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1.
A three-dimensional spectral analysis of Topex altimeter data reveals a large meridional component ky of the wavevector k for baroclinic Rossby waves of all timescales. Its existence necessitates some refinements in our estimates of certain basic properties of the Rossby wave field. In particular, by taking into account an actual off-zonal direction of k (often exceeding 70°), one finds that the wavelength, phase speed, and group velocity of mid-latitude Rossby waves (with periods less than 2 years) are much smaller than they appear to be on the assumption of a purely zonal wavenumber vector. Because of a shorter wavelength (yielding kL as high as 0.6, where L is the Rossby radius of deformation), these waves are essentially dispersive. Their group velocity vector may depart from zonal by more than 30°. An important intrinsic feature of the wave spectrum confirmed by our analysis is a broad-band distribution with respect to ky. Some of the dynamical implications of the large ky/kx ratio are discussed.  相似文献   

2.
Variability patterns of Rossby wave source   总被引：1，自引：0，他引：1  
Rossby waves (RW) propagation due to a local forcing is one of the mechanisms responsible for wave trains configurations known as teleconnections. The term teleconnection refers to anomalies patterns that are correlated in several regions of the world, causing large-scale changes in atmospheric waves patterns and temperature and precipitation regimes. The aim of teleconnections studies is to provide a better understanding of atmospheric variability and their mechanisms of action in order to identify patterns that can be tracked and predicted. The purpose of this study was to characterize seasonal and spatial variability of atmospheric RW sources. The RW source at 200?hPa was calculated for the four seasons with reanalysis data of zonal and meridional wind. In the Northern Hemisphere (NH), the RW sources were located on East Asia, North America, North Atlantic and Pacific. The main RW sources in the Southern Hemisphere (SH) were located over Intertropical, South Pacific, South Atlantic and South Indian Convergence Zones. Extratropical regions were also identified, mainly to the south of Australia. The vortex stretching term (S1) and the advection of absolute vorticity by the divergent wind (S2) were analyzed to discuss the physical mechanisms for RW generation. In the NH, the source at East Asia in DJF changed to a sink in JJA, related to the dominance of S1 term in DJF and S2 term in JJA. In the SH, the vortex stretching term had the dominant contribution for RW source located to the south of Australia. The main forcing for RW sources at east of Australia was the advection of absolute vorticity by divergent flow. Over South America, both terms contributed to the source in DJF. The main modes of RW source variability were discussed by using empirical orthogonal functions analysis. RW variability was characterized by wave trains configurations in both hemispheres over regions of jet streams and storm tracks, associated with favorable and unfavorable areas for RW generation.  相似文献   

3.
Laboratory experiments are conducted on a physical system in which an oscillatory, along-shore, free stream flow of a homogeneous fluid occurs in the vicinity of a long coastline with vertical slope; the model sea-floor is horizontal. Particular attention is given to the resulting rectified (mean) current which is along the coastline with the shore on the right, facing downstream. In the lateral far field region defined by (1), where y is the offshore coordinate and H is the depth of the fluid, the motion field is approximately independent of the lateral distance from the coast. The vertical structure of the cross-stream motion in this region consists of Ekman layers near the sea-floor and interior adjustment flows, both periodic in time. In the near field, defined by (1), the motion is strongly dependent on the cross-stream coordinate as well as time, and rectified currents are observed. The mechanism responsible for the rectification is a complex nonlinear coupling between laterally directed adjustment flows driven by the transport in the bottom Ekman layers, and the free stream motion field. The rectified current is found to be substantially wider than the Stewartson layer thickness but much narrower than the Rossby deformation radius. The characteristic width, δy, of the rectified current is shown to scale as , where Ro is the Rossby number Rot is the temporal Rossby number and E is the Ekman number. Experiments are presented which support this scaling.  相似文献   

4.
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  相似文献   

5.
罗德海 《高原气象》1992,11(1):96-101
本文进一步对旋转正压大气中的包络Rossby孤立波进行了研究，结果发现当Rossby波的波数m（m为纬向波数）满足1≤m≤2时，旋转正压大气中才存在包络Rossby孤立波，并且只有m＝2的包络Rossby孤立波才具有阻塞高压的结构。我们还对这种m＝２的包络Rossby孤立波随纬度变化的持续性进行了计算，得到了许多结果。  相似文献   

6.
In this paper,a tropical atmospheric model of relevance to shorts-term climate variations(Wang and Li 1993) is utilized for study of the development of Madden-Julian oscillation.The model contains an interactive process of boundary-layer Ekman convergence and precipitation heating.The model is solved by expanding dependent variables in terms of parabolic cylindrical functions in the meridional direction and truncating three meridional modes n=0,2,4 for equatorial symmetric solutions.The free wave solutions obtained under long-wave approximation are induced as a Kelvin wave and two Rossby waves.After considering the effect of boundary-layer dynamic process,the modified Kelvin wave becomes unstable in long-wave bands with a typical growth rate on an order of 10-6 s-1and an eastward phase speed of 10 m s-1;the most unstable mode is wavenumber one.These theoretical results are consistent with the observed Madden-Julian oscillation in equatorial area.For the two modified Rossby waves,one with a smaller meridional scale(n=4) decays except for extra long-waves;the other with a larger meridional scale(n=2) grows in short-wave bands.This may be relevant to explaining the westward propagation of super cloud clusters in the Madden-Julian oscillation.The theory suggests that the boundary-layer dynamic process is an important mechanism in the development of the Madden-Julian oscillation.  相似文献   

7.
两层正压准平衡海洋模型的中纬度自由涡旋波动解   总被引：2，自引：2，他引：0  
建立了具有瑞利摩擦且仅考虑大洋西海岸或同时考虑大洋东、西海岸的两层正压准平衡海洋模型,并做了解析求解,用以研究中纬度的自由涡旋波。得到的主要结论有:模型中该波动的解为波包。在仅考虑大洋西海岸时该波包的载频频率是连续谱;而同时考虑大洋东、西海岸时其为离散谱;且均有载频频率越高(周期越短)水平尺度越大的特点,对过分低频的波动,则会使准平衡的假定不再适用。模型中该波动波包载频的周期约在26天至24年。因考虑了摩擦,该波包的振幅随时间呈指数衰减,但摩擦系数的大小仅影响其衰减程度而不改变其空间结构,最终该波包振幅趋于0,故该两层正压海洋模型的解就趋于大气风场的强迫特解。模型中该波包的载频都是西传的;频率较高则西传较快,波包的特性和变形都很明显;频率低,则西传慢,其波形接近平面简谐波。在该两层正压模型中,该波动上层流场与正压模型中的流动类似,而下层海洋流动则其流速与上层海洋相同,而流向相反。该模型中该波动的性质是准平衡(准无辐散)的涡旋波,当摩擦不太大且其水平尺度在10km以上时,其性质则为准地转的Rossby波。  相似文献   

8.
A complete theory of the linear initial-value problem for Rossby waves on a class of smooth circular vortices in both f-plane and polar-region geometries is presented in the limit of small and large Rossby deformation radius. Although restricted to the interior region of barotropically stable circular vortices possessing a single extrema in tangential wind, the theory covers all azimuthal wavenumbers. The non-dimensional evolution equation for perturbation potential vorticity is shown to depend on only one parameter, G, involving the azimuthal wavenumber, the basic state radial potential vorticity gradient, the interior deformation radius, and the interior Rossby number.In Hankel transform space the problem admits a Schrödinger’s equation formulation which permits a qualitative and quantitative discussion of the interaction between vortex Rossby wave disturbances and the mean vortex. New conservation laws are developed which give exact time-evolving bounds for disturbance kinetic energy. Using results from the theory of Lie groups a nontrivial separation of variables can be achieved to obtain an exact solution for asymmetric balanced disturbances covering a wide range of geophysical vortex applications including tropical cyclone, polar vortex, and cyclone/anticyclone interiors in barotropic dynamics. The expansion for square summable potential vorticity comprises a discrete basis of radially propagating sheared vortex Rossby wave packets with nontrivial transient behavior. The solution representation is new, and for this class of swirling flows gives deeper physical insight into the dynamics of perturbed vortex interiors than the more traditional approach of Laplace transform or continuous-spectrum normal-mode representations. In general, initial disturbances are shown to excite two regions of wave activity. At the extrema of these barotropically stable vortices and for a certain range of wavenumbers, the Rossby wave dynamics are shown to become nonlinear for all initial conditions. Extensions of the theory are proposed.  相似文献   

9.
A new semicircle theorem is derived for unstable barotropic disturbances to a class of rectilinear barotropic currents u(y) in systems with an ambient potential vorticity gradient (f/h)y which satisfies (u—us)(f/h)y ? 0 throughout the y domain, where us is some value of u. In the conventional semicircle theorem for this flow, the radius of the semicircle is a function of both the range of u and the maximum speed of the stable Rossby waves that can exist in the system when u = 0. In the new semicircle theorem, the radius is only a function of the former when it is small compared to the latter. Currents which do not satisfy the above condition, as well as stable modes and baroclinic systems, are also discussed.  相似文献   

10.
Based on previous observational studies of the mean atmospheric circulation leading to generalized frosts (GF) in central Southern South America, it is possible to establish a hypothesis that specific large scale patterns are associated to the frequency of occurrence of these events through the propagation of Rossby waves remotely excited. This hypothesis is tested here through a teleconnection analysis for austral winters which present an extreme frequency of occurrence of GF in southeastern South America, particularly over the Wet Pampa area in Argentina. Rossby wave propagation regions are identified for two basic states given by the composition of winters with maximum and minimum frequency of GF occurrence, during the 1961–1990 period. The stationary wavenumber K s indicates the regions where the Rossby wave propagation is permitted and those where it will be inhibited (K s = 0), highlighting the importance of the jets as waveguides. Nevertheless, differences exist between both basic states analyzed. These differences indicate that the locations for wave generation and its later evolution are conditioned by the basic state. Results are validated through a baroclinic model, which simulates the Rossby wave patterns responsible for the teleconnection. Numerical experiments confirm that the principal wave activity takes place inside the subtropical and polar jets. In particular, for the basic state with maximum frequency of GF occurrence, the wave trains propagating inside the subtropical and polar waveguides merge just before entering the continent, as shown by the observations prior to the occurrence of GF events. This configuration favors the development of an intense south wind anomaly with large meridional extension which results in the intensification of anticyclonic circulation in southern South America. A conceptual model is presented to summarise all these results.  相似文献   

11.
沈新勇  刘佳  秦南南  冯琎 《大气科学》2013,37(6):1219-1234
本文推导出柱坐标系下含有粘性摩擦项的正压方程组。选取2005年台风麦莎登陆浙江过程中的8月6日15时的WRF(Weather Research and Forecasting)模式输出资料,利用数值差分方法对该正压方程组求特征波解,分析粘性摩擦对台风麦莎内部正压特征波动的影响。结果表明,重力惯性外波在粘性摩擦的影响下,最不稳定波的波数为45左右,波动在摩擦的影响下衰减,波动沿逆时针传播,在半径1000 km处,1波波速为47.43 m/s,在半径r>800 km的范围内,径向风分量扰动加大,辐合辐散运动增强;而摩擦影响下的涡旋Rossby波,2波最不稳定,波动增长率减小,在半径r=200 km处波动相速度为4.282~29.172 m/s,扰动涡度大值区范围减小,涡旋Rossby波的波动区域沿着径向向台风中心收缩。分析包含所有波动时,考虑摩擦后,最不稳定波数在45左右且波动衰减,1波波速在r=1000 km处(外螺旋雨带)为26.374 m/s;在半径r=200 km(内螺旋雨带)为5.275 m/s,考虑径向基本气流后,最不稳定波的波数保持不变,半径r=1000 km处的波速增加为30.324 m/s,r=200 km(内螺旋雨带)处波速为6.065 m/s,摩擦使得径向风分量扰动明显增大,辐合辐散运动加强。  相似文献   

12.
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.  相似文献   

13.
The steady hydrostatic flow through a channel of rectangular cross section connecting reservoirs of infinite width and depth and containing inviscid fluids of different densities and levels is studied. The main goal is the determination of the discharges of the lighter and denser fluids in terms of the external conditions (reservoir levels, fluid densities and variation of width and depth along a channel). It is shown that the key parameter is δ, which is the ratio of relative reservoir level difference, γ, to relative density difference, ε. If δ<0 then the denser fluid plunges under the stationary lighter layer. If δ>δ* (1<δ*<1.5) then the lighter fluid runs up on a wedge of stationary heavier fluid. Here δ* depends on the geometry of the constriction. The solutions describing these regimes are stated. If 0<δ<δ* then both layers are in motion. A qualitative analysis of the solution for arbitrary bottom shape and channel width and arbitrary ε is presented and the problem is reduced to a system of two equations which can be easily solved numerically for any particular channel profile. We give detailed analyses for the following two cases: 1) the narrowest width of the channel is on the side of the heavier fluid and the top of the sill is on the side of lighter fluid; 2) the minima in channel depth and width coincide. In the second case the discharges for one class of geometries in the Boussinesq approximation are calculated and discussed.  相似文献   

14.
Chen  Lilan  Fang  Jiabei  Yang  Xiu-Qun 《Climate Dynamics》2020,55(9-10):2557-2577

While recent observational studies have shown the critical role of atmospheric transient eddy (TE) activities in midlatitude unstable air-sea interaction, there is still a lack of a theoretical framework characterizing such an interaction. In this study, an analytical coupled air-sea model with inclusion of the TE dynamical forcing is developed to investigate the role of such a forcing in midlatitude unstable air-sea interaction. In this model, the atmosphere is governed by a barotropic quasi-geostrophic potential vorticity equation forced by surface diabatic heating and TE vorticity forcing. The ocean is governed by a baroclinic Rossby wave equation driven by wind stress. Sea surface temperature (SST) is determined by mixing layer physics. Based on detailed observational analyses, a parameterized linear relationship between TE vorticity forcing and meridional second-order derivative of SST is proposed to close the equations. Analytical solutions of the coupled model show that the midlatitude air-sea interaction with atmospheric TE dynamical forcing can destabilize the oceanic Rossby wave within a wide range of wavelengths. For the most unstable growing mode, characteristic atmospheric streamfunction anomalies are nearly in phase with their oceanic counterparts and both have a northeastward phase shift relative to SST anomalies, as the observed. Although both surface diabatic heating and TE vorticity forcing can lead to unstable air-sea interaction, the latter has a dominant contribution to the unstable growth. Sensitivity analyses further show that the growth rate of the unstable coupled mode is also influenced by the background zonal wind and the air–sea coupling strength. Such an unstable air-sea interaction provides a key positive feedback mechanism for midlatitude coupled climate variabilities.

  相似文献   

15.
Multi-year predictability in a coupled general circulation model   总被引：1，自引：0，他引：1  
Multi-year to decadal variability in a 100-year integration of a BMRC coupled atmosphere-ocean general circulation model (CGCM) is examined. The fractional contribution made by the decadal component generally increases with depth and latitude away from surface waters in the equatorial Indo-Pacific Ocean. The relative importance of decadal variability is enhanced in off-equatorial “wings” in the subtropical eastern Pacific. The model and observations exhibit “ENSO-like” decadal patterns. Analytic results are derived, which show that the patterns can, in theory, occur in the absence of any predictability beyond ENSO time-scales. In practice, however, modification to this stochastic view is needed to account for robust differences between ENSO-like decadal patterns and their interannual counterparts. An analysis of variability in the CGCM, a wind-forced shallow water model, and a simple mixed layer model together with existing and new theoretical results are used to improve upon this stochastic paradigm and to provide a new theory for the origin of decadal ENSO-like patterns like the Interdecadal Pacific Oscillation and Pacific Decadal Oscillation. In this theory, ENSO-driven wind-stress variability forces internal equatorially-trapped Kelvin waves that propagate towards the eastern boundary. Kelvin waves can excite reflected internal westward propagating equatorially-trapped Rossby waves (RWs) and coastally-trapped waves (CTWs). CTWs have no impact on the off-equatorial sub-surface ocean outside the coastal wave guide, whereas the RWs do. If the frequency of the incident wave is too high, then only CTWs are excited. At lower frequencies, both CTWs and RWs can be excited. The lower the frequency, the greater the fraction of energy transmitted to RWs. This lowers the characteristic frequency (reddens the spectrum) of variability off the equator relative to its equatorial counterpart. At low frequencies, dissipation acts as an additional low pass filter that becomes more effective, as latitude increases. At the same time, ENSO-driven off-equatorial surface heating anomalies drive mixed layer temperature responses in both hemispheres. Both the eastern boundary interactions and the accumulation of surface heat fluxes by the surface mixed layer act to low pass filter the ENSO-forcing. The resulting off-equatorial variability is therefore more coherent with low pass filtered (decadal) ENSO indices [e.g. NINO3 sea-surface temperature (SST)] than with unfiltered ENSO indices. Consequently large correlations between variability and NINO3 extend further poleward on decadal time-scales than they do on interannual time-scales. This explains why decadal ENSO-like patterns have a broader meridional structure than their interannual counterparts. This difference in appearance can occur even if ENSO indices do not have any predictability beyond interannual time-scales. The wings around 15–20°S, and sub-surface variability at many other locations are predictable on interannual and multi-year time-scales. This includes westward propagating internal RWs within about 25° of the equator. The slowest of these take up to 4 years to reach the western boundary. This sub-surface predictability has significant oceanographic interest. However, it is linked to only low levels of SST variability. Consequently, extrapolation of delayed action oscillator theory to decadal time-scales might not be justified.  相似文献   

16.
The momentum flux of stratospheric gravity waves generated by Typhoon Ewiniar (2006) is examined using a Weather Research and Forecasting (WRF) model. In the stratosphere, zonal momentum flux with a positive sign by eastward-propagating waves is significant during the northward moving of the typhoon, while both zonal and meridional momentum fluxes with positive signs are significant during the typhoon decaying stage in which the typhoon moves northeastward. The magnitude of the momentum flux is greater during the mature stage of the typhoon than the decaying stage, and the phase speeds of the dominant momentum flux are less than 30 m s?1 with a peak at 10–16 m s?1. Positive momentum flux decreases with height overall in the stratosphere for both zonal and meridional components. The resultant gravity-wave drag forcing plays a role to decelerate the easterly background wind in the stratosphere. This drag forcing is relatively large above z = 40 km and below z = 20 km, and lower stratospheric wave drag is expected to affect the typhoon dynamics by modifying the background wind shear and inducing the secondary circulation in the troposphere.  相似文献   

17.
Wintertime cold air outbreaks along a non-frozen sea channel or a long lake can become destructive if the related bands of heavy snowfall hit onto land. The forcing for such bands is studied with a 2D numerical model set across an east–west sea channel at 60oN (‘Gulf of Finland’), varying the basic geostrophic wind V g. Without any V g opposite coastal land breezes emerge with convergence. This results in a quasi-steady rising motion w max ~ 7.5 cm/s at 600 m in the middle of the gulf, which can force a snow band. During weak V g, the rising motion is reduced but least so for winds from 60o to 80o (~ENE), when modest alongshore bands could exist near the downstream (Estonian) coast. During V g of 4–6 m/s from any direction, the land breezes and rising motions are reduced more effectively, so snow bands are not expected during moderate basic flow. In contrast, during a strong V g of 20–25 m/s from 110o to 120o (~ESE) the land breeze perturbations are intense with w max up to 15–18 cm/s. The induced alongshore bands of heavy snowfall are located in these cases at the sea but quite close to the downstream (Finnish) coast. They can suddenly make a landfall if the basic wind turns clockwise.  相似文献   

18.
By using an ageostrophic shallow water model, it is pointed out that a kind of lateral boundary meso-scales jet can be established near the plateau or coast. The characteristic width of this kind of jet is proportional to the scale ofL c=L0(C0/Vg), whereL 0=C 0/f is the radius of Rossby deformation,C 0=(g * H)1/2 the speed of gravity wave and g* the reduced gravity. In general,L c is of the order of one hundred kilometes and tens of kilometers in the atmosphere and in the ocean respectively. The large-scale geostrophic current is an important background condition for forming this kind of jet. From this view point it seems that this kind of atmospheric meso-scale jet only occurs in late spring and summer in the eastern part of Asia, because there is a large-scale south monsoon over there. For the ocean, this kind of meso-scale jet seems to be a semi-persistant system and not to show a significant seasonal variation, and it can be established on both sides of the ocean.  相似文献   

19.
In this paper,a tropical atmospheric model of relevance to shorts-term climate variations(Wang and Li 1993)is util-ized for study of the development of Madden-Julian oscillation.The model contains an interactive process ofboundary-layer Ekman convergence and precipitation heating.The model is solved by expanding dependent variables interms of parabolic cylindrical functions in the meridional direction and truncating three meridional modes n=0,2,4 forequatorial symmetric solutions.The free wave solutions obtained under long-wave approximation are induced as aKelvin wave and two Rossby waves.After considering the effect of boundary-layer dynamic process,the modifiedKelvin wave becomes unstable in long-wave bands with a typical growth rate on an order of 10~(-6) s~(-1)and an eastwardphase speed of 10 m s~(-1);the most unstable mode is wavenumber one.These theoretical results are consistent with the ob-served Madden-Julian oscillation in equatorial area.For the two modified Rossby waves,one with a smaller meridionalscale(n=4)decays except for extra long-waves;the other with a larger meridional scale(n=2)grows in short-wavebands.This may be relevant to explaining the westward propagation of super cloud clusters in the Madden-Julianoscillation.The theory suggests that the boundary-layer dynamic process is an important mechanism in the develop-ment of the Madden-Julian oscillation.  相似文献   

20.
The system of linearized shallow water equations is formulated in this paper on any rotating and smooth surface M in terms of differential geometry. The system decouples into two separate equations: a scalar one for the height deviation and a vector one for the velocity field. For low and high frequencies these equations yield asymptotic equations whose solutions are the generalizations of the Poincare and Rossby waves to smooth surface. The application of these equations to the β-plane yields both new and previously known equations for the height deviation and for the velocity components. The application of the equations to the rotating spherical Earth shows that the meridional amplitudes of Poincare and Rossby waves are both described by the prolate angular spheroidal wave functions. The asymptotic and the power series expansions of the eigenvalues of these functions yield new approximations for the dispersion relations of these waves on a sphere. The new dispersion relations are very accurate in the physically relevant range of the single nondimensional model parameter – the square of the nondimensional gravity waves’ phase speed. The invariant formulation can also be applied to other surfaces that are of geophysical interest such as an oblate ellipsoid of revolution.  相似文献   

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