Meridional component of oceanic Rossby wave propagation

A three-dimensional spectral analysis of Topex altimeter data reveals a large meridional component k_y 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 k_y. Some of the dynamical implications of the large k_y/k_x ratio are discussed.     

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.     

The exchange of fluid mass between quasi-geostrophic and ageostrophic motions during the reflection of Rossby waves from a coast. I. The case of an infinite rectilinear coast

When the problem of the reflection of spatially localized Rossby waves from a coast is treated using the quasigeostrophic (QG) approximation, the total fluid mass and the along-shore circulation calculated from the geostrophic height field are not conserved. To understand the correct mass balance and the degree to which the QG equations and boundary conditions may be in error, we analyze an initial-value problem for the Laplace tidal equations on a β-plane in the asymptotic limit 1, where is the ratio of the spatial scale of the motion to the Earth's radius.It is shown that there is a coupling between QG and O() fields. Physically, the coupling occurs by a peculiar adjustment process in the O() approximation in which fast gravity waves are permanently generated to build up a quasi-stationary edge Kelvin wave. Different temporal scales (large for O(1) Rossby waves and small for the O() gravity waves make comparable the contributions of the waves to the mass and circulation balance equations. However, QG analysis itself describes the reflection of Rossby waves correctly, but is incomplete, and for satisfactory balances one has to take into account the fields of both orders of the approximation.Applications of the results to closed basins, baroclinicity, and variable bottom topography are discussed. It is conjectured that an interaction of strong oceanic eddies with a coast (continental slope) may give rise to noticeable along-shore jet currents.     

Stable and unstable Rossby waves in the North Pacific current as inferred from the mean stratification

We have determined free Rossby waves in the North Pacific Current by numerical methods. We have found only two stable solutions — the barotropic and first-order baroclinic Rossby shear modes. The influence of the current on the dispersion features of these waves is small for the barotropic shear mode, but is significant for the baroclinic shear mode. An explicit comparison of the dispersion relations for the baroclinic wave in case of vanishing and non-vanishing current is given. We have found at most one unstable solution per wave number. The unstable wave with largest growth rate has an e-folding time of 1.1 year. We have calculated vertical profiles of the stream function and the temperature for the various shear modes at various wave numbers. The temperature shear modes have been calculated for later usage in a Rossby wave model to be fitted to observed temperature data from the North Pacific Current area.     

THE EFFECTS OF THE PLATEAU'S TOPOGRAPHIC GRADIENT ON ROSSBY WAVES AND ITS NUMERICAL SIMULATION

By using barotropic model equations, this article analyzed the characteristics of Rossby waves, the propagation features of wave energy and the influence of dynamic and thermal effects of the Tibetan Plateau on Rossby waves, and the focus is on discussing the plateau's topographic gradient effects on atmospheric Rossby waves. Then based on the WRF3.2 and the NCEP/NCAR FNL reanalysis data, we devised comparative tests of changing the plateau's topographic gradient and simulated a process of persistent heavy rain that happened in May 2010 in South China. The results are shown as follows. The Tibetan Plateau’s topography is conducive to the formation of atmospheric Rossby waves. while the plateau's terrain, its friction and heating effects can all make the atmospheric Rossby waves develop into the planetary waves; The effects of plateau's north and south slopes on the Rossby wave’ phase velocity is opposite, and when the slope reached a certain value can the quasi-steady normal fluctuations be generated; Simultaneously, due to the plateau's topographic gradient, descending motion appears at the west side of the plateau while ascending motion appears at the east side, and the vertical movement increased with the amplification of topographic gradients. The plateau's topographic gradient also obviously amplified the precipitation in South China, and the rainfall area increased with the amplification of topographic gradients and gradually moved from south to north and from west to east, which is conducive to the occurrence and development of convective activities in the downstream areas of the Tibetan Plateau; Moreover, for the plateau’s dynamic and thermal effects, the Rossby wave’ propagation shows upstream effects of energy dispersion, so the plateau can then affect the weather in downstream areas. Moreover, the wave group velocity increased with the degree of topographic slope.     

Solitary Rossby waves over variable relief and their stability. Part I: The analytical theory

Nonlinear permanent form solutions have been found for the barotropic, quasi-geostrophic divergenceless vorticity equation describing large scale, rotating flows over zonal relief. In the linear limit these solutions are topographic Rossby waves. The analytical procedure is an expansion in two small dimensionless parameters, an amplitude parameter (the Rossby number) and the aspect ratio between North-South (cross-relief) and East-West length scales. Permanent form solutions exist when these two parameters, and the related effects of dispersion and nonlinearity, mutually balance. By the same expansion procedure, an analytical linearized stability theory has been formulated which proves the neutral stability of these solutions to infinitesimal, two-dimensional perturbations.     

大气中的包络Rossby孤立波——纬度效应的作用

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。     

Weakly non-linear Rossby waves in a rotating fluid of spheriodal configuration

A modified ray method is used to study weakly non-linear Rossby waves in a thin layer of incompressible inviscid fluid of constant density both in a rotating spheroidal shell and on a rotating spheroid bounded above by a free surface. This method yields the same dispersion relation and conservation law as in the linear case (London) but gives an equation for a new, second order mean term. This mean term is shown to be unstable for all free oscillations on any axisymmetric bottom topography in the free surface problem. This contrasts with the analogous problem on the Beta-plane where the corresponding mean term is stable.     

Neutrally Stratified Turbulent Ekman Boundary Layer: Universal Similarity for a Transitional Rough Surface

The geostrophic Ekman boundary layer for large Rossby number (Ro) has been investigated by exploring the role played by the mesolayer (intermediate layer) lying between the traditional inner and outer layers. It is shown that the velocity and Reynolds shear stress components in the inner layer (including the overlap region) are universal relations, explicitly independent of surface roughness. This universality of predictions has been supported by observations from experiment, field and direct numerical simulation (DNS) data for fully smooth, transitionally rough and fully rough surfaces. The maxima of Reynolds shear stresses have been shown to be located in the mesolayer of the Ekman boundary layer, whose scale corresponds to the inverse square root of the friction Rossby number. The composite wall-wake universal relations for geostrophic velocity profiles have been proposed, and the two wake functions of the outer layer have been estimated by an eddy viscosity closure model. The geostrophic drag and cross-isobaric angle predictions yield universal relations, which are also supported by extensive field, laboratory and DNS data. The proposed predictions for the geostrophic drag and the cross-isobaric angle compare well with data for Rossby number Ro ≥ 10⁵. The data show low Rossby number effects for Ro < 10⁵ and higher-order effects due to the mesolayer compare well with the data for Ro ≥ 10³.     

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     

Planetary geostrophic equations for the atmosphere with evolution of the barotropic flow

Atmospheric phenomena such as the quasi-stationary Rossby waves, teleconnection patterns, ultralong persistent blockings and the polar/subtropical jet are characterized by planetary spatial scales, i.e. scales of the order of the earth’s radius. This motivates our interest in the relevant physical processes acting on the planetary scales. Using an asymptotic approach, we systematically derive reduced model equations valid for atmospheric motions with planetary spatial scales and a temporal scale of the order of about 1 week. We assume variations of the background potential temperature comparable in magnitude with those adopted in the classical quasi-geostrophic theory. At leading order, the resulting equations include the planetary geostrophic balance. In order to apply these equations to the atmosphere, one has to prescribe a closure for the vertically averaged pressure. We present an evolution equation for this component of the pressure which was derived in a systematic way from the asymptotic analysis. Relative to the prognostic closures adopted in existing reduced-complexity planetary models, this new dynamical closure may provide for more realistic increased large-scale, long-time variability in future implementations.     

Vortex Rossby waves on smooth circular vortices: Part I. Theory

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.     

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。     

On the symmetrization rate of an intense geophysical vortex

Numerical models demonstrate that a broad class of geophysical vortices freely evolve toward vertically aligned, axisymmetric states. In principle, this intrinsic drive toward symmetry opposes destructive shearing by the environmental flow.This article examines the case in which a discrete vortex-Rossby-wave dominates a perturbation from symmetry, and symmetrization occurs by decay of the wave. The wave is damped by a resonance with the fluid rotation frequency at a critical radius, r_*. The damping rate is proportional to the radial derivative of potential vorticity at r_*. Until now, the theory of resonantly damped vortex-Rossby-waves (technically quasi-modes) was formally restricted to slowly rotating vortices, which obey quasigeostrophic (QG) dynamics. This article extends the theory to rapidly rotating vortices.The analysis makes use of the asymmetric balance (AB) approximation. Even at a modest Rossby number (unity), AB theory can predict damping rates that exceed extrapolated QG results by orders of magnitude. This finding is verified upon comparison of AB theory to numerical experiments, based on the primitive equations. The experiments focus on the decay of low azimuthal wave-number asymmetries.A discrete vortex-Rossby-wave can also resonate with an outward propagating inertia-buoyancy wave (Lighthill radiation), inducing both to grow. At large Rossby numbers, this growth mechanism can be dynamically relevant. All balance models, including AB theory, neglect inertia-buoyancy waves, and therefore ignore the possibility of a Rossby-inertia-buoyancy (RIB) instability. This article shows that a large potential vorticity gradient (of the proper sign) at the critical radius r_* can suppress the RIB instability, and thereby preserve balanced flow, even at large Rossby numbers.     

Nondispersive Periodic Solution of a Barotropic Semi-Geostrophic Model

The existence and solution of the non-dispersive periodic solution are achieved concerning nonlinear barotropic Rossby waves of a barotropic semi-geostrophic model, demonstrating the likelihood of the Taylor evolution, together with the related dimensionless a-criterion. Finally, the wave velocity expression is proposed with some diagnostic relations among the wave parameters.     

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.     

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.     

A simple quasi-geostrophic coupled ocean-atmosphere model

The quasi-geostrophic atmospheric and oceanic equations of momentum and thermodynamics with dissipation factors are used to create a simple coupled ocean-atmosphere model describing the large-scale shallow-water mo-tion. We discuss the ocean-atmosphere coupling effect in mid-high and low latitudes separately and analyze charac-teristics of which the oscillatory periods of coupled low-frequency modes (ocean mode) vary with the coupling fre-quency and latitudinal number. This can interpret the correlation between low-frequency oscillation and ocean-at-mosphere interaction. Then from the dispersion curves of atmosphere and ocean, we reveal effect of the coupling strength on the propagation of Rossby waves. The convection mechanism between the two modes is also discussed in view of the slowly varying wave train.The results show that Newtonian cooling and Rayleigh friction play a stable rule in oceanic Rossby waves, the period of coupled low-frequency mode grows with the increment of the coupling frequency. The larger the latitudinal number is, the more rapidly it grows. When the coupling frequency tends to critical value, the oceanic Rossby waves become static. When the ocean-atmosphere coupling strength grows to some degree, the propagation of oceanic Rossby waves will become opposite to its original direction. One part of the oceanic Rossby waves is converted into atmospheric Rossby waves, the energy conversion coefficient is also solved out.     

Oscillatory Rossby Solitary Waves in the Atmosphere

The linear Rossby wave frequency expression is expanded at higher accuracy based on the scale difference char?acteristics of atmospheric long waves in the and directions. That the nature of the waves represented by the expan?sion is identical to that of the original ones is demonstrated both in phase velocity and wave energy dispersion speed , followed by the derivation of the nonlinear expression describing atmospheric long wave behaviors with the associated approximate analytic solution obtained. Then, for the first time atmospheric’ oscillatory Rossby solitary wave’ with its dispersion relation is obtained by numerical calculation with the aid of physical parameters of the real atmosphere. The solitary wave is found to be very close to such longwave systems as blocking highs and cut-off de?pressions in the actual atmosphere.     

一个简单的准地转海气耦合模式

文章采用准地转带耗散因子的大气和海洋的动量、热力学方程,建立了一个简单的描写大尺度运动的准地转海气耦台浅水模式,分别在中高纬和低纬地区讨论了海气的耦合效应,分析了耦合低频模(海洋模)的振荡周期随耦合频率和经向波数的变化转征,并由此而说明低频振荡与海气相互作用有关。然后从海洋和大气的频散曲线中揭示出耦合强度对Rossby波传播的影响,还从缓变波列的观点,讨论了两种模之间的转换机制。 结果表明:Newton冷却Rayleigh摩擦对海洋Rossby波起稳定作用。随着耦合频率的增加,耦合低频模的周期也相应增加;经向波数越大,这种增加就越迅速。当耦合频率趋近于临界值时,海洋Rossby波趋于静止。当海气耦合强度增加到一定程度时,海洋Rossby波的传播方向变成与原来相反。通过海气相互作用,海洋Rossby波的一部分将转换成大气Rossby波,本文求解了其能量转换系数。