Basic Zonal Flow Research Articles

A higher dimensional model of geophysical fluid with the complete Coriolis force and vortex structure

Here, we present a higher dimensional model from the vorticity equation, which describes the dynamic characteristics of large scale Rossby waves by utilizing the Gardner-Morikawa coordinate transformation and the perturbation method. To reveal the influence of physical parameters on the higher dimensional model, we first give the dispersion relation of the model and the N-soliton solutions by Hirota method. Subsequently, the lump solutions are derived by using the long wave limit method. It demonstrates that the horizontal component of the Coriolis force acts as a forcing force on the nonlinear Rossby waves, and affects the amplitude of the meridional structure. Moreover, under the background of secondary zonal basic flow, for different lump solutions, the flow field will appear dipole blocking or double vortex structure. It is also indicated that the horizontal Coriolis force only causes the vortex to move in the latitudinal direction.

On zonal steady solutions to the 2D Euler equations on the rotating unit sphere

The present paper studies the structure of the set of stationary solutions to the incompressible Euler equations on the rotating unit sphere that are near two basic zonal flows: the zonal Rossby–Haurwitz solution of degree 2 and the zonal rigid rotation along the polar axis. We construct a new family of non-zonal steady solutions arbitrarily close in analytic regularity to the second degree zonal Rossby–Haurwitz stream function, for any given rotation of the sphere. This shows that any non-linear inviscid damping to a zonal flow cannot be expected for solutions near this Rossby–Haurwitz solution. On the other hand, we prove that, under suitable conditions on the rotation of the sphere, any stationary solution close enough to the rigid rotation zonal flow must itself be zonal, witnessing some sort of rigidity inherited from the equation, the geometry of the sphere and the base flow. Nevertheless, when the conditions on the rotation of the sphere fail, the set of solutions is much richer and we are able to prove the existence of both explicit stationary and travelling wave non-zonal solutions bifurcating from , in the same spirit as those emanating from the zonal Rossby–Haurwitz solution of degree 2.

Effect of quadric shear basic zonal flows and topography on baroclinic instability

On the β plane approximation, the two-layer quasigeostrophic mode is used to study the baroclinic instability of the quadric shear basic zonal flows on a uniform bottom topography. The phase speed and growth rate of instability waves are functions of the shear zonal basic flows and bottom topographic slope. The study focus is on the effects of topography and the quadric shear basic zonal flows (the second derivative of basic zonal flows is not zero). The meridional slope destabilise (stabilise) zonal flows, it plays an unstable role in disturbance, moreover the effect of the second derivative of basic zonal flows is to accelerate the instability of disturbance. The zonal slope always destabilises the zonal basic flows through zonal and meridional wavenumber. Moreover, the effect of the second derivative of basic zonal flows is to accelerate the instability of disturbance.

Spatial Asymmetric Tilt of the NAO Dipole Mode and Its Variability

The dipole structure of the North Atlantic Oscillation (NAO) is examined in this study by defining the tilt of the NAO dipole centers on synoptic time scales. All the positive NAO phase (NAO+) and negative NAO phase (NAO−) events are divided into three tilting types according to their definition; namely, northeast–southwest (NE–SW), north–south symmetric (N–S, not tilted), and northwest–southeast (NW–SE) tilting NAO events. Then, the associated surface air temperature (SAT), geopotential height, zonal wind, and SST (surface sea temperature) anomalies of each type are examined. It is found that, for different asymmetric NAO tilt types, the local SATs exhibit significantly different distributions. The zonal wind has a good match with the NAO dipole tilt, which also includes the positive feedback of the NAO circulation. The basic zonal flow that removes the NAO days also exhibits a clear tilt structure that favors the tilt of the NAO dipole. Moreover, it is found that the Atlantic Multidecadal Oscillation (AMO) may be an important factor affecting the tilt of the NAO dipole. The AMO index has a significant 15-year lead for the NAO index and basic zonal flow index, with a high correlation coefficient, which might be seen as a precondition that indicates the tilt of the NAO events, especially on decadal or multidecadal time scales. However, the physical mechanisms and processes are still not fully understood.

О СТРУКТУРЕ СЕВЕРО-АТЛАНТИЧЕСКОГО ТЕЧЕНИЯ В МАЕ–ИЮНЕ 1990 г.

О СТРУКТУРЕ СЕВЕРО-АТЛАНТИЧЕСКОГО ТЕЧЕНИЯ В МАЕ–ИЮНЕ 1990 г.

Dynamic Transitions and Baroclinic Instability for 3D Continuously Stratified Boussinesq Flows

The main objective of this article is to study the nonlinear stability and dynamic transitions of the basic (zonal) shear flows for the three-dimensional continuously stratified rotating Boussinesq model. The model equations are fundamental equations in geophysical fluid dynamics, and dynamics associated with their basic zonal shear flows play a crucial role in understanding many important geophysical fluid dynamical processes, such as the meridional overturning oceanic circulation and the geophysical baroclinic instability. In this paper, first we derive a threshold for the energy stability of the basic shear flow, and obtain a criteria for nonlinear stability in terms of the critical horizontal wavenumbers and the system parameters such as the Froude number, the Rossby number, the Prandtl number and the strength of the shear flow. Next we demonstrate that the system always undergoes a dynamic transition from the basic shear flow to either a spatiotemporal oscillatory pattern or circle of steady states, as the shear strength $\Lambda$ of the basic flow crosses a critical threshold $\Lambda_c$. Also we show that the dynamic transition can be either continuous or catastrophic, and is dictated by the sign of a transition parameter $A$, fully characterizing the nonlinear interactions of different modes. A systematic numerical method is carried out to explore transition in different flow parameter regimes. We find that the system admits only critical eigenmodes with horizontal wave indices $(0,m_y)$. Such modes, horizontally have the pattern consisting of $m_y$-rolls aligned with the x-axis. Furthermore, numerically we encountered continuous transitions to multiple steady states, continuous and catastrophic transitions to spatiotemporal oscillations.

Stability of the Divergent Barotropic Rossby-Haurwitz Wave

Stability of the barotropic Rossby-Haurwitz wave is investigated using the numerical models on the global domain. The Rossby-Haurwitz wave under investigation is composed of the basic zonal flow of super-rotation and a finite amplitude spherical harmonic wave. The Rossby-Haurwitz wave is given as either steady or unsteady wave by adjusting the strength of the super-rotating zonal flow. Stability as well as the growth rate of the wave in the numerical simulation is determined by comparing the perturbation amplitude at two different time stages. Unstable modes of the Rossby-Haurwitz wave exhibited a horizontal structure composing of various zonal-wavenumber components. The vorticity perturbation for some modes showed a discontinuity around the area of weak flow, which was found robust regardless of the horizontal resolution of the model. Fourier finite element model was shown to generate the unstable mode in earlier stage of the time integration due to less accuracy compared to the spherical harmonic spectral model. Taking the overall accuracy of the models into consideration, the time by which the unstable mode begin to dominate over the spherical harmonic wave was estimated.

Influence of the basic state zonal flow on convectively coupled equatorial waves

AbstractObservational data are used to test the hypothesis that the basic state modulates the dispersion properties of convectively coupled equatorial waves (CCEWs). This hypothesis is based on shallow water theory, which predicts that the zonal speed of propagation of such tropospheric equatorial modes is altered by the equivalent depth and the basic zonal flow. Localized space‐time spectra are calculated to investigate how CCEW spectral peaks vary across the tropics and how they are affected by the variations in zonal wind observed geographically and by season. Doppler shifting by the basic state barotropic zonal flow is readily identified. Once this Doppler shifting is taken into account, the equivalent depths of CCEWs inferred from global power spectra are surprisingly uniform, both geographically and temporally. However, there are also detectable modulations that appear consistent with changes in vertical shear of the zonal flow, along with other shifts that are not as easily explained.

Baroclinic instability in the Venus atmosphere simulated by GCM

Baroclinic instability in the super-rotation of Venus is investigated by a newly developed atmospheric general circulation model. First, we adopt an idealized super-rotation, i.e., solid-body rotating flow in a weakly stratified layer at cloud level, as an initial basic state in a nominal case. With the evolution of time, baroclinic instability occurs in a weakly stratified layer with large vertical shear of the basic zonal flow. Horizontal wind associated with the baroclinic instability modes is of a few m s−1. The initial structure of the unstable modes is similar to those obtained in previous linear stability analyses. However, it is modified by nonlinear interactions in the later stage, reaching a quasi-steady state. Meridional transport of momentum and heat by these unstable modes accelerates the super-rotation by ~ 0.05 m s−1 day−1 at midlatitudes. Furthermore, the dependence of baroclinic instability on the basic state, i.e., the meridional profiles of zonal flow and the vertical profiles of static stability, are subsequently investigated. For the super-rotation with midlatitude jets at cloud level, the modes are modified from baroclinic to barotropic in the later stage. Typically, their horizontal wind is of O(10) m s−1. Their amplitude is maintained by energy conversion from zonal-mean available potential energy associated with the baroclinic basic state. In the case where static stability is smaller than that in the nominal case, the baroclinic modes transfer angular momentum from midlatitude to the equator near a 70 km level and accelerate the super-rotation by more than 10 m s−1 in the equatorial region.

Impact of the SST–wind stress coupling on the dynamics and stability of ocean current inside and outside SST frontal zones

The robust relationship between the sea surface temperature (SST) and wind stress is used to examine the impact of the SST–wind stress coupling on the dynamics and stability of ocean currents inside and outside SST frontal zones based on the wave-activity equations for the semi-geostrophic (SG) and quasi-geostrophic (QG) models.The results show that the coupling has fundamentally different effects on the ocean current inside and outside SST fronts. Outside the frontal zones the coupling only redistributes the surface temperature perturbation but does not change the total pseudo-momentum and pseudo-energy. Therefore the QG pseudo-momentum and pseudo-energy are still conserved under the impact of the coupling, although the pseudo-energy is slightly modified. The stability conditions, more general than the ones obtained by Spall (2007), are obtained from the conservation of the wave-activities. Inside the SST frontal zones, however, the coupling, along with the nonlinear Ekman effect, destroys the conservation of the SG pseudo-momentum and pseudo-energy. Therefore no stability condition is available, indicating that the current inside the frontal zone may be unstabilized by the coupling or nonlinear Ekman transport effect. It is also found that different dynamical features inside and outside frontal zones cause the different modulation of the coupling strength. The drastic differences are closely associated with the different assumptions underlying QG and SG dynamics about the density/temperature gradient and isotropy of motions.The different impacts of the coupling are further illustrated analytically by comparing the normal mode growth rates for the SG and QG Eady models. The comparisons show that ocean current outside the SST frontal zone is stable under any normal mode disturbances when the coupling factor σQG<−U¯s where U¯s is the basic zonal flow at the surface, but it is unstable under certain normal modes when σQG>−U¯s. However the ocean current inside the frontal zone is always unstable under the influence of the SST–wind coupling or nonlinear Ekman effect. It is found that the negative coupling (when surface wind blows from cold water to warm water) tends to generate strong instability. In addition, the growing/decaying normal modes are non-dispersive and propagate only in one direction (eastward) outside the frontal zone, but they are dispersive and can propagate in both directions inside frontal zone.

Eddy kinetic energy redistribution within idealized extratropical cyclones using a two‐layer quasi‐geostrophic model

Eddy kinetic energy (EKE) redistribution within midlatitude cyclones is investigated using a two‐layer quasi‐geostrophic model. The flow is composed of synoptic localized cyclones in both layers interacting with a baroclinic zonal basic flow. The effects of the planetary vorticity gradient β and the relative vorticity gradient of the westerly basic flow are to reduce the upstream ageostrophic geopotential fluxes in the lower layer and to intensify the downstream fluxes in the upper layer. Furthermore, they act to reduce the downward ageostrophic geopotential fluxes and to intensify the upward ageostrophic fluxes. When cyclones are embedded in a cyclonic shear, EKE rapidly accumulates on the southwestern flank of the lower‐layer cyclone before being cyclonically redistributed by the rearward cyclonically oriented ageostrophic fluxes and nonlinear advection. In contrast, when cyclones are embedded in an anticyclonic shear, the lower‐layer ageostrophic fluxes are mainly westward‐oriented and the pressure work combines perfectly with nonlinear advection to maintain the EKE increase at the same place upstream or downstream of the lower‐layer cyclone, depending on the value of β. Finally, a simulation showing the crossing of a westerly jet by cyclones condenses all the above effects. At the early stages, when cyclones lie on the anticyclonic side of the jet, a strong EKE increase occurs downstream of the lower‐layer cyclone. Just after the jet crossing, the EKE is rapidly rearward and cyclonically redistributed by the ageostrophic fluxes and nonlinear advection, leading to the formation of a lower‐layer jet to the south of the cyclone.

Baroclinic Instability of the Silk Road Pattern Induced by Thermal Damping

Abstract In this paper, the internal dynamics of the Silk Road pattern has been studied. Since observation indicates that the Silk Road pattern could be considered as stationary external Rossby waves, the quasigeostrophic three-layer model has been used to study the dynamics of external Rossby waves. The three-layer model well captures the essential dynamical features of stationary external Rossby waves in accordance with the observations. Theoretical analysis indicates that the quasi-stationary external modes could be destabilized by the weak thermal damping. For destabilization to occur, the vertical structures of the external modes must have a warm ridge and a cold trough from the lower to middle layers. The effect of thermal damping could be considered as modifying the eddy streamfunction in such way that the eddy streamfunction has a vertical phase tilt, so the eddy could feed on the basic zonal flow by extracting the potential energy. The implications for this baroclinic instability on the self-maintenance of the Silk Road pattern are discussed. The observations imply that this dissipative destabilization mechanism could explain the self-maintenance of the Silk Road pattern.

Large-scale circulation patterns favourable to tropical cyclogenesis over the western North Pacific and associated barotropic energy conversions

Using the National Centers for Environmental Prediction-Department of Energy (NCEP-DOE) reanalysis and the Joint Typhoon Warning Center (JTWC) best track data for the period 1991–2010, this study classifies five large-scale circulation patterns in association with the tropical cyclone (TC) formation over the western North Pacific (WNP): the monsoon shear (MS), the monsoon confluence (MC), the reverse-oriented monsoon trough (RMT), the monsoon gyre (MG), and the trade wind easterlies (TE). The first three patterns account for about 80% of tropical cyclogeneses. Through a diagnosis of energetics, it is found that the tropical cyclogenesis in the MS, MC, and RMT patterns is highly associated with the barotropic energy conversion. Analysis shows that the horizontal shear of basic zonal flow provides a favourable condition for the eddy kinetic energy (EKE) growth in the MS pattern. When a TC forms in the MC pattern, the horizontal shear and convergence of basic zonal flow are both important for the EKE growth. When the basic flow is the RMT pattern, in addition to the horizontal shear of basic flow, zonal and meridional wind convergence play an important role for tropical cyclogenesis over the WNP and the South China Sea, respectively. However, the barotropic energy conversion appears not to be a main mechanism for the EKE growth in the MG and TE patterns. Copyright © 2013 Royal Meteorological Society

Effect of Top and Bottom Boundary Conditions on Symmetric Instability under Full-Component Coriolis Force

Abstract The linear stability of a zonal flow confined in a domain within horizontal top and bottom boundaries is examined under full consideration of the Coriolis force. The basic zonal flow is assumed to be in thermal wind balance with the density field and to be sheared in both vertical and horizontal directions under statically and inertially stable conditions. By imposing top and bottom boundary conditions in this framework, the number of wave modes increases to four, instead of two in an unbounded domain, as already reported in studies on internal gravity waves. The four modes are classified into two pairs of high- and low-frequency modes: the high modes are superinertial and the low modes are subinertial. The discriminant of symmetric instability is nevertheless determined by the sign of the potential vorticity of the basic zonal flow, as in the case of an unbounded domain. The solutions satisfying the top and bottom boundary conditions are interpreted as the superposition of incident and reflected waves, revealing that the neutral solutions consist of two neutral plane waves with oppositely directed vertical group velocities. This may explain why the properties of wave behavior, such as the instability criteria, remain the same in both the bounded and unbounded domains, although the manifestation of wave activity, such as the order of dispersion relation, is quite different in the two cases. Furthermore, the slope of the constant momentum surface, the slope of the isopycnic surface including the nontraditional effect of the Coriolis force, and the ratio between the frequencies of gravity and inertial waves form an essential set of parameters for symmetric motion. The combination of these dimensionless quantities determines the fundamental nature of symmetric motions, such as stability, regardless of boundary conditions with and without the horizontal component of the planetary vorticity.

Barotropic process contributing to the formation and growth of tropical cyclone Nargis

This study reveals the barotropic dynamics associated with the formation and growth of tropical cyclone Nargis in 2008,during its formation stage.Strong equatorial westerlies occurred over the southern Bay of Bengal in association with the arrival of an intraseasonal westerly event during the period 22-24 April 2008. The westerlies,together with strong tropical-subtropical easterlies,constituted a large-scale horizontal shear flow,creating cyclonic vorticity and thereby promoting the incipient disturbance that eventually evolved into Nargis.This basic zonal flow in the lower troposphere was barotropically unstable,with the amplified disturbance gaining more kinetic energy from the easterly jet than from the westerly jet during 25-26 April. This finding suggests that more attention should be paid to the unstable easterly jet when monitoring and predicting the development of tropical cyclones.Energetics analyses reveal that barotropic energy conversion by the meridional gradient of the basic zonal flow was indeed an important energy source for the growth of Nargis.

Analytical Solutions of Initial Value Problem of Diabatic Rossby Waves

The initial value problem of diabatic Rossby waves is analytically solved in a vertical-zonal two-dimensional quasi-geostrophic system on an f-plane. The given basic state is in thermal-wind-balance, and dry baroclinic instability is excluded. The diabatic heating (or cooling) is proportional to the vertical velocity on the middle level and generates potential vorticity (PV) disturbances on the lower and upper levels of the atmosphere. The PV disturbance propagates eastward (westward) on the lower (upper) level relative to the fluid, while the prescribed basic zonal flow advects the PV disturbance toward the opposite direction. For a zonal wavelength shorter than a marginal one, which becomes shorter as the heating becomes stronger, the advection effect is dominant, and consequently, the lower and upper PV disturbances move downstream and away from each other without effective interaction or growth. On the other hand, for a zonal wavelength longer than a marginal one, the propagation effect is dominant, and consequently, the lower and upper PV disturbances tend to move upstream and away from each other. However, this leads to strong mutual interactions between the lower and upper PV disturbances. As a result, the PV disturbances grow exponentially and attain a phase-locked upshear-tilted vertical structure. The behaviour of PV disturbances can be qualitatively explained on the basis of PV thinking.

Analytical Solutions of Vertically Propagating Gravity Waves&amp;mdash;from the Perspective of Buoyancy-Vorticity Thinking

On the basis of buoyancy-vorticity (BV) formulation of Harnik et al. (2008), the initial value problem of vertically propagating gravity waves is analytically solved in a zonal-vertical two-dimensional system. The analytical solutions provide an example of the visualization of BV thinking. Further, the analytical solutions enable a qualitative understanding of the growth of gravity waves in a vertically sheared zonal flow (so-called shear instability of gravity waves) by BV thinking. To this end, the basic buoyancy (i.e., basic potential temperature) is assumed to be piecewise uniform in the vertical direction, and the Green function method is employed. The obtained analytical solutions show the following. In a vertically uniform basic zonal flow, the gravity wave, which is initially at the lowest level, propagates vertically upwards, gets reflected from the highest level back to the lowest level and again from the lowest level to the highest level, and so on. In a vertically sheared basic zonal flow, the behavior of the gravity waves depends on the horizontal wave number. This is caused by the dependence of horizontal propagation velocity on the horizontal wave number. Here, horizontal propagation is defined relative to the fluid. If the horizontal propagation and advection by the basic zonal flow are successfully balanced so that the lower and upper phase velocities are nearly equal, then the gravity wave propagates vertically, and the upper and lower disturbances are phase-locked to each other; this results in an effective interaction between them and in growth as an exponential function of time. On the other hand, if the horizontal propagation and advection by the basic zonal flow are out of balance so that the lower and upper phase velocities are different from each other, then the gravity wave hardly propagates vertically, and the upper and lower disturbances horizontally flow away from each other resulting in an absence of interaction between them and in the oscillation (i.e., no growth). At the marginal points between oscillation and growth, the gravity wave grows as a linear function of time. The behavior of analytical solutions can be qualitatively explained by the BV thinking of Harnik et al. (2008).

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.

Analytical Solutions of Transversely Propagating Rossby Waves

In the horizontally 2-dimensional quasi-geostrophic system, we construct analytical solutions of transversely propagating Rossby waves across the basic zonal flow. On the assumption that the basic potential vorticity is piece-wise constant in the meridional direction, the solution with a meridionally localized initial disturbance can be obtained analytically. The analytical solutions show, for example, the following. In the case of a uniform basic zonal flow, the Rossby wave propagates diagonally due to the planetary potential vorticity gradient. In the case of a jet-like basic zonal flow, the oscillating Rossby wave is almost trapped along the jet-axis. However, for the growing Rossby wave, the amplitudes on the jet-axis and on the jet-flanks eventually become comparable.

Physical interpretation of unstable modes of a linear shear flow in shallow water on an equatorial beta-plane

Unstable modes of a linear shear flow in shallow water on an equatorial $\beta$-plane are obtained over a wide range of values of a non-dimensional parameter and are interpreted in terms of resonance between neutral waves. The non-dimensional parameter in the system is $E \,{\equiv}\, \gamma^{4} / (gH\beta^{2})$, where $\gamma$, $g$, $H$ and $\beta$ are the meridional shear of basic zonal flow, gravitational constant, equivalent depth and the north–south gradient of the Coriolis parameter, respectively. The value of $E$ is varied within the range $-2.50 \,{\le}\,\log E \,{\le}\,7.50$.The problem is solved numerically in a channel of width $5\gamma/\beta$. The structures of the most unstable modes, and the combinations of resonating neutral waves that cause the instability, change according to the value of $E$ as follows. For $\log E \,{<}\, 2.00$, the most unstable modes have zonally non-symmetric structures; the most unstable modes for $\log E \,{<}\, 1.00$ are caused by resonance between equatorial Kelvin modes and continuous modes, and those for $1.00 \,{\le}\,\log E \,{<}\, 2.00$ are caused by resonance between equatorial Kelvin modes and westward mixed Rossby–gravity modes. The most unstable modes for $\log E \,{\ge}\, 2.00$ have symmetric structures and are identical with inertially unstable modes. Examinations of dispersion curves suggest that non-symmetric unstable modes for $1.00 \,{\le}\,\log E \,{<}\, 2.00$ and inertially unstable modes for $\log E \,{\ge}\, 2.00$ are the same kind of instability.