热带气旋Rossby波能量频散问题研究进展

热带气旋是发生在热带洋面上的强烈气旋性涡旋.由于地转涡度梯度的存在,热带气旋在移动过程中不断发生Rossby波能量频散,并在热带气旋运动方向的后部激发出反气旋和气旋交替排列的Rossby波能量频散波列.多热带气旋共存和热带气旋的异常运动是当前国际热带气旋研究领域的热点问题,热带气旋Rossby能量频散被证实与多个热带气旋连续生成和异常运动密切相关.本文从热带气旋能量频散及波列特征、主要影响因子、反馈作用等方面,回顾总结了国内外关于热带气旋Rossby波能量频散的相关研究进展,并提出当前亟待解决的一些科学问题.目的是为深入研究热带气旋Rossby波能量频散及其影响提供基础和参考,以期使更多的研究学者关注热带气旋能量频散问题,从而进一步揭示热带气旋生成、发展和异常运动的动力学机理.     

北太平洋副热带向东逆流区Rossby波斜压稳定性

根据对卫星观测的海平面高度资料的分析，进一步证实了在北太平洋副热带两支向东的流（副热带逆流和夏威夷背风逆流）所在的区域内，海平面高度的70～210天周期振荡是主要的低频变化.发现在这两支向东的逆流区Rossby波的特性不同：副热带逆流区70～210天周期振荡对应的Rossby波西传过程中增幅，在台湾以东振幅达到最大；而在夏威夷背风逆流区，70～210天周期Rossby波在西传过程中不出现增幅现象.依据25层海洋模式得到的关于Rossby波振幅、频率与海洋层结之间的关系，揭示了周期为70～210天的Rossby波为不稳定波，这是由于副热带逆流海域模态水存在使得密度的垂直梯度变小的缘故；而在夏威夷背风逆流区位于表层逆流下的北赤道流西深东浅，70～210天周期Rossby长波在逆流的东部有可能不稳定，但其在逆流的西部是稳定的，因此不出现在西传过程中增幅现象；发现在北太平洋副热带两个向东流的海域，年周期Rossby波是稳定的，因此，在该海域海平面周期为70～210天的振荡的振幅要比年周期振荡的振幅大.     

The scattering of Rossby waves from finite abrupt topography

The scattering of first mode linear baroclinic Rossby waves by a top-hat ridge in a continuously stratified ocean, with Brunt-Väisälä frequency that decays exponentially with depth below a surface mixed layer, is the subject of this study. A numerical mode matching technique is used to calculate the transmission coefficients for the propagating modes over the ridge. It is found that the scattered field depends crucially upon the stratification. For example, when the majority of the density variation is confined to a thin thermocline, corresponding to a small e-folding scale, gamma ^?1, for the Brunt-Väisälä frequency, a large amount of the incident wave energy is reflected by a small amplitude ridge. Appreciable energy conversion between the propagating barotropic and baroclinic modes takes place in this case. An asymptotic analysis for a small amplitude ridge is presented that confirms these numerical results. In the limit gamma ^?1→ 0, it is demonstrated that the scattered field in the continuously stratified ocean model differs markedly from the two-layer solution. The latter does not exhibit appreciable reflection of the incident wave energy for a small amplitude ridge. In conclusion, the application of a two-layer ocean model to describe Rossby wave scattering by ridges in place of a continuously stratified model cannot be recommended.     

Dispersive effects of zonally varying topography on quasigeostrophic Rossby waves

Abstract

Dispersion of linear quasigeostrophic plane waves in a stratified ocean with bottom topography is discussed. Particular emphasis is given to cases for which zonal gradients in the sea floor height are important. As such, the relative importance of the topographic and planetary β-effects is strongly dependent on wave vector orientation. The magnitude of the topographic slopes considered is chosen such that these two effects (topographic and planetary β) are of comparable importance. In the interest of simplicity, stratification is taken to be independent of depth. The eigenvalue problem which must be solved to find the free modes of oscillation has already been treated in the literature (in fact, Charney and Flierl (1981) have treated the effects of a more realistic stratification). The aim of this note is to more fully expose, primarily by example, several dispersive properties of these free wave modes which have been largely overlooked.     

Influence of Pacific on Southern Indian Ocean Rossby Waves

The sea-surface height anomalies derived from Simple Ocean Data Assimilation (SODA) during 1958–2001, Topex/Poseidon satellite during 1993–2001 and the SODA heat content anomalies (125 m depth) during 1958–2001 are filtered into annual and biennial Rossby wave components using a two-dimensional Finite Impulse Response filter. The filtered Rossby wave components (both annual and biennial) in the southern Pacific and Indian Oceans have considerable strength and variability. The propagation of annual and biennial Rossby waves in the Indonesian through-flow region [12.5°S–7.5°S] of the Indian Ocean is in phase with the southern Pacific Ocean waves. So it is speculated that the Pacific Ocean influences the Indian Ocean, especially through the region 17.5°S to 7.5°S and thus the southern Pacific Rossby waves could be an unexplored contributor to the Indian Ocean Rossby waves. We also carried out Fast Fourier Transform (FFT) and wavelet analysis on the tide gauge sea-level data along the Australian coast to support our claim. Filtered annual and biennial components of SODA heat content anomalies (125 m depth) also support these findings.     

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 Rossby wave propagation in a meridionally stratified channel

Rossby wave propagation in the presence of a nonseparable Brunt-Väisälä frequency,N(y,z), and the associated geostrophic zonal flow,U(y,z), is examined in this paper. The usual quasi-geostrophic potential vorticity equation only includes vertical variations in Brunt-Väisälä frequency (i.e.N(z)). We derive a linearised quasi-geostrophic potential vorticity equation which explicitly includesN(y, z), where variations inN may occur on the internal Rossby radius length scale. A mixed layer distribution that monotonically deepens in the poleward direction leads to a nonseparableN(y,z). The resulting meridional pressure gradient is balanced by an eastward zonal geostrophic flow.By assuming mixed layer depth changes occur slowly, relative to a typical horizontal wavelength of a Rossby wave, a local analysis is presented. The Rossby wave is found to have a strongly modulated meridional wavenumber,l, with amplitude proportional to |l|^–1/2. To elucidate whether the modulations of the Rossby wave are caused by the horizontal variations inN orU we also consider the cases where eitherN orU vary horizontally. Mixed layer depth changes lead to largestl where the mixed layer is deepest, whereasl is reduced in magnitude whereU is nonzero. When bothU(y,z) andN(y,z) are present, the two effects compete with one another, the outcome determined by the size of |c|/U _max, wherec is the Rossby wave phase speed. Finally, the slowly varying assumption required for the analytical approach is removed by employing a numerical model. The numerical model is suitable for studying Rossby wave propagation in a rectangular zonal channel with generalN(y, z) andU(y, z).     

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.     

雅可比椭圆函数在大气和海洋动力学中的应用:二维非线性Rossby波研究

提出了扩展雅可比椭圆函数方法,来求得Petviashvili方程的精确解析解.Petviashvili方程被视为正压准地转位涡度方程的非地转扩展,应用该方法可以得到很多二维非线性Rossby波的周期波解,在取极限情况下,也可以得到二维Rossby孤立子解.     

Resonance induced by Rossby Lee waves

Abstract

The mutual interaction of fields induced by spatially separated potential vorticity sources in a quasi-geostrophic barotropic flow is investigated using the weakly nonlinear approach. It is found that a powerful nonlinear response can be triggered by Rossby lee waves. This resonance phenomenon which dominates all other nonlinear corrections depends on certain global resonance conditions and on the change in the phase of the Rossby lee wave across the distance separating the sources. The response is particularly strong for topographic forcing possessing δ-function characterisitics.     

An evaluation of the classical and extended Rossby wave theories in explaining spectral estimates of the first few baroclinic modes in the South Pacific Ocean

Previous literature has suggested that multiple peaks in sea level anomalies (SLA) detected by two-dimensional Fourier Transform (2D-FT) analysis are spectral components of multiple propagating signals, which may correspond to different baroclinic Rossby wave modes. We test this hypothesis in the South Pacific Ocean by applying a 2D-FT analysis to the long Rossby wave signal determined from filtered TOPEX/Poseidon and European Remote Sensing-1/2 satellite altimeter derived SLA. The first four baroclinic mode dispersion curves for the classical linear wave theory and the Killworth and Blundell extended theory are used to determine the spectral signature and energy contributions of each mode. South of 17°S, the first two extended theory modes explain up to 60% more of the variance in the observed power spectral energy than their classical linear theory counterparts. We find that Rossby wave modes 2–3 contribute to the total Rossby wave energy in the SLA data. The second mode contributes significantly over most of the basin. The third mode is also evident in some localized regions of the South Pacific but may be ignored at the large scale. Examination of a selection of case study sites suggests that bathymetric effects may dominate at longer wavelengths or permit higher order mode solutions, but mean flow tends to be the more influential factor in the extended theory. We discuss the regional variations in frequency and wave number characteristics of the extended theory modes across the South Pacific basin.     

真实基流中非线性Rossby波演变特征(二):能量、结构演变及初始场影响

针对非线性的准地转正压位涡方程,利用自行设计的差分格式和高斯函数拟合得到的真实基流分布,数值研究了线性和非线性Rossby波流场结构和总能量的演变以及初值对总能量演变的影响.发现在非线性的真实基流中,线性和非线性Rossby波的相对总能量出现振荡型增长或衰减,非线性波动的振荡周期明显小于线性波动,非线性项不仅抑制能量的...     

A note on the general concept of wave breaking for Rossby and gravity waves

A recently proposed general definition of wave breaking is further discussed, in order to deal with some points on which misunderstanding appears to have arisen. As with surface and internal gravity waves, the classification of Rossby waves into breaking and not breaking is a generic classification based on dynamical considerations, and not a statement about any unique signature or automatically recognizable shape. Nor is it a statement about passive tracers uncorrelated with potential vorticity on isentropic surfaces. A strong motivation for the definition is that proofs of the nonacceleration theorem of wave, mean-flow interaction theory rely, explicitly or implicitly, on a hypothesis that the waves do not break in the sense envisaged.The general definition refers to the qualitative behaviour of a certain set of material contours, namely those, and only those, which would undulate reversibly, with small slopes, under the influence of the waves' restoring mechanism, in those circumstances for which linearized, nondissipative wave theory is a self-consistent approximation to nonlinear reality. The waves' restoring mechanism depends upon the basic-state vertical potential density gradient in the case of gravity waves, and upon the basic-state isentropic gradient of potential vorticity in the case of Rossby waves. In the usual linearized theory of planetary scale Rossby waves on a zonal shear flow, the relevant material contours lie along latitude circles when undisturbed.     

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.     

简单热带海气耦合模型中不同扰动形式的作用

在局地热平衡情况下,将物理量先用韦伯函数展开,然后去掉相应分量的滤波方 法,讨论了简单热带海气耦合模型中不同形式扰动的作用和贡献,结果表明,在热带海气耦合 系统中,大气准定常 Ｒｏｓｓｂｙ波和海洋 Ｒｏｓｓｂｙ波对于耦合系统贡献较大,它们决定着耦合系统 与耦合扰动的性质,而大气准定常Ｋｅｌｖｉｎ波和海洋Ｋｅｌｖｉｎ波对于耦合系统贡献相对较小．     

Rossby wave resonance in the presence of a nonlinear critical layer

Abstract

The behavior of Rossby waves on a shear flow in the presence of a nonlinear critical layer is studied, with particular emphasis on the role played by the critical layer in a Rossby wave resonance mechanism. Previous steady analyses are extended to the resonant case and it is found that the forced wave dominates the solution, provided the flow configuration is not resonant for the higher harmonics induced by the critical layer. Numerical simulations for the forced initial value problem show that the solution evolves towards the analysed steady state when conditions are resonant for the forced wave, and demonstrate some of the complications that arise when they are resonant for higher harmonics. In relating the initial value and steady problems, it is argued that the time dependent solution does not require the large mean flow distortion that Haberman (1972) found to be necessary outside the critical layer in the steady case.     

On isallobaric effect in a quasi-geostrophic topographic-drag problem

Abstract

Isallobaric effect of a slowly varying quasi-geostrophic flow represented by propagating waves may give rise to a mean steady topographic drag component which turns out to be the principal one when viscous effects are negligibly small. This drag component decreases, in contrast to the quasi-geostrophic component, when statistical properties of the topography become isotropic. When the phase velocity of the incident wave is much larger (smaller) than the phase speed of Rossby waves, the isallobaric drag becomes independent (dependent) on the sign of that velocity.     

一种新水平网格的Rossby波计算特性

提出了一个新的水平跳点网格（LE网格）,这种网格将h放置在格点上,u,v同时放置在x方向和y方向格点中间.并采用一种推导频散关系的通用方法,研究在该LE网格上与Arakawa A E网格上描述Rossby波产生误差的情况,分可分辨和不可分辨两种情况.采用二阶中央差或四阶紧致差分格式从频率和群速度两个方面进行对比分析,结果表明不论在可分辨或不可分辨情况下,还是采用二阶中央差或四阶紧致差分格式,在频率和群速度两方面,LE网格在描述Rossby波产生的误差均较Arakawa A E网格要小,同时也表明不论在可分辨还是不可分辨的情况下,采用高精度的四阶紧致差分格式,LE网格和Arakawa A_E网格在描述Rossby波时产生的频率误差和x、y方向群速度误差并非必然减少.     

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.