Barotropic Atmosphere Research Articles

Exact Simple Waves on Shear Flows in a Compressible Barotropic Medium

Self‐similar solutions describing simple waves on shear flows in a finite compressible barotropic atmosphere are found. These include the simple waves on shear flows in water as a special case. By making use of a number of transformations it becomes possible to write these solutions in an exact form. This form, though not explicit, is similar to the incomplete Beta function which seems to characterize this class of nonlinear physical problems.

Abrupt change of flow pattern in baroclinic atmosphere forced by joint effects of diabatic heating and orography

Based on the catastrophic theory, the possible causes of abrupt change in the atmospheric circulation over the Northern Hemisphere during June and October have been explored by Li and Luo (1983) and Miao and Ding (1985). However these studies are confined to the barotropic atmosphere without consideration of orography. The purpose of this paper is to further study the physical mechanism of the abrupt change of flow pattern within the baroclinic atmosphere in the presence of orography. Results show that the abrupt change of flow pattern can be stimulated by the gradual variation of a diabatically heating parameter, which is similar to the observed fact about the rapid shift of position of the subtropical high center in the upper troposphere along the zonal direction during seasonal transition from the summer half year to the winter one.

Evolution of large scale disturbances and their interaction with mean flow in a rotating barotropic atmosphere—Part II

In part I of this paper, we have discussed two problems: the general properties of two-dimensional barotropic motion and the evolution and structure of both Rossby wave packet and inertio-gravity wave packet. In this part, we shall continue our discussion. Third, normal modes and continuous spectra of both quasi-geostrophic and non-geostrophic models, their different behaviour, and the comparison of normal mode approach to the wave packet approach. Fourth, weakly nonlinear theory of interaction based on the analysis of eddy transports. A nonzonal basic flow as well as non-geostrophic model is also included in the consideration. The last, the fully nonlinear theory, making emphasis on the conditions for the maintenance of nonzonal disturbances and the conditions for their continuous and complete absorption by the zonal flow. A comparison of Rossby wave absorption to energy cascade in the two-dimensional turbulence is also given.

Evolution of large scale disturbances and their interaction with mean flow in a rotating barotropic atmosphere—Part I

Evolution of large scale disturbances and their interaction with mean flow in a rotating barotropic atmosphere—Part I

The second order approximation to the nonlinear wave in barotropic atmosphere

A kind of technique of computer extension of perturbation series is presented and used in seeking for the second-order approximation to a large-scale travelling wave solution of the barotropic primitive equations. Numerical experiments show that the second-order approximation keeps major characters of the travelling wave solution and is indeed more exact than the zero-order and the first order approximations.

Nonlinear waves in barotropic model

In this paper, from the system of equation describing a barotropic atmosphere using the method of Taylor expansion for the nonlinear terms, the periodic solutions of the nonlinear inertio-surface gravity waves and Rossby waves have been obtained. The finite-amplitude nonlinear inertio-surface gravity waves and Rossby waves with horizontal divergence satisfy all the KdV equation. The solutions are all the cnoidal function, i. e., the cnoidal waves which include the linear waves and form the solitary waves under certain conditions. For the finite-amplitude Rossby waves with horizontal divergence, we find the new dispersive relation including both the wave number and the amplitude parameter. In case of small amplitude it is reduced to the Yeh formula. It is shown that the larger the amplitude and width, the faster the finite-amplitude inertio-surface gravity waves and the slower the finite-amplitude Rossby waves with horizontal divergence propagate. The blocking or cut-off system in which the amplitude and width are large may be considered as Rossby solitary waves.

Multiple non-linear interaction of Rossby waves via zonal flow

The non-linear interaction between large-scale Rossby waves is considered making use of a spectral model of a barotropic atmosphere in spherical geometry. It is found that, if an arbitrary number of zonal components is taken into account it is possible to predict the non-linear energy and enstrophy flux between Rossby waves whose interaction cannot be predicted by single triadic resonance. It is shown, referring to the results of a paper by Baines, that such kind of, zonally mediated, non-linear energy flux is capable of explaining some relevant features of numerical integrations of truncated models with a large number of components and, could, as a consequence be responsible of some features of the large-scale circulation.

Forced Coherent Structures and Local Multiple Equilibria in a Barotropic Atmosphere

We consider the response of the barotropic vorticity equation on a zonally infinite f-plane or beta-plane to a weak localized vorticity source accompanied by weak Ekman damping. By performing an expansion about the unforced, undamped problem, we derive a solvability condition determining when a slight modification of a solution to the inviscid problem can occur as a solution to the weakly forced and damped problem. This condition states simply that forcing must balance dissipation in the average along each closed streamline. Much of the degeneracy of the inviscid problem is removed by the solvability condition. The above considerations are used to show that under a fairly general set of circumstances the weakly forced system possesses a high amplitude equilibrium state (identified with blocking) and a low amplitude equilibrium state. The high amplitude response is maintained by a local nonlinear resonance phenomenon, and requires the existence of a suitable solution to the inviscid problem, such as the “modon” solution. In contrast to cases previously discussed, the multiple equilibrium mechanism we treat is not dependent on global resonance. Explicit examples of local multiple equilibria are constructed through numerical integrations on the f-plant and on a zonally infinite beta-channel. Through introduction of a reasonable amount of meridional confinement, a high amplitude solution can be obtained on the beta-plane without the use of a small radius of deformation. It is suggested that transient eddy fluxes may be able to play the role of the forcing required in our model. A tentative comparison with a blocking event is presented, indicating a number of problematic aspects of the theory.

Truncated model of a barotropic atmosphere with a periodic forcing

The effect of variations in time of the zonal flow is investigated by the study of a simplified truncated model of a barotropic atmosphere in the presence of an oscillating zonal forcing.

Horizontal Energy propagation in a Barotropic Atmosphere with Meridional and Zonal Structure

Abstract To investigate how the propagation of energy away from steady sources may be influenced by the horizontal structure of the time-averaged flow in the troposphere, solutions to a barotropic model are displayed and interpreted. The model is steady and linearized about a basic state which varies in latitude and longitude. Emphasis is placed on cases where the longitudinal variations are gradual. Many of the results can be analyzed by locally applying tools developed for zonally symmetric basic states, e.g., ray tracing and refractive indices. Simple background flows are constructed which have longitudinally confined critical lines, reflective surfaces, wave guides, and regions conducive to propagation. An example is given in which longitudinal derivatives of the basic state are significant. The theory of ray tracing in a two-dimensional wind must be employed as an interpretive tool in this case. It is concluded that zonal variations tend to enhance poleward (equatorward) propagation in large-scale tr...

Rossby wave propagation in a barotropic atmosphere

The ideas of ray tracing from geometrical optics and wave propagation in a slowly varying medium are applied to Rossby waves propagating in a barotropic atmosphere. The propagation of low-frequency Rossby waves in a zonally symmetric basic state is compared with that for stationary waves presented by Hoskins and Karoly (1981). These ideas are then used to study the propagation of Rossby waves in a basic state with zonally varying middle latitude or low latitude jets. Conditions which allow cross-equatorial wave propagation are presented. For a zonally varying middle latitude jet, there is weak wave convergence in regions of decreasing jet speed, However, this is not sufficient to explain the enhanced wave amplitude found in numerical-model experiments using a zonally varying basic state.

Über ein abgeschnittenes 3-Komponenten-Modell einer barotropen nicht-divergierend rotierenden Atmosphäre in sphärischer Geometrie

The set of ordinary differential equations of the fifth order describing the triadic interaction of planetary waves and zonal flow in a rotating barotropic atmosphere is solved analytically for all initial configurations of mode amplitudes. Periodic and aperiodic trajectories in the phase space are found to occur with oscillation periods depending non-linearly on the mode of amplitudes.

回転順圧大気中における波動擾乱と帯状流の発達と相互作用について

The evolution and interaction of quasi-geostrophic disturbances and zon barotropic atmosphere on a rotating sphere are investigated by integral properties as well as by the WKB method. The results obtained by these two methods are in full agreement and supplement with each other. Two concepts, the available zonal energy and rotational adaptation, are introduced. It is indicated that the atmospheric motion on a rotating sphere always keeps some anisotropy, and can become a completely zonal flow under favorable conditions. Developing (decaying) disturbance superimposed on zonal flow or ultra-long wave enlarges (shortens) its size, i.e., local wave length, provided the jet is moderate and satisfies the stable condition. Developing (decaying) disturbances transfer angular momentum out from (into) the jet region; and weaken (strengthen) both the jet and its shear. At the same time, the propagation of developing (decaying) disturbance decelerates (accelerates).

A Simple Mechanism for Blocking

Numerical experiments show that blocking in a barotropic atmosphere can occur as a resonant enhancement of Rossby lee waves forced by two stationary sources of potential vorticity. In particular, if an upstream source of stationary forcing enhances the northerly flow over orography, then blocking occurs downstream of the mountain. In an analytical study, we show that, in the presence of friction, Rossby lee waves generate a rectified current downstream of the mountain, which does not vanish in the limit of zero friction. The relevance of this study to observed generation of blocking in the Atlantic Ocean and immediately upstream of the Rockies is discussed.

Effect of Zonal Flows on the Free Oscillations of a Barotropic Atmosphere

Abstract Solutions of the linearized global shallow-water equations (Laplace tidal equations) including the effect of a mean zonal flow are obtained by the Galerkin-transform method. Free oscillations of the first kind (gravity-inertia modes) are little affected by the zonal flow. Solutions of the second kind (rotational modes of the Rossby-Haurwitz type) are significantly affected by a zonal flow different from solid rotation. Only a few lowest rotational modes, whose angular phase velocities are less than the minimum velocity in the zonal flow, appear as discrete. The remaining angular phase velocities fall into a continuous spectrum which covers the interval between the minimum and maximum zonal velocities. An approximate, but accurate, frequency formula is obtained for the discrete modes of free oscillations under the effect of a mean zonal flow. The frequencies and latitudinal structures of a few lowest rotational modes under the effect of a mean zonal flow are examined in detail and compared to obse...

The Influence of Realistic Dissipation on Planetary Normal Structures

Abstract The effect of realistic dissipation on the rotational normal modes of a barotropic atmosphere is investigated. Vertical growth of amplitude of the Lamb(10km equivalent depth)modes is found to diminish with increasing meridional index n. The fastest traveling modes are most sensitive to radiative-photo-chemical damping above 4 scale heights. However, with increasing n, thermal and viscous diffusion dissipate more of the energy below this level. The energy flux is virtually attenuated by 8 scale heights. Thus the particular details above this level should have little bearing on the nature of the modes below. Damping time scales (relaxation periods) are estimated for several modes. These are smallest for wavenumber 1, roughly 10 wave periods, and increase with zonal wavenumber. The role of dissipation in determining these relaxation periods is more than just the local damping of energy. It significantly enhances the “vertical leakage” and thus allows energy to flow more readily to levels of greater ...

On the Solution of the Homogeneous Vertical Structure Problem for Long-Period Oscillations

Abstract The problem of determining the long-period normal modes of a barotropic atmosphere with realistic temperature, distribution and in uniform motion is examined over the entire range of equivalent depth. It is demonstrated that there are only two solutions which satisfy a radiation/finite energy condition and approximately satisfy the homogeneous surface boundary condition. Outside of a particular interval of equivalent depth, it is shown that there exist no solutions. The problem is solved numerically over the restricted interval where two sharp dips in the surface error are found. The first of these corresponds to a 9.6 km equivalent depth and a Lamb structure. This mode, which is the counterpart of the thin film solutions on a sphere, is due to the hydrostatic nature of the basic state and exists despite the temperature variation. The second dip, corresponding to a 5.8 km equivalent depth here, is a result of buoyancy ducting and is a consequence of the temperature variation. The energy density o...

Solitary Rossby Waves in Zonal Shear Flows and Their Interactions

Interactions of long-wave solitons propagating in shear flows are described by a coupled pair of Korteweg-de Vries equations. The basic equation of motion for the analysis is the quasi-geostrophic forecast equation, and the interaction of two wave modes is studied. The solution for mode 1-mode 2 interaction of solitary waves in an asymmetric shear flow of a barotropic atmosphere with divergence is constructed. Streamline patterns for certain flows are obtained. An unsteady solitary wave solution for a modified Korteweg-de Vries equation is derived.

Energy dispersion in a barotropic atmosphere

AbstractThe propagation of energy on the sphere as described by the linear barotropic vorticity equation is studied. For simple flows, the concept of group velocity is examined. Planetary‐scale vorticity anomalies exhibit a surprising lack of dispersion in a hemispheric domain. On the sphere, there is more dispersion and a significant cross‐equatorial propagation of energy. Planetary‐scale vorticity sources tend to produce an orderly downstream train of waves which exhibit a strong tilt (NE‐SW for sources in the northern hemisphere) and cross the equator. Zonally elongated sources produce an almost north‐south train of waves. For realistic zonal flows with equatorial easterlies, large‐scale transients cross the equator, but the long‐term forced response in the opposite hemisphere is small.Comparison of the results with observations of atmospheric wave behaviour is made, and some possible implications are presented.

Energy dispersion in a barotropic atmosphere

The propagation of energy on the sphere as described by the linear barotropic vorticity equation is studied. For simple flows, the concept of group velocity is examined. Planetary-scale vorticity anomalies exhibit a surprising lack of dispersion in a hemispheric domain. On the sphere, there is more dispersion and a significant cross-equatorial propagation of energy. Planetary-scale vorticity sources tend to produce an orderly downstream train of waves which exhibit a strong tilt (NE-SW for sources in the northern hemisphere) and cross the equator. Zonally elongated sources produce an almost north-south train of waves. For realistic zonal flows with equatorial easterlies, large-scale transients cross the equator, but the long-term forced response in the opposite hemisphere is small. Comparison of the results with observations of atmospheric wave behaviour is made, and some possible implications are presented.