure does not often oscillate across the channel but is trapped near one the channel's boundaries in mid latitudes or behaves as Hermite function in the case of an equatorial channel. The phase speed of Kelvin-like waves is modified by the presence of a mean flow compared to the classical gravity wave speed but their meridional velocity does not vanish. The gaps between the dispersion curves of adjacent Poincaré modes are not uniform but change with the zonal wavenumber, and the convexity of the dispersion curves also changes with the zonal wavenumber. In some cases, the Kelvin-like dispersion curve crosses those of Poincaré modes, but it is not an evidence for the existence of instability since the Kelvin waves are not part of the solutions of an eigenvalue problem. </p>

scholarly journals Southern Annular Mode Dynamics in Observations and Models. Part II: Eddy Feedbacks

2013 ◽  
Vol 26 (14) ◽  
pp. 5220-5241 ◽  
Author(s):  
Isla R. Simpson ◽  
Theodore G. Shepherd ◽  
Peter Hitchcock ◽  
John F. Scinocca
Keyword(s):  
Negative Feedback ◽  
Planetary Wave ◽  
Southern Annular Mode ◽  
Summer Season ◽  
Substantial Contribution ◽  
Mean Flow ◽  
Annular Mode ◽  
Planetary Scale ◽  
Zonal Wavenumber ◽  
Climatological Circulation

Abstract Many global climate models (GCMs) have trouble simulating southern annular mode (SAM) variability correctly, particularly in the Southern Hemisphere summer season where it tends to be too persistent. In this two-part study, a suite of experiments with the Canadian Middle Atmosphere Model (CMAM) is analyzed to improve the understanding of the dynamics of SAM variability and its deficiencies in GCMs. Here, an examination of the eddy–mean flow feedbacks is presented by quantification of the feedback strength as a function of zonal scale and season using a new methodology that accounts for intraseasonal forcing of the SAM. In the observed atmosphere, in the summer season, a strong negative feedback by planetary-scale waves, in particular zonal wavenumber 3, is found in a localized region in the southwest Pacific. It cancels a large proportion of the positive feedback by synoptic- and smaller-scale eddies in the zonal mean, resulting in a very weak overall eddy feedback on the SAM. CMAM is deficient in this negative feedback by planetary-scale waves, making a substantial contribution to its bias in summertime SAM persistence. Furthermore, this bias is not alleviated by artificially improving the climatological circulation, suggesting that climatological circulation biases are not the cause of the planetary wave feedback deficiency in the model. Analysis of the summertime eddy feedbacks in the models from phase 5 of the Coupled Model Intercomparison Project (CMIP5) confirms that this is indeed a common problem among GCMs, suggesting that understanding this planetary wave feedback and the reason for its deficiency in GCMs is key to improving the fidelity of simulated SAM variability in the summer season.

scholarly journals Planetary Scale Selection of the Madden–Julian Oscillation*

2009 ◽  
Vol 66 (8) ◽  
pp. 2429-2443 ◽  
Author(s):  
Tim Li ◽  
Chunhua Zhou
Keyword(s):  
Boundary Layer ◽  
Rossby Wave ◽  
Initial Perturbation ◽  
Madden Julian Oscillation ◽  
Kelvin Wave ◽  
Scale Selection ◽  
Planetary Scale ◽  
Zonal Wavenumber ◽  
Nonlinear Heating ◽  
Selection Of

Abstract Numerical experiments with a 2.5-layer and a 2-level model are conducted to examine the mechanism for the planetary scale selection of the Madden–Julian oscillation (MJO). The strategy here is to examine the evolution of an initial perturbation that has a form of the equatorial Kelvin wave at zonal wavenumbers of 1 to 15. In the presence of a frictional boundary layer, the most unstable mode prefers a short wavelength under a linear heating; but with a nonlinear heating, the zonal wavenumber 1 grows fastest. This differs significantly from a model without the boundary layer, in which neither linear nor nonlinear heating leads to the long wave selection. Thus, the numerical simulations point out the crucial importance of the combined effect of the nonlinear heating and the frictional boundary layer in the MJO planetary scale selection. The cause of this scale selection under the nonlinear heating is attributed to the distinctive phase speeds between the dry Kelvin wave and the wet Kelvin–Rossby wave couplet. The faster dry Kelvin wave triggered by a convective branch may catch up and suppress another convective branch, which travels ahead of it at the phase speed of the wet Kelvin–Rossby wave couplet if the distance between the two neighboring convective branches is smaller than a critical distance (about 16 000 km). The interference between the dry Kelvin wave and the wet Kelvin–Rossby wave couplet eventually dissipates and “filters out” shorter wavelength perturbations, leading to a longwave selection. The boundary layer plays an important role in destabilizing the MJO through frictional moisture convergences and in retaining the in-phase zonal wind–pressure structure.

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 Wave and Jet Maintenance in Different Flow Regimes

2016 ◽  
Vol 73 (6) ◽  
pp. 2465-2484 ◽  
Author(s):  
Orli Lachmy ◽  
Nili Harnik
Keyword(s):  
Wave Energy ◽  
Wave Spectrum ◽  
Flow Regimes ◽  
Wave Mode ◽  
Hadley Cell ◽  
Model Parameters ◽  
Mean Flow ◽  
Eddy Heat Flux ◽  
Subtropical Jet ◽  
Zonal Wavenumber

Abstract The wave spectrum and zonal-mean-flow maintenance in different flow regimes of the jet stream are studied using a two-layer modified quasigeostrophic (QG) model. As the wave energy is increased by varying the model parameters, the flow transitions from a subtropical jet regime to a merged jet regime and then to an eddy-driven jet regime. The subtropical jet is maintained at the Hadley cell edge by zonal-mean advection of momentum, while eddy heat flux and eddy momentum flux convergence (EMFC) are weak and concentrated far poleward. The merged jet is narrow and persistent and is maintained by EMFC from a narrow wave spectrum, dominated by zonal wavenumber 5. The eddy-driven jet is wide and fluctuating and is maintained by EMFC from a wide wave spectrum. The wave–mean flow feedback mechanisms that maintain each regime are explained qualitatively. The regime transitions are related to transitions in the wave spectrum. An analysis of the wave energy spectrum budget and a comparison with a quasi-linear version of the model show that the balance maintaining the spectrum in the merged and subtropical jet regimes is mainly a quasi-linear balance, whereas in the eddy-driven jet regime nonlinear inverse energy cascade takes place. The amplitude and wavenumber of the dominant wave mode in the merged and subtropical jet regimes are determined by the constraint that this mode would produce the wave fluxes necessary for maintaining a mean flow that is close to neutrality. In contrast, the equilibrated mean flow in the eddy-driven jet regime is weakly unstable.

The stability of spatially periodic flows

1981 ◽  
Vol 108 ◽  
pp. 461-474 ◽  
Author(s):  
D. N. Beaumont
Keyword(s):  
Velocity Profile ◽  
Phase Speed ◽  
Neutral Curve ◽  
Long Waves ◽  
Inviscid Fluid ◽  
Periodic Flows ◽  
A Value ◽  
Parallel Flows ◽  
Spatially Periodic ◽  
The Stability

The stability characteristics for spatially periodic parallel flows of an incompressible fluid (both inviscid and viscous) are studied. A general formula for the determination of the stability characteristics of periodic flows to long waves is obtained, and applied to approximate numerically the stability curves for the sinusoidal velocity profile. The neutral curve for the sinusoidal velocity profile is obtained analytically. The stability of two broken-line velocity profiles in an inviscid fluid is studied and the results are used to describe the overall pattern for the sinusoidal velocity profile in the case of long waves. In an inviscid fluid it is found that all periodic flows (other than the trivial flow in which the basic velocity is constant) are unstable to long waves with a value of the phase speed determined by simple integrals of the basic flow. In a viscous fluid it is found that the sinusoidal velocity profile is very unstable with the inviscid solution being a good approximation to the solution of the viscous problem when the value of the Reynolds number is greater than about 20.

scholarly journals Tibetan High and Upper Tropospheric Tropical Circulations during Northern Summer

1973 ◽  
Vol 54 (12) ◽  
pp. 1234-1250 ◽  
Author(s):  
T. N. Krishnamurti ◽  
S. M. Daggupaty ◽  
Jay Fein ◽  
Masao Kanamitsu ◽  
John D. Lee
Keyword(s):  
General Circulation ◽  
Large Scale ◽  
Zonal Flow ◽  
General Circulation Models ◽  
Initial Time ◽  
Necessary Condition ◽  
Motion Field ◽  
High Pressure Cell ◽  
Northern Summer ◽  
Zonal Wavenumber

The zonally asymmetric climatology of the tropical large-scale motion field is an interesting GARP topic. Understanding of the maintenance of various quasi-stationary features will be a challenging problem during the FGGE (the First GARP Global Experiment) and Monex (the Monsoon Experiment). In this paper we present some current thoughts that are relevant to the climatology of the tropical upper troposphere during the northern summer. A review of some of the results from various numerical general circulation models and theoretical studies is presented for northern summer conditions. The relative success or failure of simulations of 200-mb climatology is discussed. It is pointed out that a proper simulation of the belt of anticyclones over the Asian highlands is somewhat crucial for a proper simulation of the summer climatology over the rest of the tropics. Observations of the semipermanence of the Tibetan high pressure cell during northern summer at 200 mb suggests that it acts somewhat like a barrier. In order to illustrate this we consider a problem related to the evolution of barotropic non-divergent flows past a barrier. The flows are initially zonal, with speeds varying in the north-south direction according to northern summer observations. The barrier, whose shape is based on observations of a blocking thermal high, is impulsively introduced at initial time. The flows are kept zonal at frictionless walls at 25S and 45N. The initial north-south distribution of the zonal flows is shown to have no inflection point in its profile, thus it does not satisfy the necessary condition for barotropic instability. The presence of an impulsively introduced barrier, however, results in the evolution of transient as well as steady wave motions in long term numerical integrations. It is shown that a 30-day mean motion field contains many of the well known climatological features such as the African high, the mid-Atlantic trough, the mid-Pacific trough, the Mexican high and a weak easterly jet south of the Tibetan high. Calculations of kinetic energy exchanges between waves and zonal flow in this simple experiment is compared with corresponding calculations for tropical observations and recent general circulation experiments carried out by Abbott. The impulsively introduced barrier simulates an energy source for zonal wavenumber 1, quite similar to observations in a tropical belt. Although this experiment is fairly crude, it is found to be very illustrative in many respects. Many diverse experiments along these lines can be carried out to reveal various aspects of atmospheric circulations.

scholarly journals Rossby waves and two-dimensional turbulence in a large-scale zonal jet

1987 ◽  
Vol 183 ◽  
pp. 467-509 ◽  
Author(s):  
Theodore G. Shepherd
Keyword(s):  
Large Scale ◽  
Zonal Flow ◽  
Order Effect ◽  
Spatial Inhomogeneity ◽  
Mean Flow ◽  
Scale Separation ◽  
Zonal Flows ◽  
Beta Plane ◽  
Zonal Wavenumber ◽  
Scale Shear

The theory of homogeneous barotropic beta-plane turbulence is here extended to include effects arising from spatial inhomogeneity in the form of a zonal shear flow. Attention is restricted to the geophysically important case of zonal flows that are barotropically stable and are of larger scale than the resulting transient eddy field.Because of the presumed scale separation, the disturbance enstrophy is approximately conserved in a fully nonlinear sense, and the (nonlinear) wave-mean-flow interaction may be characterized as a shear-induced spectral transfer of disturbance enstrophy along lines of constant zonal wavenumber k. In this transfer the disturbance energy is generally not conserved. The nonlinear interactions between different disturbance components are turbulent for scales smaller than the inverse of Rhines's cascade-arrest scale κβ≡ (β0/2urms)½ and in this regime their leading-order effect may be characterized as a tendency to spread the enstrophy (and energy) along contours of constant total wavenumber κ ≡ (k2 + l2)½. Insofar as this process of turbulent isotropization involves spectral transfer of disturbance enstrophy across lines of constant zonal wavenumber k, it can be readily distinguished from the shear-induced transfer which proceeds along them. However, an analysis in terms of total wavenumber K alone, which would be justified if the flow were homogeneous, would tend to mask the differences.The foregoing theoretical ideas are tested by performing direct numerical simulation experiments. It is found that the picture of classical beta-plane turbulence is altered, through the effect of the large-scale zonal flow, in the following ways: (i) while the turbulence is still confined to KKβ, the disturbance field penetrates to the largest scales of motion; (ii) the larger disturbance scales K < Kβ exhibit a tendency to meridional rather than zonal anisotropy, namely towards v2 > u2 rather than vice versa; (iii) the initial spectral transfer rate away from an isotropic intermediate-scale source is significantly enhanced by the shear-induced transfer associated with straining by the zonal flow. This last effect occurs even when the large-scale shear appears weak to the energy-containing eddies, in the sense that dU/dy [Lt ] κ for typical eddy length and velocity scales.

scholarly journals A Major Stratospheric Sudden Warming Event in January 2009

2010 ◽  
Vol 67 (6) ◽  
pp. 2052-2069 ◽  
Author(s):  
Yayoi Harada ◽  
Atsushi Goto ◽  
Hiroshi Hasegawa ◽  
Norihisa Fujikawa ◽  
Hiroaki Naoe ◽  
...  
Keyword(s):  
Wave Packets ◽  
Development Stage ◽  
Japan Meteorological Agency ◽  
Eastern Siberia ◽  
Climate Data ◽  
Stratospheric Sudden Warming ◽  
Upper Troposphere ◽  
Planetary Scale ◽  
The North ◽  
Zonal Wavenumber

Abstract The major stratospheric sudden warming (SSW) event of January 2009 is analyzed using the Japan Meteorological Agency (JMA) Climate Data Assimilation System (JCDAS). This SSW event is characterized by the extraordinary predominance of the planetary-scale wave of zonal wavenumber 2 (wave 2). The total amount of the upward Eliassen–Palm (EP) flux for wave 2 was the strongest since the winter of 1978/79. It is found that the remarkable development of the upper troposphere ridge over Alaska played important roles in the SSW in January 2009. During the first development stage, the ridge excited wave packets upward as well as eastward over around Alaska. The eastward-propagating packets intensified a trough over eastern Siberia, which led to the development of the planetary wave over eastern Siberia during the second development stage. The results of this study indicate that the pronounced wave-2 pattern observed in the stratosphere was brought about by accumulative effects of rather localized propagation of wave packets from the troposphere during the course of this SSW event rather than by the ubiquitous propagation of planetary-scale disturbances in the troposphere. The features of the SSW in January 2009 are quite similar to those during the major stratospheric warming event in February 1989: both SSWs are characterized by the predominance of wave 2, the remarkable development of the upper troposphere ridge over around Alaska, and positive SSTs in the eastern part of the North Pacific corresponding to a La Niña condition.

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