Absolute Vorticity Gradient Research Articles

On the Dynamics of Indian Ocean Teleconnections into the Southern Hemisphere during Austral Winter

Abstract Stationary Rossby waves, forced by the Indian Ocean dipole (IOD), have an important role in Southern Hemisphere (SH) weather and climate, including promoting Australian drought and driving Antarctic sea ice variations. However, the dynamics of these teleconnections are not fully understood. During winter, the subtropical jet (STJ) should prohibit continuous propagation of a stationary Rossby wave into the SH extratropics due to the negative meridional gradient of absolute vorticity () on its poleward flank. The mechanisms that enable this teleconnection are investigated using observational and reanalysis datasets, a hierarchy of atmospheric model experiments and Rossby wave diagnostics. We conduct 90-member simulations using the Community Atmosphere Model, version 5, with an imposed local diabatic heating anomaly over the eastern Indian Ocean. We find an initial zonal propagation along the STJ waveguide, but after about 10 days, a poleward-arcing wave train appears in the extratropics that has the characteristics of the observed IOD teleconnection. Our results suggest that the Rossby wave can overcome the negative barrier by (i) propagating directly poleward in the midtroposphere and thus avoiding this evanescent region in the upper troposphere, (ii) partly propagating directly through this barrier, and (iii) propagating around this barrier farther upstream to the west. A transient eddy feedback, previously postulated to be the key mechanism to allow the stationary Rossby wave to appear on the poleward side of the negative region, reinforces the response but is not a requisite, which we confirm through comparison with a simplified linear model.

Possible Dynamic Mechanisms of High‐ and Low‐Latitude Wave Trains Over Eurasia and Their Impacts on Air Pollution Over the North China Plain in Early Winter

AbstractThe Rossby wave train in boreal winter sometimes bifurcates into two branches near the Mediterranean, sometimes not. However, causes for bifurcating of the wave train are still being debated. Additionally, discussions about the differences in the deterioration ability of these wave trains on air pollution are also insufficient. This study uses the empirical orthogonal function (EOF) to obtain two dominant modes of the November‐January season wave trains over Eurasia and discusses their different influences on air pollution over the North China Plain (NCP). From the EOF1 mode, bifurcation of the wave train appears to stem from the Rossby wave reflection near the Mediterranean because the Rossby wave source is located outside of a strong absolute vorticity gradient. From the EOF2 mode, the wave train propagates only along the subtropical westerly jet because the Rossby wave source is located inside of a strong absolute vorticity gradient, so that the wave train tends to be refracted near the Mediterranean. In addition, the wave train associated with the EOF1 is suggested to be related to the eastern Pacific El Niño. The eastern Pacific El Niño tends to force a wave train propagating into East Asia under the charger effect from positive feedback of air‐sea coupling near the far eastern Atlantic and Mediterranean, while the wave train associated with the EOF2 is suggested to be mainly induced by natural internal variability. Furthermore, the results indicate that the bifurcation type wave train tends to cause higher PM2.5 concentrations over the NCP through a strengthened Northeast Asia anomalous anticyclone.

Combined impacts of ENSO and MJO on the 2015 growing season drought on the Canadian Prairies

Abstract. Warm-season precipitation on the Canadian Prairies plays a crucial role in agricultural production. This research investigates how the early summer 2015 drought across the Canadian Prairies is related to the tropical Pacific forcing. The significant deficit of precipitation in May and June 2015 coincided with a warm phase of the El Niño–Southern Oscillation (ENSO) and a negative phase of Madden–Julian Oscillation (MJO)-4 index, which favour a positive geopotential height (GPH) anomaly in western Canada. Our further investigation during the instrumental record (1979–2016) shows that warm-season precipitation in the Canadian Prairies and the corresponding atmospheric circulation anomalies over western Canada teleconnected with the lower boundary conditions in the tropical western Pacific. Our results indicate that MJO can play a crucial role in determining the summer precipitation anomaly in the western Canadian Prairies when the equatorial central Pacific is warmer than normal (NINO4 > 0) and MJO is more active. This teleconnection is due to the propagation of a stationary Rossby wave that is generated in the MJO-4 index region. When the tropical convection around MJO-4 index region (western tropical Pacific, centred over 140∘ E) is more active than normal (NINO4 > 0), Rossby wave trains originate from the western Pacific with wavenumbers determined by the background mean wind and meridional absolute vorticity gradient. Under warm NINO4 conditions waves are generated with smaller wavenumbers compared to cold NINO4 conditions. These waves under warm NINO4 can propagate into the mid-latitudes over North America, causing a persistent anomalous ridge in the upper level over western Canada, which favours dry conditions over the region.

Effect of boreal spring precipitation anomaly pattern change in the late 1990s over tropical Pacific on the atmospheric teleconnection

Observational evidence showed that the leading mode of precipitation variability over the tropical Pacific during boreal spring experienced a pronounced interdecadal change around the late 1990s, characterized by a precipitation pattern shift from an eastern Pacific (EP) type to a central Pacific (CP) type. The distinct impacts of such a precipitation pattern shift on the extratropical atmospheric teleconnection were examined. An apparent poleward teleconnection extending from the tropics to the North Atlantic region was observed after 1998, while, there was no significant teleconnection before 1998. To understand why only the CP–type precipitation mode is associated with a striking atmospheric teleconnection after 1998, diagnostic analyses with the Eliassen–Palm flux and Rossby wave source (RWS) based on the barotropic vorticity equation were performed. The results show that for the EP–type precipitation mode, no significant RWS anomalies appeared over the subtropical Pacific due to the opposite effect of the vortex stretching and absolute vorticity advection processes. For the CP–type precipitation mode, however, there are both significant vorticity forcing source over the subtropical CP and clear poleward–propagation of Rossby wave. The spatial distribution of the CP–type precipitation pattern tends to excite a conspicuous anomalous southerly and a well–organized negative vorticity center over the subtropical CP where both the mean absolute vorticity gradient and mean divergence flow are large, hence, the interaction between the heating–induced anomalous circulation and the basic state made the generation of Rossby waves conceivable and effective. Such corresponding teleconnection responses to the prescribed heating were also examined by using a Linear Baroclinic Model (LBM). It turned out that significant poleward teleconnection pattern is only caused by the CP–type precipitation mode, rather than by the EP–type precipitation mode. Further sensitive experiments demonstrated that the change in spring basic state before and after 1998 played a relatively minor role in exciting such a teleconnection pattern, when compared with the tropical precipitation anomaly pattern change.

Understanding Rossby wave trains forced by the Indian Ocean Dipole

Convective variations over the tropical Indian Ocean associated with ENSO and the Indian Ocean Dipole force a Rossby wave train that appears to emanate poleward and eastward to the south of Australia and which causes climate variations across southern Australia and more generally throughout the Southern Hemisphere extratropics. However, during austral winter, the subtropical jet that extends from the eastern Indian Ocean into the western Pacific at Australian latitudes should effectively prohibit continuous propagation of a stationary Rossby wave from the tropics into the extratropics because the meridional gradient of mean absolute vorticity goes to zero on its poleward flank. The observed wave train indeed exhibits strong convergence of wave activity flux upon encountering this region of vanishing vorticity gradient and with some indication of reflection back into the tropics, indicating the continuous propagation of the stationary Rossby wave train from low to high latitudes is inhibited across the south of Australia. However, another Rossby wave train appears to emanate upstream of Australia on the poleward side of the subtropical jet and propagates eastward along the waveguide of the eddy-driven (sub-polar) jet into the Pacific sector of the Southern Ocean. This combination of evanescent wave train from the tropics and eastward propagating wave train emanating from higher latitudes upstream of Australia gives the appearance of a continuous Rossby wave train propagating from the tropical Indian Ocean into higher southern latitudes. The extratropical Rossby wave source on the poleward side of the subtropical jet stems from induced changes in transient eddy activity in the main storm track of the Southern Hemisphere. During austral spring, when the subtropical jet weakens, the Rossby wave train emanating from Indian Ocean convection is explained more traditionally by direct dispersion from divergence forcing at low latitudes.

Understanding the geographic distribution of tropical cyclone formation for applications in climate models

Projections of Tropical cyclone (TC) formation under future climate scenarios are dependent on climate model simulations. However, many models produce unrealistic geographical distributions of TC formation, especially in the north and south Atlantic and eastern south Pacific TC basins. In order to improve confidence in projections it is important to understand the reasons behind these model errors. However, considerable effort is required to analyse the many models used in projection studies. To address this problem, a novel diagnostic is developed that provides compelling insight into why TCs form where they do, using a few summary diagrams. The diagnostic is developed after identifying a relationship between seasonal climatologies of atmospheric variables in 34 years of ECMWF reanalysis data, and TC detection distributions in the same data. Geographic boundaries of TC formation are constructed from four threshold quantities. TCs form where Emanuel’s Maximum Potential Intensity, $$V_{{PI}}$$ , exceeds $$40\,\,{\text{ms}}^{{ - 1}}$$ , 700 hPa relative humidity, $$RH_{{700}}$$ , exceeds 40%, and the magnitude of the difference in vector winds between 850 and 200 hPa, $$V_{{sh}}$$ , is less than $$20~\,\,{\text{ms}}^{{ - 1}}$$ . The equatorial boundary is best defined by a composite quantity containing the ratio of absolute vorticity $$(\eta )~$$ to the meridional gradient of absolute vorticity ( $$\beta ^{*}$$ ), rather than $$\eta$$ alone. $${\beta ^*}$$ is also identified as a potentially important ingredient for TC genesis indices. A comparison of detected Tropical Depression (TD) and Tropical Storm (TS) climatologies revealed TDs more readily intensify further to TS where $${V_{PI}}$$ is elevated and $${V_{sh}}$$ is relatively weak. The distributions of each threshold quantity identify the factors that favour and suppress TC formation throughout the tropics in the real world. This information can be used to understand why TC formation is poorly represented in some climate models, and shows potential for understanding anomalous TC formation behaviour in the real world.

Influence of the Barotropic Mean Flow on the Width and the Structure of the Atlantic Equatorial Deep Jets

AbstractA representation of an equatorial basin mode excited in a shallow-water model for a single high-order baroclinic vertical normal mode is used as a simple model for the equatorial deep jets. The model is linearized about both a state of rest and a barotropic mean flow corresponding to the observed Atlantic Equatorial Intermediate Current System. It was found that the eastward mean flow associated with the North and South Intermediate Counter Currents (NICC and SICC, respectively) effectively shields the equator from off-equatorial Rossby waves. The westward propagation of these waves is blocked, and focusing on the equator due to beta dispersion is prevented. This leads to less energetic jets along the equator. On the other hand, the westward barotropic mean flow along the equator reduces the gradient of absolute vorticity and hence widens the cross-equatorial structure of the basin mode. Increasing lateral viscosity predominantly affects the width of the basin modes’ Kelvin wave component in the presence of the mean flow, while the Rossby wave is confined by the flanking NICC and SICC. Independent of the presence of the mean flow, the application of sufficient lateral mixing also hinders the focusing of off-equatorial Rossby waves, which is hence an unlikely feature of a low-frequency basin mode in the real ocean.

The Relationship between the Speed and the Latitude of an Eddy-Driven Jet in a Stirred Barotropic Model

Abstract A stirred barotropic model on a sphere is used to investigate the relationship between the speed and the latitude of an eddy-driven jet. When the wind speed is increased in the model, the jet shifts poleward, despite the fact that the stirring of vorticity remains statistically constant. The cause is found to be increasing meridional shear that results from increasing the wind speed in a meridionally confined region and reduces the absolute vorticity gradient on the flanks of the jet. This has two related consequences. The first is that wave propagation is discouraged, as a turning latitude is created where the absolute vorticity gradient tends to zero. On the sphere, this occurs first at high latitudes, thereby shifting wave dissipation toward the equator. The reduced high-latitude dissipation causes a poleward shift of the jet. The second consequence occurs when the vorticity gradient actually becomes negative, in which case the waves may overreflect where an instability is present, providing a high-latitude source of pseudomomentum. This may further encourage the jet to shift poleward. The relevance of the barotropic dynamics to more realistic atmospheres is unclear, but the intermodel variability of the poleward shift of the jet in response to increasing CO2 across a suite of state-of-the-art GCMs is consistent with the barotropic dynamics, suggesting that further investigation is warranted.

Structure and characteristics of submonthly-scale waves along the Indian Ocean ITCZ

This study examines wave disturbances on submonthly (6–30-day) timescales over the tropical Indian Ocean during Southern Hemisphere summer using Japanese Reanalysis (JRA25-JCDAS) products and National Oceanic and Atmospheric Administration outgoing longwave radiation data. The analysis period is December–February for the 29 years from 1979/1980 through 2007/2008. An extended empirical orthogonal function (EEOF) analysis of daily 850-hPa meridional wind anomalies reveals a well-organized wave-train pattern as a dominant mode of variability over the tropical Indian Ocean. Daily lagged composite analyses for various atmospheric variables based on the EEOF result show the structure and evolution of a wave train consisting of meridionally elongated troughs and ridges along the Indian Ocean Intertropical Convergence Zone (ITCZ). The wave train is oriented in a northeast–southwest direction from Sumatra toward Madagascar. The waves have zonal wavelengths of about 3,000–5,000 km and exhibit westward and southwestward phase propagation. Individual troughs and ridges as part of the wave train sequentially travel westward and southwestward from the west of Sumatra into Madagascar. Meanwhile, eastward and northeastward amplification of the wave train occurs associated with the successive growth of new troughs and ridges over the equatorial eastern Indian Ocean. This could be induced by eastward and northeastward wave energy dispersion from the southwestern to eastern Indian Ocean along the mean monsoon westerly flow. In addition, the waves modulate the ITCZ convection. Correlation statistics show the average behavior of the wave disturbances over the tropical Indian Ocean. These statistics and other diagnostic measures are used to characterize the waves obtained from the composite analysis. The waves appear to be connected to the monsoon westerly flow. The waves tend to propagate through a band of the large meridional gradient of absolute vorticity produced by the mean monsoon westerly flow. This suggests that the monsoon westerly flow provides favorable background conditions for the propagation and maintenance of the waves and acts as a waveguide over the tropical Indian Ocean. The horizontal structure of the wave train may be interpreted as that of a mixture of equatorial Rossby waves and mixed Rossby-gravity wavelike gyres.

Rossby Wave Scales, Propagation, and the Variability of Eddy-Driven Jets

Abstract The eddy-driven jet is located in the midlatitudes, bounded on one side by the pole and often bounded on the opposite side by a strong Hadley-driven jet. This work explores how the eddy-driven jet and its variability persist within these limits. It is demonstrated in a barotropic model that as the jet is located at higher latitudes, the eddy length scale increases as predicted by spherical Rossby wave theory, and the leading mode of variability of the jet changes from a meridional shift to a pulse. Looking equatorward, a similar change in eddy-driven jet variability is observed when it is moved equatorward toward a constant subtropical jet. In both the poleward and equatorward limits, the change in variability from a shift to a pulse is due to the modulation of eddy propagation and momentum flux. Near the pole, the small value of beta (the meridional gradient of absolute vorticity) and subsequent lack of wave breaking near the pole account for the change in variability, whereas on the equatorward side of the jet the strong subtropical winds can affect eddy propagation and restrict the movement of the eddy-driven jet or cause bimodal behavior of the jet latitude. Barotropic quasilinear theory thus suggests that the leading mode of zonal-wind variability will transition from a shift to a pulse as the eddy-driven jets move poleward with climate change, and that the eddy length scale will increase as the jet moves poleward.

Budget study of the internal variability in ensemble simulations of the Canadian Regional Climate Model at the seasonal scale

Previous investigations with nested regional climate models have revealed that simulations are sensitive to the initial conditions (IC). This results in internal variability (IV) in ensembles of simulations initialized with small differences in IC. In a previous study, a quantitative budget calculation has documented the physical processes responsible for the rapid growth of IV in simulations with the Canadian Regional Climate Model (CRCM). By using an ensemble of 20 simulations performed for the 1993 summer season, we extend the previous study to further our understanding about the physical processes responsible for the maintenance and fluctuations of IV in a seasonal simulation with CRCM. We have identified and quantified various terms in the prognostic budget equations of IV for the potential temperature and the absolute vorticity. For these studied variables, the covariance of fluctuations acting on the gradient of the ensemble mean of variables generally contributes to increasing the IV, indicating that the transport of heat and vorticity is down the gradient of ensemble mean potential temperature and absolute vorticity. The horizontal transport of IV by ensemble mean flow acts as a sink term, the IV transport out of the study domain contributing to reduce the IV. On average in the troposphere and at the seasonal scale, results confirm that there is no trend in IV although it greatly fluctuates in time. Our results also show that IV is a natural phenomenon arising from the chaotic nature of the atmosphere. In a time-averaged sense, the IV budget reduces to a balance between generation and destruction terms.

Effect of Tropical Waves on the Tropical Tropopause Transition Layer Upwelling

Abstract An initial-value problem is employed with a GCM to investigate the role of the convectively driven Rossby and Kelvin waves for tropopause transition layer (TTL) upwelling in the tropics. The convective heating is mimicked with a prescribed heating field, and the Lagrangian upwelling is identified by examining the evolution of passive tracer fields whose initial distribution is identical to the initial heating field. This study shows that an overturning circulation, induced by the tropical Rossby waves, is capable of generating the TTL upwelling. Even when the heating is placed in the eastern Pacific, the TTL upwelling occurs only over the western tropical Pacific, indicating that the background flow plays a crucial role. The results from a Rossby wave source analysis suggest that a key feature of the background flow is the strong absolute vorticity gradient associated with the Asian subtropical jet. In addition, static stability is relatively weak over the western Pacific, suggesting that this may also contribute to the TTL upwelling in that region. The background flow also modulates the internal Kelvin waves in such a manner that the coldest region in the TTL (resembling the observed “cold trap”) occurs over the western tropical Pacific. As a consequence, the upwelling air, induced by the meridional momentum flux of the Rossby wave, passes through the cold trap generated by the Kelvin wave. Since in reality the background flow is shaped by the convective heating, the climatological western tropical Pacific heating is ultimately responsible for both the TTL upwelling and the cold trap; however, both processes are realized indirectly through its impact on the background flow and the generation of the tropical waves.

Emergence of Jets from Turbulence in the Shallow-Water Equations on an Equatorial Beta Plane

Abstract Coherent jets, such as the Jovian banded winds, are a prominent feature of rotating turbulence. Shallow-water turbulence models capture the essential mechanism of jet formation, which is systematic eddy momentum flux directed up the mean velocity gradient. Understanding how this systematic eddy flux convergence is maintained and how the mean zonal flow and the eddy field mutually adjust to produce the observed jet structure constitutes a fundamental theoretical problem. In this work a shallow-water equatorial beta-plane model implementation of stochastic structural stability theory (SSST) is used to study the mechanism of zonal jet formation. In SSST a stochastic model for the ensemble-mean turbulent eddy fluxes is coupled with an equation for the mean jet dynamics to produce a nonlinear model of the mutual adjustment between the field of turbulent eddies and the zonal jets. In weak turbulence, and for parameters appropriate to Jupiter, both prograde and retrograde equatorial jets are found to be stable solutions of the SSST system, but only the prograde equatorial jet remains stable in strong turbulence. In addition to the equatorial jet, multiple midlatitude zonal jets are also maintained in these stable SSST equilibria. These midlatitude jets have structure and spacing in agreement with observed zonal jets and exhibit the observed robust reversals in sign of both absolute and potential vorticity gradient.

Intraseasonal modulation of tropical cyclogenesis in the western North Pacific: a case study

The temporal clustering of the western North Pacific tropical cyclogenesis and its modulation by the Madden–Julian oscillation (MJO) during the 1991 summer were examined based on the tropical cyclone best track, outgoing longwave radiation, and NCEP/NCAR reanalysis datasets. The wavelet analysis shows that convective activities around the monsoon trough in the western North Pacific possessed a distinct MJO with a period of 20–60 days. Two or more tropical cyclones were observed to form successively during each active phase of the MJO, and tropical cyclones tended to generate around the southeastern part of the maximum vorticity of the low-frequency cyclonic circulation during the developing and peak stages of the active MJO phase. But tropical cyclogenesis scarcely occurred during inactive MJO phases. Thus the MJO was a major agent in modulating repeated development of tropical cyclones in the western North Pacific during the 1991 summer. The MJO in circulation was characterized by a huge anomalous cyclone (anticyclone) in the lower troposphere existing alternately over the western North Pacific, leading to an enhanced (weakened) monsoon trough. An examination of the meridional gradient of absolute vorticity associated with the zonal flow indicates that the zonal flow in the monsoon trough region satisfied the necessary conditions for barotropic instability, with both zonal flow and the meridional gradient of absolute vorticity varying on the similar MJO timescale. The intraseasonal oscillation of such an unstable zonal flow might thus be an important mechanism for temporal clustering of tropical cyclogenesis in the western North Pacific. The barotropic conversion could provide a major energy source for the formation and growth of tropical cyclones in the western North Pacific during active MJO phases, with the eddy kinetic energy generation being dominated by both terms of eddies interacting with zonal and meridional gradients of the basic zonal flow.

A semi-circle theorem for unstable perturbation in tropical cyclone-scale vorticles

In this paper, we discusses the spectrum distribution of baroclinic disturbances in tropical cyclone-scale vortices with the assumption that the basic flow does not vary with height. The semi-circle theorem for the unstable perturbation is obtained and the upper bound of growth rate can be estimated. The upper bound of instability growth rate increases with the increase of the maximum basic-state tangential wind speed, angular speed, inertial parameter, absolute vorticity, radial gradient of absolute vorticity and static stability. The upper bound of instability growth rate is greater for vortices of larger horizontal scale and smaller vertical scale and lower wave-number disturbances.

A Vortex-Based Perspective of Eastern Pacific Tropical Cyclone Formation

Abstract Tropical cyclone formation over the eastern Pacific during 2005 and 2006 was examined using primarily global operational analyses from the National Centers for Environmental Prediction. This paper represents a “vortex view” of genesis, adding to previous work on tropical cyclone formation associated with tropical waves. Between 1 July and 30 September during 2005 and 2006, vortices at 900 hPa were tracked and vortex-following diagnostic quantities were computed. Vortices were more abundant during periods of an enhanced “Hadley” circulation with monsoon westerlies around 10°N in the lower troposphere. This zonally confined Hadley circulation was significantly stronger during the genesis of developing vortices. Developing vortices were stronger at the outset, with a deeper potential vorticity maximum, compared to nondeveloping vortices. This implies that developing disturbances were selected early on by favorable synoptic-scale features. The characteristic time-mean reversal of the meridional gradient of absolute vorticity in the lower troposphere was found to nearly vanish when the aggregate contribution of strong vortices was removed from the time-mean vorticity. This finding implies that it is difficult to unambiguously attribute development to a preexisting enhancement of vorticity on the synoptic scale. The time-mean enhancement of cyclonic vorticity primarily results from the accumulated effect of vortices. It is suggested that horizontal deformation in the background state helps distinguish developing vortices from nondevelopers, and also biases the latitude of development poleward of the climatological ITCZ axis.

Two-Dimensional Turbulence and Persistent Zonal Jets in a Global Barotropic Model

The dynamics of two-dimensional turbulence on a rotating sphere are examined. The anisotropic Rhines scale is derived and verified in decaying turbulence simulations. Due to the anisotropic nature of the Rossby waves, the Rhines barrier is displaced toward small total wavenumber n with decreasing zonal wavenumber m. Up-scale energy transfer along the zonal axis (m = 0) is not directly arrested by beta. A forced dissipative model with high-wavenumber forcing is used to investigate the dynamics of persistent zonal jets. Persistent jets form in the low energy (strong rotation) cases with the root-mean-square velocity V*rms ≪ aΩ. Under a fixed rotation rate, the jet scale decreases with the energy. The equilibrated jets generally stay at fixed latitudes. The zonal bands are nearly uniformly distributed in latitude, except that bands in the high latitudes tend to be wider and weaker, as clearly affected by a decreasing beta with latitude. The time-mean zonal winds in the forced simulations appear to be stable, with their absolute vorticity gradient dominated by beta. The increase of the jet scale with energy as required by stability is consistent with the simulated results. Diagnostic analysis shows that the persistent jets are primarily maintained by the shear-straining mechanism involving small-scale eddies and large-scale zonal jets, with a clear scale separation between them. Although large-scale eddies, those at scales near the Rhines scale, possess most of the eddy energy, in the time mean they contribute little to the maintenance of the zonal jets. Thus, despite the similarity between the Rhines scale and the jet scale, their dynamical link is not obvious in the time-mean statistics. The presence of persistent zonal jets modifies the normal modes of the system. Pure Rossby–Haurwitz modes at small and medium scales are severely modified and fall into the continuum. Large-scale modes, however, may remain discrete. The discreteness of the large-scale modes limits their ability to exchange energy with the zonal jets in the time mean.

The Nonlinear Evolution of Disturbances to a Parabolic Jet

Abstract It has been shown that the linearized equations for disturbances to a parabolic jet on a β plane, with curvature Un0(y) such that the basic-state absolute vorticity gradient β − Un0(y) is zero, ultimately become inconsistent in the neighborhood of the jet axis and that nonlinear effects become important. Numerical solutions of the nonlinear long-time asymptotic form of the equations are presented. The numerical results show that the algebraic decay of the disturbances as t−1/2 predicted by the linear equations is inhibited by the nonlinear formation of coherent vortices new the jet axis. These lead to a disturbance amplitude that decays only through the action of weak numerical diffusion but is otherwise as t0. The linear theory is extended to the case when the basic-state absolute vorticity gradient is nonzero but weak. When the gradient is weak and negative the decay is modified and is ultimately as t−3/2. When the gradient is weak and positive, on the other hand, a discrete eigenmode is excite...

Numerical Studies of the Beta Effect in Tropical Cyclone Motion. Part II: Zonal Mean Flow Effects

Abstract The motion of tropical vortices in east–west mean flows is studied with the barotropic vorticity equation on the beta plane. The vorticity equation is integrated numerically from an initially symmetric vortex embedded in (i) a linear shear flow or (ii) a parabolic jet. The first experiment with flow (i) has β = 0 and it is linearized about the mean flow. The vortex is distorted by the mean flow so that the even Fourier components around the vortex grow, but the vortex does not move. When nonlinear effects are included the distortion is damped in the inner part of the vortex, but wavenumber two grows in the outer region. The addition of the beta effect causes the vortex to move in the same direction as the no mean flow solution provided the mean flow advection is removed from the trajectories. The trajectory for the anticyclonic mean flow is significantly longer than the cyclonic and no mean flow trajectories, which are about equal. For mean flow (ii), with the same absolute vorticity gradient as ...

An extended analytic theory of tropical‐cyclone motion in a barotropic shear flow

AbstractAn earlier analytic theory for the motion of a barotoropic vortex in a zonally varying basic shear flow on a beta‐plane is consolidated and extended. It is shown that the theory can be derived from a power‐series expansion of variables representing the vortex asymmetry in terms of a single nondimensional parameter ϵ = BL2/U, where B is the Meridional gradient of basis state absolute vorticity and L and U are the lenght and velocity scales, respectively, for the outer part of the vortex. The derivation requires inter alia that ϵ ≪ 1 and that the magnitude of the basis flow scales with ϵ. Insight is provided into the dynamics of vortex motion when the latter condition is not fulfilled, as in cases of moderate and large shear.For vortices that decay appreciably more rapidly with radius than those studies in the earlier work it is necessary to include additional terms when calculating the asymmetric vorticity to obtain an accurate prediction of the vortex track. Analytic expressions have been obtained for these terms that lead to a theory that is valid for a broad range of vortex profiles.Comparisons are made between the present theory and two recent analyses for the case of zero basis flow, contrasting the important differences in approach. The present theory gives results that are very close to one of these, a semi‐spectral numerical Method.The paper concludes with a brief discussion of aspects of vortex stability.