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1.
Abstract

The weakly nonlinear evolution of a free baroclinic wave in the presence of slightly supercritical, vertically sheared zonal flow and a forced stationary wave field that consists of a single zonal scale and an arbitrary number of meridional harmonics is examined within the context of the conventional two-layer model. The presence of the (planetary-scale) stationary wave introduces zonal variations in the supercriticality and is shown to alter the growth rate and asymptotic equilibrium of the (synoptic-scale) baroclinic wave via two distinct mechanisms: The first is due to the direct interaction of the stationary wave with the shorter synoptic wave (wave-wave mechanism), and the second is due to the interaction of the synoptic wave with that portion of the mean field that is corrected by the zonally rectified stationary wave fluxes (wave-mean mechanism). These mechanisms can oppose or augment each other depending on the amplitude and spatial structure of the stationary wave field. If the stationary wave field is confined primarily to the upper (lower) layer and consists of only the gravest cross-stream mode, conditions are favorable (unfavorable) for nonzero equilibrium of the free wave.

In addition to the time dependent heat flux generated by baroclinic growth of the free wave, its interaction with a stationary wave field consisting of two or more meridional harmonics generates time dependent heat fluxes that vary with period of the free wave. However, if the stationary wave field contains several meridional harmonics of sufficiently large amplitude, the free baroclinic wave is destroyed.  相似文献   

2.
The paper presents and analyzes, from the point of view of smooth dynamic systems theory, a two-layer baroclinic model of the troposphere in geostrophic approximation. The model describes airflow in β-channel within the tropospheric part of the main Hadley circulation cell. It enables to obtain, after application of the Galerkin method, a fairly simple low-parametric dynamic system describing the phenomena of non-linear interactions, bifurcations and blocking in the atmosphere. This enables to take into consideration such basic factors influencing the atmospheric dynamics like the heat exchange within the surface, orography, vertical variability of zonal wind and hydrostatic stability. Impact of zonal thermal variability of the surface and vertical shear of zonal wind in the troposphere on the orographic bifurcation was investigated and the oscillation character in the dynamic system after Hopf bifurcation of the second kind was analyzed. Additionally, the model dynamics was investigated in conditions including momentum forcing in the upper and lower parts of the troposphere and excluding orographic interaction, as well as in the conditions of thermal interaction between the troposphere and the surface for the vertical shear of zonal wind in both tropospheric layers. Impact of the mean zonal wind in the troposphere on the properties of model dynamics was assessed. It was proved that zonally varied surface temperature and layered mean zonal wind in the atmosphere are the parameters that have basic influence on the model dynamics. They cause numerous bifurcations and strongly influence the periods of oscillations of the model variables. They are often Hopf bifurcations of the second kind during which tropospheric states fairly distant from the ones before the bifurcations are generated. This significantly influences the model predictability.  相似文献   

3.
Abstract

It is shown that, even for vanishingly small diffusivities of momentum and heat, a rotating stratified zonal shear flow is more unstable to zonally symmetric disturbances than would be indicated by the classical inviscid adiabatic criterion, unless σ, the Prandtl number, = 1. Both monotonic instability, and growing oscillations ("overstability") are involved, the former determining the stability criterion and having the higher growth rates. The more σ differs from 1, the larger the region in parameter space for which the flow is stable by the classical criterion, but actually unstable.

If the baroclinity is sufficiently great for the classical criterion also to indicate instability, the corresponding inviscid adiabatic modes usually have the numerically highest growth rates. An exception is the case of small isotherm slope and small σ.

A single normal mode of the linearized theory is also, formally, a finite amplitude solution; however, no theoretical attempt is made to assess the effect of finite amplitude in general. But, in a following paper, viscous overturning (the mechanism giving rise to the sub‐classical monotonic instability when σ > 1) is shown to play an important role at finite amplitude in certain examples of nonlinear steady thermally‐driven axisymmetric flow of water in a rotating annulus. Irrespective of whether analogous mechanisms turn out to be identifiable and important in large‐scale nature, it appears then that a Prandtl‐type parameter should enter the discussion of any attempt to make laboratory or numerical models of zonally‐symmetric baroclinic geophysical or astrophysical flows.  相似文献   

4.
The interaction between a planetary wave damped by cooling to space and the zonally averaged circulation in the middle atmosphere is examined for a steady-state situation in middle latitudes. Quasi-geostrophic scaling of Type 2 is assumed (i.e. the space scales are planetary and the superrotation is small).A set of mean equations is derived for this scaling which is complementary to the set of perturbation equations previously studied. The mean equations show that a planetary wave induces a mean meridional circulation which is balanced by an eddy momentum forcing function and a mean diabatic heating which is balanced by an eddy heat flux forcing function. The vertical eddy fluxes enter the forcing at the same order as the horizontal eddy fluxes.An analytical wave solution is found for the case of an atmosphere in constant superrotation. The eddy fluxes and forcing functions are evaluated for this special case. It is found that they are very sensitive to the values of the radiative damping coefficient and the superrotation. Since the damping coefficient depends on the ozone concentration and the intensity of the solar ultraviolet flux, the results suggest that changes in these quantities can strongly modify the wave-mean flow interaction in the middle atmosphere. Possible implications for climate change are discussed.  相似文献   

5.
The mechanism of acceleration of the mean zonal flow by a planetary wave is explained intuitively by considering the wave drag which a corrugated bottom feels when it excites the wave. The explanation is justified by solving the problem of vertical propagation of a planetary wave packet and the second order mean motion induced around it. The discussion is slightly extended to the case of small damping, to illustrate in a compact form the fact that the mean zonal acceleration is determined by a forcing due to wave transience plus that due to wave dissipation.The mean flow induced by a steady, dissipating planetary wave is discussed, and it is shown that it depends largely on the dissipation scale-height of the wave whether the northern region is heated or cooled. For example, if the wave velocity-amplitude increases upward in spite of dissipation, the induced easterly flow increases with height and the temperature of the northern region increases relative to that in the southern region. A similar point has been made byDunkerton (1979) in connection with westerly flows induced by Kelvin waves.The Lagrangian-mean motion induced by a planetary wave is briefly discussed in connection with the mechanism of acceleration of the mean zonal flow, in the case of a slowly varying wave packet. Further, in order el elucidate the effects of wave dissipation and time dependence of wave amplitude, the results obtained for a steady, dissipating wave and for a growing baroclinic wave are mentioned.  相似文献   

6.
Abstract

A spectral low-order model is proposed in order to investigate some effects of bottom corrugation on the dynamics of forced and free Rossby waves. The analysis of the interaction between the waves and the topographic modes in the linear version of the model shows that the natural frequencies lie between the corresponding Rossby wave frequencies for a flat bottom and those applying in the “topographic limit” when the beta-effect is zero. There is a possibility of standing or eastward-travelling free waves when the integrated topograhic effect exceeds the planetary beta-effect.

The nonlinear interactions between forced waves in the presence of topography and the beta-effect give rise to a steady dynamical mode correlated to the topographic mode. The periodic solution that includes this steady wave is stable when the forcing field moves to the West with relatively large phase speed. The energy of this solution may be transferred to the steady zonal shear flow if the spatial scale of this zonal mode exceeds the scale of the directly forced large-scale dynamical mode.  相似文献   

7.
A numerical simulation of secondary waves generated by nonlinear interaction has been used to interpret the behaviour of planetary waves observed by a meteor radar in the UK (53°27′N, 1°35′W) during the summer of 1992. A new explanation is proposed for the long-period variability of the (3,0) mode quasi-two-day wave in the mesosphere and lower-thermosphere, involving the (2,0) Rossby-gravity mode and pseudo-two-day secondary waves with the same zonal wavenumbers as those of the primary (2,0) and (3,0) modes. These pseudo-two-day secondary waves arise from the nonlinear interaction of the Rossby-gravity modes with long-period oscillations of the zonally averaged flow in the equatorial stratosphere, which can be generated by the interaction between the 10 and 16 day planetary waves. Other maxima existing in the neutral wind power spectra can be identified with various secondary waves originating from nonlinear interaction between the quasi-two-day and long-period planetary waves.  相似文献   

8.

The dynamics of solitary Rossby waves (SRWs) embedded in a meridionally sheared, zonally varying background flow are examined using a non-divergent barotropic model centered on a midlatitude g -plane. The zonally varying background flow, which is produced by an external potential vorticity (PV) forcing, yields a modified Korteweg-de Vries (K-dV) equation that governs the spatial-temporal evolution of a disturbance field that contains both Rossby wave packets and SRWs. The modified K-dV equation differs from the classical equation in that the zonally varying background flow, which varies on the same scale as the disturbance field, directly affects the disturbance linear translation speed and linear growth characteristics. In the limit of a locally parallel background flow, equations governing the amplitude and propagation characteristics of SRWs are derived analytically. These equations show, for example, that a sufficiently large (small) translation speed and/or a sufficiently weak (strong) background zonal shear favor transmission (reflection) of the SRW through (from) the jet. Conservation equations are derived showing that time changes in the domain averaged amplitude ("mass") or squared amplitude ("momentum") are due to zonal variation in both the linear, long-wave phase speed and linear growth; dispersion and nonlinearity do not affect the "mass" or "momentum". Provided (1) the background PV forcing is sufficiently small, or (2) the background PV forcing is meridionally symmetric and the disturbance is a SRW, the dynamics of the disturbance field is Hamiltonian and mass and energy are thus conserved. Numerical solutions of the K-dV equation show that the zonally varying background flow yields three general classes of behavior: reflection, transmission, or trapping. Within each class there exists SRWs and Rossby wave packets. SRWs that become trapped within the zonally localized jet region may exhibit the following behaviors: (1) an oscillatory decay to a steady state at the jet center, (2) the creation of additional SRWs within the jet region, or (3) a steady-state wherein the solution has a smoothed step-like structure located downstream along the jet axis.  相似文献   

9.
The present paper focuses on planetary wave type responses of the thermosphere/ionosphere system to forcing from above and below during the Arctic winter of 2005/2006. The forcing from above is described by the sunspot numbers, the solar wind speed, the Bz-component of the IMF and the geomagnetic Kp-index, while the forcing from below, i.e. by upward propagating atmospheric waves, is represented by the SABER/TIMED temperatures. The observed global ionospheric zonally symmetric oscillations with periods of ～9, ～14 and ～24–27 days were approved to be of solar origin. The most persistent ～9-day oscillation is linked to a triad of solar coronal holes distributed roughly 120° apart in solar longitude. The ～18-day westward propagating wave with zonal wavenumber 1, observed in the ionospheric currents (detected by magnetometer data), and in the F-region plasma (foF2 and TEC) could be allocated to a simultaneous 18-day westward propagating planetary wave observed in the stratosphere/mesosphere/lower thermosphere region with large (～70 km) vertical wavelength.  相似文献   

10.
Nonhydrostatic Atmospheric Normal Modes on Beta-Planes   总被引：1，自引：0，他引：1  
--To facilitate the understanding of nonhydrostatic effect in global and regional nonhydrostatic models, the normal modes of a nonhydrostatic, stratified, and compressible atmosphere are studied using Cartesian coordinates on midlatitude and equatorial #-planes. The dynamical equations without forcing and dissipation are linearized around the basic state at rest, and solved by using the method of separation of variables. An eigenvalue-eigenfunction problem is formulated, consisting of the horizontal and vertical structure equations with suitable boundary conditions. The wave frequency and the separation parameter, referred to as "equivalent height," appear in both the horizontal and vertical characteristic equations as a coupled problem, unlike the hydrostatic case. Therefore, the nonhydrostatic equivalent height depends not only on the vertical modal scale, as in the hydrostatic case, but also on the zonal and meridional modal scales. Numerical resu lts on the dispersion relations are presented for an isothermal atmosphere. Three kinds of normal modes, namely acoustic, gravity, and Rossby modes, are solved and compared with the corresponding global solutions. Nonhydrostatic effects are studied in terms of normal modes in a wide range of wavelengths from small to planetary scales. It is demonstrated that Rossby modes are hardly affected by nonhydrostatic effects regardless of wavelengths. However, nonhydrostatic effects on gravity modes become significant for smaller horizontal and deeper vertical scales of motion. The equivalent height plays a particularly important role in evaluating nonhydrostatic effects of normal modes on the equatorial #-plane, because the equivalent height appears in the scaling of meridional distance variable of the eigenfunctions. The implementation of nonhydrostatic normal mode analysis on high-resolution numerical modeling is also discussed.  相似文献   

11.
Abstract

The stability of a baroclinic zonal current to symmetric perturbations on an equatorial β-plane is considered. The fluid is assumed to be Boussinesq, inviseid, adiabatic, hydrostatic, and stably stratified. The solutions exhibit the same stability properties as those on an f-plane: instability occurs whenever Ri < 1/(1 + d), where Ri is the Richardson number and d is a measure of the horizontal shear of the current; the most unstable motions tend to parallel the isotherms of potential temperature; and they have infinitely small scales of variation perpendicular to the isotherms. The variation of Coriolis parameter leads to one important difference in the structure of the eigenfunctions: the rapidly growing modes are concentrated in high latitudes, and the slowly growing ones in low latitudes.

The suggestion that the symmetric cloud bands observed at low latitudes in Jupiter's atmosphere are caused by symmetric instabilities is re-examined in the light of these results. These cloud bands would have to be associated with the slowly-growing, low-latitude modes. These modes consist of small scale motions parallel to the isotherms, with the magnitude of the motions having a large scale modulation as a function of latitude. The time scales of these modes and the latitude scales of their modulation agree qualitatively with the observations of Jupiter's cloud bands, so long as Ri is not very close to zero or to its critical value.  相似文献   

12.
The long-term variability of stationary and traveling planetary waves in the lower stratosphere has been investigated using the data of NCEP/NCAR reanalysis. The results obtained show that during the last decades winter-mean amplitude of the stationary planetary wave with zonal wave number 1 (SPW1) increases at the higher middle latitudes of the Northern Hemisphere. It has been suggested that the observed increase in the SPW1 amplitude should be accompanied by the growth in the magnitude of the stratospheric vacillations. The analysis of the SPW1 behavior in the NCEP/NCAR data set supports this suggestion and shows a noticeable increase with time in the SPW1 intra-seasonal variability. The amplitudes of the long-period normal atmospheric modes, the so-called 5-, 10- and 16-day waves, diminish. It is supposed that one of the possible reasons for this decrease can be a growth of radiative damping rate caused, for instance, by the increase of CO2. To investigate a possible climatic change of the middle atmosphere dynamics caused by observed changes in the tropospheric temperature, two sets of runs (using zonally averaged temperature distributions in the troposphere typical for January 1960 and 2000) with the middle and upper atmosphere model (MUAM) have been performed. The results obtained show that on average the calculated amplitude of the SPW1 in the stratosphere increased in 2000 and there is also an increase of its intra-seasonal variability conditioned by nonlinear interaction with the mean flow. This increase in the amplitudes of stratospheric vacillations during the last four decades allows us to suggest that stratospheric dynamics becomes more stochastic.  相似文献   

13.
Abstract

The stability properties are described for two general types of zonal mean flows: solid body rotation and a mid-latitude jet. Growth rates are plotted versus zonal wavenumber and mean flow vertical shear in both cases. The structure of the most unstable modes is described and some physical interpretation given.  相似文献   

14.
ABSTRACT

The instability of ideal non-divergent zonal flows on the sphere is determined numerically by the instability criterion of Arnold (Ann. Inst. Fourier 1966, 16, 319) for the sectional curvature. Zonal flows are unstable for all perturbations besides for a small set which are in approximate resonance. The planetary rotation is stable and the presence of rotation reduces the instability of perturbations.  相似文献   

15.
The instability of an internal gravity wave due to nonlinear wave-wave interaction is studied theoretically and numerically. Three different aspects of this phenomenon are examined. 1. The influence of dissipation on both the resonant and the nonresonant interactions is analysed using a normal mode expansion of the basic equations. In particular, the modifications induced in the interaction domain are calculated and as a result some modes are shown to be destabilised by dissipation. 2. The evolution of an initial unstable disturbance of finite vertical extent is described as the growth of two secondary wave packets travelling at the same group velocity. A quasi-linear correction to the basic primary wave is calculated, corresponding to a localised amplitude decrease due to the disturbance growth. 3. Numerical experiments are carried out to study the effect of a basic shear on wave instability. It appears that the growing secondary waves can have a frequency larger than that of the primary wave, provided that the shear is sufficient. The instability of waves with large amplitude and long period, such as tides or planetary waves, could therefore be invoked as a possible mechanism for the generation of gravity waves with shorter period in the middle atmosphere.  相似文献   

16.
Abstract

The linear stability of a non-divergent barotropic parallel shear flow in a zonal and a non-zonal channel on the β plane was examined numerically. When the channel is non-zonal, the governing equation is slightly modified from the Orr-Sommerfeld equation. Numerical solutions were obtained by solving the discretized linear perturbation equation as an eigenvalue problem of a matrix. When the channel is zonal and lateral viscosity is neglected the problem is reduced to the ordinary barotropic instability problem described by Kuo's (1949) equation. The discrepancy between the stability properties of westward and eastward flows, which have been indicated by earlier studies, was reconfirmed. It has also been suggested that the unstable modes are closely related to the continuous modes discretized by a finite differential approximation. When the channel is non-zonal, the properties of unstable modes were quite different from those of the zonal problem in that: (1) The phase speed of the unstable modes can exceed the maximum value of the basic flow speed; (2) The unstable modes are not accompanied by their conjugate mode; and (3) The basic flow without an inflection point can be unstable. The dispersion relation and the spatial structure of the unstable modes suggested that, irrespective of the orientation of the channel, they have close relation to the neutral modes (Rossby channel modes) which are the solutions in the absence of a basic shear flow. The features mentioned above are not dependent on whether or not the flow velocity at the boundary is zero.  相似文献   

17.
Summary The zonally asymmetric stationary component of the general circulation is studied for small Rossby number without the beta-plane approximation. The equations for this component are linearized about a mean flow. An analytic solution for the meridional wind is found when the zonal wind and static stability of the mean flow are independent of the vertical coordinate. The solution is used to compute the transports of angular momentum and heat. The angular momentum transports give rise to a net convergence of the order of Rossby number and are balanced by the zonal mean Coriolis torque. However, the heat transports vanish at this order of magnitude.  相似文献   

18.
Abstract

Analysis of a two-layer, flat-bottom, steady-wind driven, eddy-resolving general circulation model reveals a distinct separation in frequency of baroclinic and barotropic motion in the region distant from the model Gulf Stream. The far-field motions at periods less (greater) than about 100 days are predominantly barotropic (baroclinic), unlike the near-field, eddy-generating, free-jet region which contains barotropic and baroclinic energy throughout the modei frequency range. The far-field barotropic energy produces a peak in the model sea-level spectra between 25 and 50 days with a magnitude comparable to energy levels observed in spectra of sea level from oceanic island tide gauges. The far-field barotropic motion is clearly composed of large-scale, resonant, barotropic normal modes drive by mesoscale activity of the turbulent, free-jet region. Oceanic mesoscale turbulence may therefore provide for planetary normal modes an excitation mechanism distinct from atmospheric forcing. The open-ocean, barotropic, model response is very similar to that of a fluctuating-wind driven model, which suggests that atmospheric and intrinsic forcing of mid-ocean eddies may be of comparable importance.  相似文献   

19.
Part 2 of the present paper is focused on the planetary wave coupling from the stratosphere to the lower thermosphere (30–120 km) during the Arctic winter of 2003/2004. The planetary waves seen in the TIMED/SABER temperature data in the latitudinal range 50°N–50°S are studied in detail. The altitude and latitude structures of the planetary wave (stationary and travelling) clearly indicate that the stratosphere and mesosphere (30–90 km) are coupled by direct vertical propagation of the planetary waves, while the lower thermosphere (above 90–95 km altitude) is only partly connected with the lower levels probably indirectly through in-situ generation of disturbances by the dissipation and breaking of gravity waves filtered by lower atmospheric planetary waves. A peculiar feature of the thermal regime in the lower thermosphere is that it is dominated by zonally symmetric planetary waves.  相似文献   

20.
冬季平流层波动模型的分岔特性   总被引：1，自引：0，他引：1  
从描述波流相互作用的Ｈｏｌｔｏｎ－Ｄｕｎｋｅｒｔｏｎ简称Ｈ－Ｄ)模型出发，应用延拓方法求解常微分方程的分岔问题，研究冬季平流层波动模型的分岔特性．给出了大气行星波２与流相互作用的底部边界强迫波、底部边界平均纬向风场、风切变等参数的分岔特性，同时给出了波１与流相互作用的底部边界强迫波的分岔特性的结果．  相似文献   

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