On Production of Long-term Mean Zonal Current and Eddy Momentum and Heat Transports in Atmosphere

— The mean zonal velocity in the atmosphere is taken as being created continually by the global scale Hadley circulation produced by the differential solar heating through the balance between the Coriolis effect and vertical diffusion, and not by conservation of absolute momentum. Hence a proper determination of the diffusion coefficient becomes the key to the solution of the zonal flow problem. In this study we take the flow field as composed of a primary global scale Hadley circulation, and a secondary flow created by the convergences of the eddy transports of heat and momentum and surface friction, which give rise to the classical three cell structure of the meridional circulation but which only modifies the zonal velocity distribution slightly.¶Finally, we use the equilibrium solution of the perturbation potential vorticity equation to obtain the eddy transports of momentum and heat, with the zonal velocity given by the primary Hadley flow as the basic flow, and we found that they are close to the statistically observed values, demonstrating that the system can maintain itself.     

Numerical studies of transient planetary circulations in a wind-driven ocean

Summary The time-dependent primitive equations for a shallow homogeneous ocean with a free surface are solved for a bounded basin on the sphere, driven by a steady zonal wind stress and subject to lateral viscous dissipation. These are the vertically integrated equations for a free-surface model, and are integrated to 60 days from an initial state of rest by an explicit centered-difference method with zero-slip lateral boundary conditions. In a series of comparative numerical solutions it is shown that at least a 2-deg resolution is needed to resolve the western boundary currents adequately and to avoid undue distortion of the transient (Rossby waves. The -plane formulation is shown to be an adequate approximation for the mean circulation in the lower and middle latitudes, but noticeably intensifies the transports poleward of about 50 deg and both slows and distorts the transients in the central basin. The influence of the (southern) zonal boundary on the transport solutions is confined to the southernmost gyre, except in the region of the western boundary currents where its influence spreads to the northern edge of the basin by 30 days. The total boundary current transport is shown to be approximately proportional to the zonal width of the basin and independent of the basin's (uniform) depth, while the elevation of the free water surface is inversely proportional to the basin depth, in accordance with linear theory. The introduction of bottom friction has a marked damping effect on the transient Rossby waves, and also reduces the maximum boundary-current transport. The solutions throughout are approximately geostrophic and are only slightly nonlinear.The root-mean-square (rms) transport variability during the period 30 to 60 days is concentrated in the southwest portion of the basin through the reflection of the transient Rossby waves from the western shore and has a maximum corresponding to an rms current variability of about 3 cm sec^–1. The transport variabilities are about 10 percent of the mean zonal transport and more than 100 percent of the mean meridional transport over a considerable region of the western basin (outside the western boundary current regime). Some 99 percent of the total kinetic energy is associated with the zonal mean and standing zonal waves, which are also responsible for the bulk of the meridional transport of zonal angular momentum. Although the transient Rossby waves systematically produce a momentum flux convergence at the latitude of the maximum eastward current, much in the manner of their atmospheric counterparts, this is only a relatively small contribution to the zonal oceanic momentum balance; the bulk of the mean zonal stress is here balanced by a nearly stationary net pressure torque exerted against the meridional boundaries by the wind-raised water. In an ocean without such boundaries the role of the transient circulations may be somewhat more important.     

On the maintenance of the axisymmetric part of the flow in the atmosphere

Summary The maintenance of the axisymmetric component of the flow in the atmosphere is investigated by means of a steady-state, quasi-geostrophic formulation of the meteorological equations. It is shown that the meridional variations in the time-averaged axisymmetric variables can be expressed as the sum of three contributions, one being due to the eddy heat transport, another to the eddy momentum transport, and a third to the convective-radiative equilibrium temperature which enters the problem through the specification of a Newtonian form of diabatic heating. The contributions by the large scale eddies are evaluated through the use of observed values for the eddy heat and momentum transports.The contributions from each of the three forcing mechanisms to the temperature and zonal wind fields are invstigated individually and found to be of about equal importance. The sum of the three contributions are also presented for the temperature, the zonal wind, the stream function associated with the mean meridional circulation and the corresponding vertical motion. Although the results fail to reproduce the main observed features of the lower stratosphere, they are found to be in good agreement with observations in the middle latitude troposphere. At any pressure level, for example, the computed mean zonal wind has a jet-like profile and the axis of the jet is found to slope to the south with height, as observed in the atmosphere.Based in part on a thesis submitted by the first author as partial fulfillment of the requirements for the Ph.D. degree at the University of Michigan. — Publication No. 194 from the Department of Meteorology and Oceanography, The University of Michigan.     

Preconditioning and ozone hole filling in the Antarctic Spring

The temporal variations in mean zonal wind, horizontal temperature gradient at 30 mb and Total Ozone in Antarctic Spring (1 Sept.–30 Nov.) for nine seasons (1979–1987) were examined. The ozone hole filling commenced when the zonal flow decelerated to 50–58 m.sec^–1 at 30 mb. Our calculation of Rossby critical wave number with vertical shear suited for Antarctic Spring indicated that flow is preconditioned for vertical propagation of Rossby critical wave number two at this range of zonal flow. This preconditioning can be attributed to the diabatic heating in the Antarctic Spring since no sudden minor warmings/coolings have occurred during the period.     

Effects of the earth's rotation and the balance of zonal kinetic energy

Summary According to the symmetric formulation of the zonal kinetic energy equation, positive generations arise through countergradient transports of angular momentum. Five years of northern hemispheric upper air data are used to investigate two of the terms in the equation, which represent the effects of the transport, by the mean general circulation cells, of the angular momentum associated with the earth's rotation. These two -generation terms do not usually appear in the more traditional form of the conservation equation, and results of their evaluation have not appeared previously. It is found that positive generation largely dominates in the -term involving horizontal (meridional) transports of angular momentum, and negative generation in the -term involving vertical transport. In fall and particularly winter, both terms are responsible for very large amounts of generation of opposing sign for the whole atmosphere.The five years of data are also used to evaluate the balance of zonal kinetic energy implied by the symmetric equation in northern hemispheric polar caps of various pressure thicknesses. The vertical processes involved are not directly measured but rather are obtained from observed horizontal motions through use of continuity of mass and angular momentum requirements. Possible reasons for the lack of a perfect balance are offered, but in any case the residuals are generally not large enough to be of too much concern. Vertical eddies are found to play an important role in the balance of zonal kinetic energy. A study of the balance in the upper half of the atmosphere reveals that in spring the vertical eddies (summed for all scales) must tranport angular momentum and zonal kinetic energy upward toward the jet in order to counter the net effect of the mean cells in reducing the zonal kinetic energy in this volume. In the fall however, there is a dramatic change in the direction in which these vertical eddies act, as they now remove zonal kineticenergy from the upper half of the atmosphere in this season.The research reported in this paper was sponsored by the U.S. National Science Foundation under Grant No. GA-1310X.     

热带大洋对纬向和经向风应力的联合响应

考虑了经向风应力和纬向风应力联合作用下热带大洋的响应问题.结果表明,只有一阶的经向风应力或具有辐合辐散的经向风应力才对最后的速度场和位势场造成影响.零阶的扰动温跃层和纬圈流受风应力的直接驱动和Kelvin波、Rossby短波的影响,而Rossby短波由经向风应力直接造成;二阶模则受风应力的直接驱动和Rossby短波的作用,同时经向风应力也产生了附加的Rossby短波.另外,在西边界处存在很强的暖水补充到赤道的现象,经向风应力有使暖水向赤道输送的作用,而西风应力使西边界处的暖水向东输送.     

On the reynolds stress and lateral eddy viscosity due to transient oceanic Rossby waves

Summary From numerical solutions of a wind-driven homogeneous ocean model, anegative lateral eddy viscosity of the order 10⁴ cm² sec^–1 is inferred from the large-scale time-dependent currents in the interior of an enclosed shallow basin. The transient Rossby waves in this region produce a systematic convergence of eddy momentum at the latitude of the maximum average eastward current, and thus effect a transfer of zonal momentum from the large-scale eddies to the mean flow. In this sense they are analogous to the Rossby waves in the atmospheric general circulation, and it is speculated that such waves may help to maintain the mean zonal ocean currents. Although this negative viscosity induced by the large-scale transients is relatively small compared with the prescribed lateral viscosity of 10⁸ cm² sec^–1 and should be given a quite different physical interpretation, it is evidently an important viscous effect for the mean flow in the interior of the basin. The prescribed viscosity, on the other hand, is effective in controlling the model's simulated sub-grid scale dissipation, which occurs almost entirely in the nearby steady boundary currents.     

The generation of baroclinic rossby waves by meridional oscillations of a zonal wind stress

Abstract

This paper investigates the generation of linear baroclinic Rossby waves by meridional oscillations of a climatological zonal wind stress in a reduced gravity ocean bounded by an eastern coastline. Using a power series technique an analytical solution is derived for the interfacial displacement. It is found that for a given period of oscillation of the zonal winds, a finite number of propagating Rossby waves will be generated with frequencies equal to a harmonic of the forcing frequency. The number of propagating modes increases with increasing period of the wind stress. In addition to the propagating waves the complete solution for the interfacial displacement consists of a rapidly convergent infinite sum of evanescent terms. The displacement field is calculated for atmospheric forcing parameters typical of those found at mid-latitudes. Further, it is shown that a near resonant response can be generated using atmospheric parameter values typical of those found over the North Pacific.     

Atmosphere and Earth's rotation

The theoretical aspects of the transfer of angular momentum between atmosphere and Earth are treated with particular emphasis on analytical solutions. This is made possible by the consequent usage of spherical harmonics of low degree and by the development of large-scale atmospheric dynamics in terms of orthogonal wave modes as solutions of Laplace's tidal equations.An outline of the theory of atmospheric ultralong planetary waves is given leading to analytical expressions for the meridional and height structure of such waves. The properties of the atmospheric boundary layer, where the exchange of atmospheric angular momentum with the solid Earth takes place, are briefly reviewed. The characteristic coupling time is the Ekman spin-down time of about one week.The axial component of the atmospheric angular momentum (AAM), consisting of a pressure loading component and a zonal wind component, can be described by only two spherical functions of latitude : the zonal harmonicP ₂ ⁰ (), responsible for pressure loading, and the spherical functionP ₁ ¹ () simulating supperrotation of the zonal wind. All other wind and pressure components merely redistributeAAM internally such that their contributions toAAM disappear if averaged over the globe. It is shown that both spherical harmonics belong to the meridional structure functions of the gravest symmetric Rossby-Haurwitz wave (0, –1)^*. This wave describes retrograde rotation of the atmosphere within the tropics (the tropical easterlies), while the gravest symmetric external wave mode (0, –2) is responsible for the westerlies at midlatitudes. Applying appropriate lower boundary conditions and assuming that secular angular momentum exchange between solid Earth and atmosphere disappears, the sum of both waves leads to an analytical solution of the zonal mean flow which roughly simulates the observed zonal wind structure as a function of latitude and height. This formalism is used as a basis for a quantitative discussion of the seasonal variations of theAAM within the troposphere and middle atmosphere.Atmospheric excitation of polar motion is due to pressure loading configurations, which contain the antisymmetric functionP ₂ ¹ () exp(i) of zonal wavenumberm=1, while the winds must have a superrotation component in a coordinate system with the polar axis within the equator. The Rossby-Haurwitz wave (1, –3)^* can simulate well the atmospheric excitation of the observed polar motion of all periods from the Chandler wobble down to normal modes with periods of about 10 days. Its superrotation component disappears so that only pressure loading contributes to polar motion.The solar gravitational semidiurnal tidal force acting on the thermally driven atmospheric solar semidiurnal tidal wave can accelerate the rotation rat of the Earth by about 0.2 ms per century. It is speculated that the viscous-like friction of the geomagnetic field at the boundary between magnetosphere and solar wind may be responsible for the westward drift of the dipole component of the internal geomagnetic field. Electromagnetic or mechanical coupling between outer core and mantle may then contribute to a decrease of the Earth's rotation rate.     

Observational evidence of the semiannual oscillation in the tropical middle atmosphere—A review

Observational studies on the semiannual oscillation in the tropical stratosphere and mesosphere are reviewed. Results of many statistics based on rocket and satellite observations reveal that the long-term behavior of the mean zonal wind exhibits two semiannual cycles which have their maximum amplitudes centered at the stratopause level and the mesopause level, each one being associated with the semiannual temperature variations predominating at levels about 10 km lower.Observational evidence obtained from recent studies of the dynamical properties of upper stratospheric waves strongly supports the theoretical consideration that the stratospheric semiannual oscillation is the manifestation of the wave-zonal flow interaction with alternating accelerations of the westerly flow by Kelvin waves and the easterly flow by planetary Rossby waves.Regarding the semiannual variation in the upper mesosphere, however, very little is known about the possible momentum source. Therefore, emphasis is placed on the need for further observations of the structure and behavior of the tropical middle atmosphere.     

切变基本纬向流中非线性赤道Rossby长波

为了解决观测和理论研究中的一些问题以及更好地了解热带大气动力学 ,有必要进一步研究基本气流的变化对大气中赤道Rossby波动的影响 .本文研究分析基本气流对赤道Rossby长波的影响 ,利用一个简单赤道 β平面浅水模式和摄动法 ,研究纬向基本气流切变中非线性赤道Rossby波 ,推导出在切变基本纬向流中赤道Rossby长波振幅演变所满足的非线性KdV方程并得到其孤立波解 .分析表明 ,孤立波存在的必要条件是基本气流有切变 ,而且基流切变不能太强 ,否则将产生正压不稳定 .     

On the mean atmospheric circulation over Antarctica

Abstract

The south-easterly surface flow down the slopes of Antarctica induces a transfer of westerly angular momentum to the atmosphere, which must be removed from the Antarctic domain by atmospheric transports. It is suggested that synoptic eddies protruding from the northern baroclinic zone into the polar regions are modified by the topography such that they are able to perform these meridional transports. A simple linear two-layer model of the axisymmetric circulation of Antarctica is presented where the eddy effects are incorporated via a K-ansatz. It is shown that qualitatively realistic mean flow patterns can be obtained with this model. The limitations of this approach are exposed.     

Rossby wave patterns in zonal and meridional winds

The propagation properties of Rossby waves in zonal and meridional winds are analyzed using the local dispersion relation in its wave number form, the geometry of which plays a crucial role in illuminating radiation patterns and ray trajectories. In the presence of a wind/current, the classical Rossby wave number curve, an offset circle, is distorted by the Doppler shift in frequency and a new branch, consisting of a blocking line with an eastward facing indentation, arises from waves convected with or against the flow. The radiation patterns generated by a time harmonic compact source in the laboratory frame are calculated using the method of stationary phase and are illustrated through a series of figures given by the reciprocal polars to the various types of wave number curves. We believe these results are new. Some of these wave patterns are reminiscent of a “reversed” ship wave pattern in which cusps (caustics) arise from the points of inflection of the wave number curves; whilst others bear a resemblance to the parabolic like curves characteristic of the capillary wave pattern formed around an obstacle in a stream. The Rossby stationary wave in a westerly is similar to the gravity wave pattern in a wind, whereas its counterpart in a meridional wind exhibits caustics, again arising from points of inflection in the wavenumber curve.     

On the meridional circulation and balance of momentum in the Southern Ocean of POP

 The circulation of the Southern Ocean is studied in the eddy-resolving model POP (Parallel Ocean Program) by an analysis of zonally integrated balances. The TEM formalism (Transformed Eulerian Mean) is extended to include topography and continental boundaries, thus deviations from a zonally integrated state involve transient and standing eddies. The meridional circulation is presented in terms of the Eulerian, eddy-induced, and residual streamfunctions. It is shown that the splitting of the meridional circulation into Ekman and geostrophic transports and the component induced by subgrid and Reynolds stresses is identical to a particular form of the zonally integrated balance of zonal momentum. In this balance, the eddy-induced streamfunctions represent the interfacial form stresses by transient and standing eddies and the residual streamfunction represents the acceleration of the zonal current by density fluxes in a zonally integrated frame. The latter acceleration term is directly related to the surface flux of density and interior fluxes due to the resolved and unresolved eddies. The eddy-induced circulation is extremely vigorous in POP. In the upper ocean a shallow circulation, reversed in comparison to the Deacon cell and mainly due to standing eddies, appears to the north of Drake Passage latitudes, and in the Drake Passage belt of latitudes a deep-reaching cell is induced by transient eddies. In the resulting residual circulation the Deacon cell is largely cancelled and the residual advection of the zonal mean potential density is balanced by diapycnal eddy and subgrid fluxes which are strong in the upper few hundred meters but small in the ocean interior. The balance of zonal momentum is consistent with other eddy-resolving models; a new aspect is the clear identification of density effects in the zonally integrated balance. We show that the wind stress and the stress induced by the residual circulation drive the eastward current, whereas both eddy species result in a braking. Finally, we extend the Johnson–Bryden model of zonal transport to incorporate all relevant terms from the zonal momentum balance. It is shown that wind stress and induction by the residual circulation carry an eastward transport while bottom form stress and the stress induced by standing eddies yield westward components of transport. Received: 26 June 2001 / Accepted: 2 November 2001     

Turbulent transport of angular momentum and differential rotation

Abstract

With the help of simplifying approximations, we have derived expressions for the non-diffusive fluxes of the angular momentum which are brought about by the action of Coriolis forces on the convective motion. The original turbulence, which is not perturbed by the Coriolis forces, is considered given and weakly anisotropic, the anisotropy having a preferred radial direction. The eddy viscosities are evaluated. Hence, a closed equation for the angular velocity is derived, and then solved for the case of slow rotation. It is shown that the differential rotation is generated most effectively in the case of moderate rotation when the Rossby number is of order unity. At small Rossby numbers, the rotation differentiality is inhibited. A negative eddy viscosity is suggested for the case of rapid rotation. Some implications for the Sun and other astrophysical objects are discussed.     

Effect of atmospheric action center in low-frequency teleconnection mechanism: an explicit analytic study

In consideration of the characteristics of spectral average of the Rossby wave trains and the adoption of a climatic mean stream field as the basic stream field, an approximate analytical formula for the period of atmospheric low-frequency oscillation (LFO) and the group velocity is deduced from a barotropic and non-divergent linearized vorticity equation. All the action centers of atmosphere are found to be the oscillators of low frequency. The LFO propagates southward across the streamlines in the wind field with a southward component or propagates northward across the streamlines in the wind field with northward component instead of along a great circle. The switch of the propagation direction takes place near the top of ridge or the bottom of trough. The angle between the wave rays and the zonal direction can be determined. Project supported by the National Natural Science Foundation of China (Grant No. 49175241).     

On steady and travelling waves over bottom topography in the model of homogeneous flow in a beta-plane channel

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.     

Solitary Rossby Waves in Zonally Varying Jet Flows

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.     

Mean meridional circulations of the stratosphere and mesosphere

Observations from the Nimbus 6 pressure modulator radiometer (PMR) have been used to estimate monthly mean planetary wave fluxes of heat and momentum in the stratosphere and mesosphere. While the eddy heat fluxes play an important role in the mean meridional circulation of the winter stratosphere they are shown to be less important in the upper mesosphere. Incorporation of the observed momentum fluxes into the Oxford two-dimensional circulation model has shown that they are incapable of providing the momentum transport necessary to balance the zonal flow accelerations induced by the mean meridional motion. Other unspecified transfer processes represented by Rayleigh frictional damping of the zonal fow are shown to dominate. In contrast the observed fluxes in the stratosphere achieve the necessary redistribution of momentum. Moreover their interannual variability profoundly influences the stratospheric circulation, as demonstrated in the model by the use of two different annual sets of observed momentum fluxes. The desirability of calculating the planetary wave behaviour within the model is indicated.