Stationary Rossby wave propagation in a shear flow along a reflective boundary

Summary This study investigates the impact of lateral boundary conditions on the propagation and dispersion of locally excited Rossby waves in a zonally periodic, barotropic, quasigeostrophic channel model on the β-plane. We use basic flows with either a linear meridional shear or a jet-like profile. On the southern boundary of the channel we impose either a rigid wall or a radiation condition, whereas the northern sidewall is permeable for Rossby waves. We compare the numerical solutions found for a reflecting southern boundary in a weakly dissipative flow to the solutions obtained from a WKB-analysis for the corresponding unforced nondissipative situation. Furthermore, we compare the generalized Eliassen-Palm flux vectors to the ray paths of Rossby wave packets, obtained from WKB ray tracing. In particular, we focus our investigation on the two-dimensional structure of trapped modal waves and wavetrains in a simple linear numerical model. Summarizing our results, we find that along the reflective wall, trapped modal wave structures as well as reflected wavetrains occur with characteristics (e.g., wavenumbers, turning latitudes) similar to the ones computed using asymptotic methods. In a linear sheared flow wave packets are trapped for all zonal wave numbers in contrast to a jet-like mean flow which has a selective effect on the waves; i.e., a turning latitudes phenomenon between the coast and the flow maximum occurs for short waves, while long waves can propagate freely across the zonal mean flow. This comes out clearly when studying the stream lines of the Eliassen-Palm flux vectors of the numerical model simulations. Furthermore, due to the reflected wave activity, the dispersion of Rossby waves is influenced by the southern boundary condition not only in the vicinity of the border but also in regions away from the boundary. These results appear to be important on the one hand for the existence of trapped Rossby waves in large-scale oceanic shear flows along a zonally oriented coast. And, on the other hand for large-scale boundary waves in conceptional atmospheric channel models which can lead to unwanted resonance effects. Received July 18, 2000/Revised June 9, 2001     

On the low-frequency,planetary-scale motion in the tropical atmosphere and oceans

Scale analyses for long wave, zonal ultralong wave (with zonal scale of disturbance L1~104 km and meridional scale L2~103 km) and meridional ultralong wave (L1~103 km, L2~104 km) are carried out and a set of approximate equations suitable for the study of these waves in a dry tropical atmosphere is obtained. Under the condition of sheared basic current, frequency analyses for the equations are carried out. It is found that Rossby waves and gravity waves may be separated for n ≥ l where n is the meridional wave number, whereas for n = 0 and L1~1000 km, the mixed Rossby-gravity wave will appear. Hence it is confirmed that the above results of scale analyses are correct. The consistency be-tween frequency analysis and scale analysis is established.The effect of shear of basic current on the equatorial waves is to change their frequencies and phase velocities and hence their group velocities. It increases the velocity of westward travelling Rossby waves and inertia-gravity and mixed waves, but decelerates the eastward inertia-gravity waves and the Kelvin wave. The recently observed low-frequency equatorial ocean wave may be interpreted as an eastward Kelvin wave in a basic current with shear.     

Topographically forced three-wave quasi-esonant and non-resonant interactions among barotropic rossby waves on an infinnite beta-plane

In this paper, we first apply the assumption h = εh′ of topographic variation (h is the nondimensional topographic height and is a small parameter) to obtain nonlinear equations describing three-wave quasi-resonant and non-resonant interactions among Rossby waves for zonal wavenumbers 1—3 over a wavenumber-two bottom topography (WTBT). Some numerical calculations are made with the fourt-order Rung-Kutta Scheme. It is found that for the case without topographic forcing, the period of three-wave quasi-resonance (TWQR) is found to be independent of the zonal basic westerly wind, but dependent on the meridional wavenumber and the initial amplitudes. For the fixed initial data, when the frequency mismatch is smaller and the meridional wavelength is moderate, its period will belong to the 30–60-day period band. However, when the wavenumber-two topography is included, the periods of the forced quasi-resonant Rossby waves are also found to be strongly dependent on the setting of the zonal basic westerly wind. Under the same conditions, only when the zonal basic westerly wind reaches a moderate extent, intraseasonal oscillations in the 30–60-day period band can be found for zonal wavenumbers 1–3. On the other hand, if three Rossby waves considered have the same meridional wavenumber, three-wave non-resonant interaction over a WTBT can occur in this case. When the WTBT vanishes, the amplitudes of these Rossby waves are conserved. But in the presence of a WTBT, the three Rossby waves oscillate with the identical period. The period, over a moderate range of the zonal basic westerly wind, is in the intraseasonal, 30–60-Day range.     

Structures and mechanisms of the first-branch northward-propagating intraseasonal oscillation over the tropical Indian Ocean

The first-branch northward-propagating intraseasonal oscillation (FNISO) over the tropical Indian Ocean (IO) often triggers the onset of the Asian summer monsoon. In this study we investigate the structures and mechanisms associated with FNISO through the diagnosis of ERA-Interim reanalysis data for the period of 1990–2009. A composite analysis is conducted to reveal the structure and evolution characteristics of the FNISO and associated background circulation changes. It is found that the FNISO convection originates from the southwestern IO and propagates eastward. After reaching the eastern IO, the major convective branch moves northward toward the northern Bay of Bengal (BoB). Two possible mechanisms may contribute to the northward propagation of the FNISO. One is the meridional asymmetry of the background convective instability. A greater background convective instability over the northern BoB may destabilize Rossby waves and cause convection to shift northward. The other is the meridional phase leading of perturbation humidity in the planetary boundary layer (PBL). Maximum PBL moisture appears to the north of the convection center, which promotes a convectively unstable stratification ahead of the convection and leads to the northward propagation of the FNISO. A PBL moisture budget analysis reveals that anomalous zonal advection is a dominant process in contributing to the moisture asymmetry.     

Topographic generation of intermediate-scale motions by wind-driven currents — A model for the circulation in the vicinity of the Indian-Antarctic ridge

When a broad ocean current encounters a large-scale topographic feature, standing Rossby wave patterns can be generated. Short Rossby waves with a scale L_i = √ Q/β (Q is the speed of the approaching flow; β is the meridional gradient of f) are generated east of the topography. If the zonal scale of the topography, L, is planetary, long standing Rossby waves can be generated west of the topography, when the current has a meridional component. The long waves focus the disturbance zonally and produce alternating regions of intensified or reduced zonal flow. The meridional scale that characterizes these zonal bands is the intermediate scales, L = L_i^2/3L^1/3. When the meridional topographic scale is comparable to L, the amplitude of the long-wave disturbance is dominant. Using multiple-scale methods to exploit the scale gap between the planetary, intermediate and Rossby wave scales, the topographically induced pressure and velocity fields due to a zonal ridge are obtained. When the planetary-scale flow field is directed poleward, a westward counterflow can occur along the poleward flank of the ridge. The meridional scales of these topographically induced flows are comparable to those observed along the Indian-Antarctic Ridge by Callahan (1971).     

大气定常波传播的运动学特征的时空变化

利用时间平均全球大气环流资料,本文计算了纬向平均位涡的南北梯度的时空分布,以及波动水平传播的临界波数n_s,和垂直传播的临界波数K_c的时空分布。由此研究全球大气定常波传播的运动学特征及其年变化。     

Possible impact of equatorially trapped waves on the tropical cyclone drift

The effect of equatorially trapped waves on the movement of tropical cyclones (TC) is studied numerically based on a two-dimensional barotropic model in a beta-plane approximation. According to recent studies, equatorially trapped waves contribute to the genesis of TCs. It is thus natural to assume that these waves affect also the movement of the TC. The effect of three types of equatorially trapped waves, namely Kelvin, Rossby, and n = 0 eastward inertio-Gravity (EIG) waves, on the TC trajectory is investigated with a focus on the sensitivity on some key physical parameters such as the wavenumber and wavespeed. Using a simple barotropic model forced by a prescribed baroclinic flow, the barotropic response to equatorially trapped waves is simulated for a period of 50 days, under various wave parameter configurations. This response is then used as a background flow where TC’s can evolve and propagate. TC-like flows are injected into this wavefield background at arbitrary times during the simulation, and the TC trajectories are tracked and recorded for 48h after the injection time. The resulting TC trajectory patterns with respect to the injection times and wave parameters appear to be stochastic and the mean paths and the associated standard deviations are calculated and reported here. The statistics are different for different wave types. Kelvin waves make shorter length of TC trajectories and small divergence of direction. On the contrary, Rossby waves cause rather dramatic changes in the TC path and yield longer trajectories. Meanwhile, TCs in EIG waves maintain fairly the same direction and typically have longer trajectories though less dramatic. A robustness test using a random forcing instead has also been conducted.

     

切变基本纬向流中赤道Rossby包络孤立波

利用多重尺度摄动法，从描写赤道Rossby波的正压大气位涡度方程中推导出在切变基本纬向流中非线性赤道Rossby波包演变所满足的非线性Schrodinger方程，并得到其单个包络孤立子波解，分析基本流切变对非线性赤道Rossby波动的影响。     

青藏高原热力作用下的非绝热Rossby波

从含非绝热项的准地转运动方程组出发，分析了青藏高原大尺度热力作用下非绝热Rossby波的一些性质，从理论上证明当背景西风气流为正压时，冬季高原冷却作用有利于Rossby波的经向传播，夏季高原大尺度热力作用不利于波动的经向传播。非绝热Rossby波的频率方程说明冬季高原的热力作用是中纬季节内振荡的重要激发机制。同时，在背景西风气流为纯斜压条件下，求解了高原热力作用下非绝热Rossby波的频率，并由频率方程说明冬季高原热力作用有利于波动向不稳定方向发展，而夏季高原的大尺度热力作用对波动稳定性的影响存在临界值。     

大气动力学中三种Rossby波作用通量的特征差异和适用性比较

大气动力学诊断Rossby波的传播时,通常用波作用通量来表示。常用的三种波作用通量分别为Plumb波作用通量,T-N波作用通量和局地E-P通量。本文详细讨论了这三种方法的特征差异,并结合2016年1月的一次寒潮事件,比较了三种方法在该事件中的适用性。结果表明:1)Plumb波作用通量的纬向分量较大而经向分量较小,适用于振幅较小的纬向均匀的西风带Rossby长波的诊断。2)T-N波作用通量是对Plumb波作用通量的改进,经向分量得以增强,能更好地描述纬向非均匀气流中的较大振幅的西风带Rossby长波扰动。T-N波作用通量计算时,背景场取多年平均的当月气候场较合适,能更好地反映当前季节内的Rossby波传播异常。3)局地E-P通量可以诊断一段时间内天气尺度瞬变波对背景场(定常波)总的调控作用,但无法直接反映Rossby长波的逐时演变(T-N波或Plumb波作用通量则可以)。     

On the contribution of Rossby waves driven by surface buoyancy fluxes to low-frequency North Atlantic steric sea surface height variations

Previous studies have shown that wind-forced baroclinic Rossby waves can capture a large portion of low-frequency steric sea surface height (SSH) variations in the North Atlantic. In this paper, the classical wind-driven Rossby wave model derived in a 1.5-layer ocean is extended to include surface buoyancy forcing, and the new model is then used to assess the contribution from buoyancy-forced Rossby waves to low-frequency North Atlantic steric SSH variations. Buoyancy forcing is determined from surface heating as freshwater fluxes are negligible. It is found that buoyancy-forced Rossby waves are important in only a few regions belonging to the subtropical-to-midlatitude and eastern subpolar North Atlantic. In these regions, the new Rossby wave model accounts for 25%–70% of low-frequency steric SSH variations. Furthermore, as part of the analysis it is also shown that a simple static model driven by local surface heat fluxes captures 60%–75% of low-frequency steric SSH variations in the Labrador Sea, which is a region where Rossby waves are found to have no influence on the steric SSH.     

El Niño事件发生对南北半球大气环流异常的对称及非对称性影响及其机理分析

利用合成分析方法, 分析了1971～2003年间7个El Niño事件发生时南、北半球大气环流异常的对称与反对称特性。分析结果表明, El Niño事件发生期间, 在热带地区15°S～15°N大气环流异常以对称性为主, 但也有一定的反对称分量: 高度场异常和纬向风异常的对称性较强, 而经向风异常的反对称较强; 同时在El Niño事件演变的各阶段, 高度场异常和纬向风异常的变化较明显, 而经向风的变化较小, 高度场和风场异常在低层 (700 hPa) 和高层 (200 hPa) 呈明显的反位相分布。并且, 为探讨El Niño事件对南、北半球大气环流异常的非对称性影响的机理, 本研究进一步利用ERA－40逐日资料, 应用Hough函数分析了El Niño事件发生期间这些赤道波动的演变特征。结果表明, El Niño事件发生期间, 热带地区大气环流异常对称性较强的主要原因是对称性Rossby波异常较强, 而Rossby重力混合波异常对经向风场的反对称分量有重要作用; 并且, 研究结果还表明, 在El Niño事件发生期间, 热带东太平洋的海温正异常能够激发由对称性Rossby波和Kelvin波组成的Gill型环流异常。此外, 分析表明Hough函数在分析热带大气波动的对称性及反对称性上具有明显的优越性。     

Rossby wave propagation into the tropics in two GFDL general circulation models

During the northern winter the eastern Pacific is characterized by upper level westerly flow extending from the equator into the midlatitudes of both hemispheres. Theoretical and simple modeling studies suggest that such a region should favor the penetration of Rossby waves into the tropics from higher latitudes. Observational results by Kiladis and Weickmann using 200 mb data indicate that Rossby waves do indeed propagate freely into the tropical eastern Pacific during the northern winter from the Asian jet exit region. They also confirmed that cross-equatorial dispersion of energy from the Northern into the Southern Hemisphere occurs frequently. The present study examines these interactions in climatological runs of two GFDL GCMs. The northern wintertime mean states of these models are characterized by a rather realistically simulated upper level westerly regime in the tropical Pacific. Despite the relative weakness of the Asian jet and wave activity with respect to observations, propagation of Rossby waves into the tropics is present in both models, and these waves are strongly positively tilted as seen in the observations. A momentum budget of the zonal wind and E vector diagnostics over the tropical Pacific indicate that these transients are an important component of the momentum balance of the equatorial westerlies in both the observations and in the models.This paper was presented at the Second International Conference on Modelling of Global Climate Variability, held in Hamburg 7–11 September 1992 under the auspices of the Max Planck Institute for Meteorology. Guest Editor for these papers is L. Dümenil     

线性准地转模型中副热带环流对潜热加热的定常响应I.基本性质及特征分析

利用线性理论模型进行解析和模拟是大气科学的重要基础研究方法之一, 其简单明了, 解释了如Rossby波形成等重要的环流现象。近年, 有研究 (Chen et al., 2001) 运用定常线性准地转模型研究副热带高压的形成, 在相似加热强迫下, 其结果与理论研究和GCM的研究不同。本文运用该模型系统研究了由季风降水产生的潜热加热所激发的副热带定常波的结构特征, 以理解其结果与GCM不一致的原因。研究表明基本流对热强迫的定常波的结构有重要的影响: (1) 当基本流为东风或为零时, 定常波在垂直方向上表现为第一斜压结构, 波动振幅随东风的增大而减小; (2) 当基本流为西风时, 呈现向上的传播特征, 振幅随高度的升高而增大。而且存在一个临界风速Uc(约3 m/s), 此时, 波动振幅最强; 基本流的平流作用具有非对称性, 西风时平流作用远远强于东风。由此揭示了该线性模型解的本质: 加热在热源区所激发的经向地转涡度输送必须能够平衡加热的位涡制造和纬向位涡平流; 基本流的经向和垂直方向的变化使得气旋和反气旋中心偏向热源中心北侧, 并进一步发现当基本流为夏季亚洲季风区纬向平均的纬向风场时, 线性模型的解中位于中低层的反气旋中心显著抬升, 而不出现在地面上, 与完整的大气环流模式的结果接近。说明即使在线性模式中, 洋面副高的形成也不能完全用季风潜热加热来解释; 另外, 静力稳定度对热强迫的副热带环流的影响也很重要, 使热源的强迫作用放大。     

SPATIAL AND TEMPORAL VARIATIONS OF THE KINEMATIC CHARACTERISTICS IN THE PROPAGATION OF ATMOSPHERIC STATIONARY WAVES

Time-mean global general circulation data are employed to analyze the temporal and spatial variations ofthe meridional gradient of zonal mean potential vorticity,the critical wavenumber n_s for horizontal wave-propagation,and the critical wavenumber K_c for vertical wave-propagation.Thereby the kinematic charac-teristics in the propagation of atmospheric stationary waves and their annual variations are studied.Resultsshow that in the troposphere n_s and K_c usually decrease with the increase of either latitude or altitude.Synoptic and near-resonant Rossby waves could be trapped during their upward and meridional propagations.These characteristics possess prominent annual variations,especially in the Northern Hemisphere.It is foundthat the spatial and temporal variations of these kinematic characteristics are in good agreement with those ofthe atmospheric wave patterns.     

Development and propagation of equatorial waves

Development and propagation of equatorial waves are investigated with the model which includes convection -wave convergence feedback and convection-frictional convergence feedback. Two experiments with an initial Kelvin wave (Exp. K) and with an initial Rossby wave (Exp. R) are carried out. The equatorial waves in Exp. R grow much faster than those in Exp. K. The equatorial waves in both experiments follow zonal (eastward / westward) and meridional (poleward) propagation. The equatorial waves can be partitioned into two meridional modes using Parabolic Cylinder Function. An equa?tor mode denotes a wave component with a positive precipitation center at the equator and an off-equator mode rep?resents a wave component with positive precipitation centers off the equator. The equator mode dominates in Exp. K whereeas the off-equator mode dominates in Exp. R. The rapid wave growth in Exp. R is interpreted by analyzing the eddy available potential energy (EAPE) generation. Stronger off-equator mode in Exp. R obtains more EAPE through convection-frictional convergence feedback which results in more rapid wave growth. The relative vorticity tendency is determined by interactions between Earth’s vorticity and lower-troposphere convergence (divergence effect) and between the meridional gradient and lower-troposphere circulation (beta effect). The eastward and poleward propagation of equatorial waves is a result of the divergence effect, and the westward movement is caused by the beta effect.     

Resonance of baroclinic waves in the tropical oceans: The Indian Ocean and the far western Pacific

The Indian Ocean has a particularity, its width is close to half the wavelength of a Rossby wave of biannual frequency, this coincidence having been capitalized on by several authors to give the observations a physical basis. The purpose of this article is to show that this is not the case since the resonance of tropical baroclinic waves occurs in all three oceans. This is because the westward-propagating Rossby wave is retroflexed at the western boundary to form off-equatorial Rossby waves dragged by countercurrents before receding and turning back as a Kelvin wave. Thus a quasi-stationary baroclinic wave is formed, whose mean period is tuned to the forcing period. Two independent basin modes resonantly forced are highlighted – 1) a nearly symmetric zonal 1/2-yr period Quasi-Stationary Wave (QSW) that is resonantly forced by the biannual monsoon. It is formed from first baroclinic mode equatorial-trapped Rossby and Kelvin waves and off-equatorial Rossby waves at the western antinode. This QSW controls the Equatorial Counter Current at the node. The Indian Ocean Dipole (IOD) results from a subharmonic mode locking resulting from the coupling of this QSW and the 2nd, 3rd and 4th baroclinic modes - 2) a 1-yr period QSW formed from an off-equatorial baroclinic Rossby wave, which is induced from the southernmost current of the Indonesian Throughflow through the Timor passage, propagating in the southern and northern hemispheres: the drivers are south-easterlies in the southern hemisphere and monsoon wind in the northern hemisphere.     

THE FOUNDATION AND MOVEMENT OF TROPICAL SEMI-GEOSTROPHIC ADAPTATION

The breakdown and foundation of geostrophic balance is one of the important movements inthe mid-and high-latitude atmosphere and oceans.In the tropical area,the value of Coriolis pa-rameter is so small that it is difficult to satisfy the bi-geostrophic equilibrium between the pressureand velocity fields.However,in the tropical area,the zonal velocity of some motions in the atmo-sphere and oceans is large,so the Coriolis force is not small,geostrophic balance can exist in zonaldirection,i.e.semi-geostrophic balance.Furthermore,in the dominant area of Hadley circulationin the atmosphere or the area near the ocean meridional boundary,the meridional velocity is large,so geostrophic balance can also exist in meridional direction.In this paper,the process of the dis-persion of inertial gravity wave and the foundation of semi-geostrophic balance are first discussed.Second,the adjustment process between the velocity and pressure fields after adaptation is alsoviewed,and the scale criterion of the semi-geostrophic adaptation is discussed,i.e.for the motionwith meridional scale greater than the equatorial Rossby radius of deformation,the velocity andpressure fields after adaptation change to fit the initial pressure field;on the contrary,the fieldschange to fit the initial zonal velocity field,and the strength of the fields after adaptation dependson the zonal scale.     

热带大气对单一型赤道非对称热源的响应

本文采用Gill模式得到了热带大气对单一型赤道非对称热源响应的理论解析通解,从理论上完善了单一型赤道非对称热源激发的赤道非对称的大气响应结果。同时在单一型赤道非对称热源的位置、强度及范围变化对大气响应的影响方面做了详细的研究。当热源中心位置北移,北半球气旋强度增加、位置北移,同时赤道辐合气流减弱而越赤道气流增强;当热源强度增强(减弱),热源激发的大气响应整体增强(减弱),但大气分布型不发生变化;当热源范围不断增大(减小)时,北半球气旋强度增强(减弱)、位置西移(东移)、范围增大(减小),同时越赤道气流增强(减弱)。将上述结论应用于分析孟加拉湾地区海温对夏季风爆发影响的研究,指出当孟加拉湾地区经向最大暖海温位于赤道附近时,其两侧表现为Rossby波响应的Gill型气旋环流,而海温暖轴北移后,其南侧激发出有利于季风爆发的越赤道气流,这是Rossby重力混合波对热源响应的结果。这是上述理论结果的一个很好例证,同时也为孟加拉湾夏季风的爆发给出一种动力学解释。