Long Wave Resonance in Tropical Oceans and Implications on Climate: the Atlantic Ocean

Based on the well established importance of long, non-dispersive baroclinic Kelvin and Rossby waves, a resonance of tropical planetary waves is demonstrated. Three main basin modes are highlighted through joint wavelet analyses of sea surface height (SSH) and surface current velocity (SCV), scale-averaged over relevant bands to address the co-variability of variables: (1) a 1-year period quasi-stationary wave (QSW) formed from gravest mode baroclinic planetary waves which consists of a northern, an equatorial and a southern antinode, and a major node off the South American coast that straddles the north equatorial current (NEC) and the north equatorial counter current (NECC), (2) a half-a-year period harmonic, (3) an 8-year sub-harmonic. Contrary to what is commonly accepted, the 1-year period QSW is not composed of wind-generated Kelvin and Rossby beams but results from the excitation of a tuned basin mode. Trade winds sustain a free tropical basin mode, the natural frequency of which is tuned to synchronize the excitation and the ridge of the QSWs. The functioning of the 1-year period basin mode is confirmed by solving the momentum equations, expanding in terms of Fourier series both the coefficients and the forcing terms. The terms of Fourier series have singularities, highlighting resonances and the relation between the resonance frequency and the wavenumbers. This ill-posed problem is regularized by considering Rayleigh friction. The waves are supposed to be semi-infinite, i.e. they do not reflect at the western and eastern boundaries of the basin, which would assume the waves vanish at these boundaries. At the western boundary the equatorial Rossby wave is deflected towards the northern antinode while forming the NECC that induces a positive Doppler-shifted wavenumber. At the eastern boundary, the Kelvin wave splits into coastal Kelvin waves that flow mainly southward to leave the Gulf of Guinea. In turn, off-tropical waves extend as an equatorially trapped Kelvin wave, being deflected off the western boundary. The succession of warm and cold waters transferred by baroclinic waves during a cycle leaves the tropical ocean by radiation and contributes to western boundary currents. The main manifestation of the basin modes concerns the variability of the NECC, of the branch of the South Equatorial Current (SEC) along the equator, of the western boundary currents as well as the formation of remote resonances, as will be presented in a future work. Remote resonances occur at midlatitudes, the role of which is suspected of being crucial in the functioning of subtropical gyres and in climate variability.     

Can a minimalist model of wind forced baroclinic Rossby waves produce reasonable results?

The linear theory predicts that Rossby waves are the large scale mechanism of adjustment to perturbations of the geophysical fluid. Satellite measurements of sea level anomaly (SLA) provided sturdy evidence of the existence of these waves. Recent studies suggest that the variability in the altimeter records is mostly due to mesoscale nonlinear eddies and challenges the original interpretation of westward propagating features as Rossby waves. The objective of this work is to test whether a classic linear dynamic model is a reasonable explanation for the observed SLA. A linear-reduced gravity non-dispersive Rossby wave model is used to estimate the SLA forced by direct and remote wind stress. Correlations between model results and observations are up to 0.88. The best agreement is in the tropical region of all ocean basins. These correlations decrease towards insignificance in mid-latitudes. The relative contributions of eastern boundary (remote) forcing and local wind forcing in the generation of Rossby waves are also estimated and suggest that the main wave forming mechanism is the remote forcing. Results suggest that linear long baroclinic Rossby wave dynamics explain a significant part of the SLA annual variability at least in the tropical oceans.     

Generation of baroclinic topographic waves by a tropical cyclone impacting a low-latitude continental shelf

Numerical model experiments have been performed to analyze the low-latitude baroclinic continental shelf response to a tropical cyclone. The theory of coastally trapped waves suggests that, provided appropriate slope, latitude, stratification and wind stress, bottom-intensified topographic Rossby waves can be generated by the storm. Based on a scale analysis, the Nicaragua Shelf is chosen to study propagating topographic waves excited by a storm, and a model domain is configured with simplified but similar geometry. The model is forced with wind stress representative of a hurricane translating slowly over the region at 6 km h⁻¹. Scale analysis leads to the assumption that baroclinic Kelvin wave modes have minimal effect on the low-frequency wave motions along the slope, and coastal-trapped waves are restricted to topographic Rossby waves. Analysis of the simulated motions suggests that the shallow part of the continental slope is under the influence of barotropic topographic wave motions and at the deeper part of the slope baroclinic topographic Rossby waves dominate the low-frequency motions. Numerical solutions are in a good agreement with theoretical scale analysis. Characteristics of the simulated baroclinic waves are calculated based on linear theory of bottom-intensified topographic Rossby waves. Simulated waves have periods ranging from 153 to 203 h. The length scale of the waves is from 59 to 87 km. Analysis of energy fluxes for a fixed volume on the slope reveals predominantly along-isobath energy propagation in the direction of the group velocity of a topographic Rossby wave. Another model experiment forced with a faster translating hurricane demonstrates that fast moving tropical cyclones do not excite energetic baroclinic topographic Rossby waves. Instead, robust inertial oscillations are identified over the slope.     

Quasigeostrophic planetary waves in a two-layer ocean with one-dimensional periodic bottom topography

Although the study of topographic effects on the Rossby waves in a stratified ocean has a long history, the wave property over a periodic bottom topography whose lateral scale is comparable to the wavelength is still not clear. The present paper treats this problem in a two-layer ocean with one-dimensional periodic bottom topography by a simple numerical method, in which no restriction on the wavelength and/or the horizontal scale of the topography is required. The dispersion diagram is obtained for a wavenumber range of [?π/L _b , π/L _b ], where L _b is the periodic length of the topography. When the topographic?β?is not negligible compared to the planetary β, the Rossby wave solutions around the wavenumbers which satisfy the resonant condition among the waves and topography disappear and separate into an infinite number of discrete modes. For convenience, each mode is numbered in order of frequency. As topographic height is increased, the high frequency barotropic Rossby wave (mode 1) becomes a topographic mode which can exist even on the f plane, and the highfrequency baroclinic mode (mode 2) becomes a surface intensified mode. Behaviors of low frequency modes are somewhat complicated. When the topographic amplitude is small, the low frequency baroclinic modes tend to be bottom trapped and the low frequency barotropic modes tend to be surface intensified. As topographic amplitude further increases, the relation between the mode number and vertical structure changes. This change can be attributed to the increase of the frequency of the topographic mode with the topographic amplitude.     

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.     

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.     

On the origin of jets in the ocean

We show a mechanism whereby the jets result during the development of β-plumes (i.e., low-frequency Rossby waves that establish gyre circulations) in a model of ocean-basin circulation. The energy originates in baroclinic meanders of circulation at the eastern boundary of the ocean. Eddies are intimately related and occur as a result of the instability of this process. This mechanism does not rely on the existence of the small-scale turbulence to establish zonal flows. Zonal jets can then be amplified by eddies arranged in certain order in the flow. The underlying dynamics include the propagation of linear and nonlinear basin scale Rossby waves. The related barotropic theory for these waves is developed here. We demonstrate the radiative development of jets and β-plumes in a laboratory experiment using a rotating fluid with a paraboloidal free surface. The dynamical fields are measured by the laboratory analog of the satellite altimetry.     

Barotropic and baroclinic processes in the transport variability of the Antarctic Circumpolar Current

Synoptic scale variability of the Southern Ocean wind field in the high-frequency range of barotropic Rossby waves results in transport variations of the Antarctic Circumpolar Current (ACC), which are highly coherent with the bottom pressure field all around the Antarctic continent. The coherence pattern, in contrast to the steady state ACC, is steered by the geostrophic f/h contours passing through Drake Passage and circling closely around the continent. At lower frequencies, with interannual and decadal periods, the correlation with the bottom pressure continues, but baroclinic processes gain importance. For periods exceeding a few years, variations of the ACC transport are in geostrophic balance with the pressure field associated with the baroclinic potential energy stored in the stratification, whereas bottom pressure plays a minor role. The low-frequency variability of the ACC transport is correlated with the baroclinic state variable in the entire Southern Ocean, mediated by baroclinic topographic–planetary Rossby waves that are not bound to f/h contours. To clarify the processes of wave dynamics and pattern correlation, we apply a circulation model with simplified physics (the barotropic–baroclinic-interaction model BARBI) and use two types of wind forcing: the National Centers for Environmental Prediction (NCEP) wind field with integrations spanning three decades and an artificial wind field constructed from the first three empirical orthogonal functions of NCEP combined with a temporal variability according to an autoregressive process. Experiments with this Southern Annular Mode type forcing have been performed for 1,800 years. We analyze the spin-up, trends, and variability of the model runs. Particular emphasis is placed on coherence and correlation patterns between the ACC transport, the wind forcing, the bottom pressure field and the pressure associated with the baroclinic potential energy. A stochastic dynamical model is developed that describes the dominant barotropic and baroclinic processes and represents the spectral properties for a wide range of frequencies, from monthly periods to hundreds of years.     

斜压基本气流对东亚夏季风区气旋扰动低频发展影响的数值模拟研究

本文将夏季气候平均的基本气流分解为正压和斜压分量,使用一个线性斜压模式,研究了不同斜压基本气流对热带西北太平洋地区初始气旋性环流扰动低频发展演变的重要作用.其中,控制试验较好地模拟出初始气旋扰动向西北方向传播、在西北太平洋季风槽附近停滞增强、在东亚地区出现经向波列和在南海到海洋大陆地区形成西北—东南向波列等特征.改变斜压分量的敏感性试验结果表明,正压基流不能为西传的初始扰动供给足够的能量;海陆热力差异引起东亚地区的纬向温度梯度和北风垂直切变,是东亚太平洋型经向波列形成和维持的重要因素;当基本气流中的斜压纬向偏差部分线性增大时,扰动的能量会呈e指数迅速增强,提示在气候变化的背景下,基本气流微小的改变可能带来天气或季节内扰动强度的剧烈响应.     

Variability in Solomon Sea circulation derived from altimeter sea level data

The Solomon Sea is a key region in the Pacific Ocean where equatorial and subtropical circulations are connected. The region exhibits the highest levels in sea level variability in the entire south tropical Pacific Ocean. Altimeter data was utilized to explore sea level and western boundary currents in this poorly understood portion of the ocean. Since the geography of the region is extremely intricate, with numerous islands and complex bathymetry, specifically reprocessed along-track data in addition to standard gridded data were utilized in this study. Sea level anomalies (SLA) in the Solomon Sea principally evolve at seasonal and interannual time scales. The annual cycle is phased by Rossby waves arriving in the Solomon Strait, whereas the interannual signature corresponds to the basin-scale ENSO mode. The highest SLA variability are concentrated in the eastern Solomon Sea, particularly at the mouth of the Solomon Strait, where they are associated with a high eddy kinetic energy signal that was particularly active during the phase transition during the 1997–1998 ENSO event. Track data appear especially helpful for documenting the fine structure of surface coastal currents. The annual variability of the boundary currents that emerged from altimetry compared quite well with the variability seen at the thermocline level, as based on numerical simulations. At interannual time scales, western boundary current transport anomalies counterbalance changes in western equatorial Pacific warm water volume, confirming the phasing of South Pacific western boundary currents to ENSO. Altimetry appears to be a valuable source of information for variability in low latitude western boundary currents and their associated transport in the South Pacific.     

南亚高压区Rossby波能量向上穿越对流层顶传播的特征与机制

夏季平流层盛行强东风,Rossby波能量难以从对流层向上传播至平流层,而冬季平流层盛行西风,Rossby波能量容易上传,因此以往对Rossby波能量向平流层传播的研究多考虑冬季的情况.而事实上,因为夏季高原上空南亚高压反气旋环流,并非只有强东风存在,所以Rossby波能量也可能在南亚高压区向上传播,从而影响平流层的温度、风场及大气成分等.因此,本文利用ERA-interim逐日再分析资料,分析了1979—2015年夏季南亚高压区Rossby波能量穿越对流层顶传播的特征与机制.结果表明:Rossby波能量可以从南亚高压西北部的窗口区上传至平流层,最高可到达平流层顶,而在南亚高压的其他部分,Rossby波能量均不能穿越对流层顶上传或穿越对流层顶后无法继续上传.南亚高压西北区Rossby波能量可以穿越对流层顶传播的原因是盛行西风,且西风急流出现的频率很小,同时涡动热量通量异常引起的垂直分量的第一项对其上传有很大贡献.南亚高压东北区也盛行西风,然而Rossby波能量不能向上穿越对流层顶的原因是强西风出现频率较高,且温度脊与高度脊位相相近,不利于上传.南亚高压南部均盛行东风,在平流层中下层均为稳定层结,因此Rossby波能量很难上传.南亚高压西南区在对流层位于青藏高原环流的伊朗高原下沉区附近,层结稳定,并且温度脊超前于高度脊,所以Rossby波能量很难上传.而南亚高压东南区在对流层位于南海-西太平洋热带幅合带,层结不稳定,存在Rossby波能量较弱的上传,达到对流层顶后无法继续上传,该区域温度脊落后于高度脊的温压场配置也为Rossby波能量在对流层内的传播提供了条件.     

The effects of vertical shear and stratification on stationary rossby waves

Abstract

The generation of stationary Rossby waves by sources of potential vorticity in a westerly flow is examined here in the context of a two-layer, quasi-geostrophic, β-plane model. The response in each layer consists of a combination of a barotropic Rossby wave disturbance that extends far downstream of the source, and a baroclinic disturbance which is evanescent or wave-like in character, depending on the shear and degree of stratification. Contributions from each of these modes in each layer are strongly dependent on the basic flows in each layer; the degree of stratification; and the depths of the two layers. The lower layer response is dominated by an evanescent baroclinic mode when the upper layer westerlies are much larger than those in the lower layer. In this case, weak stationary Rossby waves of large wavelengths are confined to the upper layer and the disturbance in the lower layer is confined to the source region.

Increasing the upper layer flow (with the lower layer flow fixed) increases the Rossby wavelength and decreases the amplitude. Decreasing the lower layer flow (with the upper layer flow fixed) decreases the wavelength and increases the amplitude. Stratification increases the contribution from the barotropic wave-like mode and causes the response to be confined to the lower layer.

The finite amplitude response to westerly flow over two sources of potential vorticity is also considered. In this case stationary Rossby waves induced by both sources interact to reinforce or diminish the downstream wave pattern depending on the separation distance of the sources relative to the Rossby wavelength. For fixed separation distance, enhancement of the downstreatm Rossby waves will only occur for a narrow range of flow variables and stratification.     

Connection of sea level variability between the tropical western Pacific and the southern Indian Ocean during recent two decades

Based on the merged satellite altimeter data and in-situ observations,as well as a diagnosis of linear baroclinic Rossby wave solutions,this study analyzed the rapidly rise of sea level/sea surface height(SSH)in the tropical Pacific and Indian Oceans during recent two decades.Results show that the sea level rise signals in the tropical west Pacific and the southeast Indian Ocean are closely linked to each other through the pathways of oceanic waveguide within the Indonesian Seas in the form of thermocline adjustment.The sea level changes in the southeast Indian Ocean are strongly influenced by the low-frequency westward-propagating waves originated in the tropical Pacific,whereas those in the southwest Indian Ocean respond mainly to the local wind forcing.Analyses of the lead-lag correlation further reveal the different origins of interannual and interdecadal variabilities in the tropical Pacific.The interannual wave signals are dominated by the wind variability along the equatorial Pacific,which is associated with the El Ni?o-Southern Oscillation;whereas the interdecadal signals are driven mainly by the wind curl off the equatorial Pacific,which is closely related to the Pacific Decadal Oscillation.     

Causes and underlying dynamic processes of the mid-winter suppression in the North Pacific storm track

Baroclinic wave activity in the North Pacific exhibit peaks in late fall and early spring, and a local minimum in midwinter, when by linear baroclinic instability theory it should attain its maximum. This counterintuitive phenomenon, or"midwinter suppression"(MWM) as called, is investigated with a functional analysis apparatus, multiscale window transform(MWT), and the MWT-based theory of canonical transfer and localized multi-scale energetics analysis, together with a feature tracking technique, using the data from the European Centre for Medium-Range Weather Forecasts ReAnalysis(ERA-40). It is found that the MWM results from a variety of different physical processes, including baroclinic canonical transfer, diabatic effect, energy flux divergence, and frictional dissipation. On one hand, baroclinic canonical transfer and diabatic effect achieve their respective maxima in late fall. More transient available potential energy is produced and then converted to transient kinetic energy, resulting in a stronger storm track in late fall than in midwinter. On the other hand, in early spring, although baroclinic instability and buoyancy conversion are weak, energy flux convergences are substantially strengthened, leading to a net energy inflow into the storm track. Meanwhile, frictional dissipation is greatly reduced in spring; as a result, less transient energy is dissipated in early spring than in midwinter. It is further found that the weakening of baroclinic canonical transfer in midwinter(compared to late fall) is due to the far distance between the storm and the jet stream(located at its southernmost point), which suppresses the interaction between them. Regarding the increase in energy flux convergence in early spring, it appears to originate from the increase(enhancement) in the number(strength) of storms from the upstream into the Pacific.     

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 emergence of equatorial deep jets in an idealised primitive equation model: an interpretation in terms of basin modes

Ocean circulation models do not generally exhibit equatorial deep jets (EDJs), even though EDJs are a recognised feature of the observed ocean circulation along the equator and they are thought to be important for tracer transport along the equator and even equatorial climate. EDJs are nevertheless found in nonlinear primitive equation models with idealised box geometry. Here we analyse several such model runs. We note that the variability of the zonal velocity in the model is dominated by the gravest linear equatorial basin mode for a wide range of baroclinic vertical normal modes and that the EDJs in the model are dominated by energy contained in vertical modes between 10 and 20. The emergence of the EDJs is shown to involve the linear superposition of several such neighbouring basin modes. Furthermore, the phase of these basin modes is set at the start of the model run and, in the case of the reference experiment, the same basin modes can be found in a companion experiment in which the amplitude of the forcing has been reduced by a factor of 1000. We also argue that following the spin-up, energy must be transferred between different vertical modes. This is because the model simulations are dominated by downward phase propagation following the spin-up whereas our reconstructions imply episodes of upward and downward propagation. The transfer of energy between the vertical modes is associated with a decadal modulation of the EDJs.     

Energy distributions of the large-scale horizontal currents caused by wind in the baroclinic ocean

Wind is the main energy source for the generation of the internal waves and the ocean mixing. Wunsch[1] estimated that about 1 TW (1 TW = 1012 W) energy was transported into the ocean from the winds by us-ing the altimeter data. Watanabe et al.[2] numerically calculated that the mixing processes obtained 0.7 TW energy from the global wind, which afforded most of the energy needed by the maintenance of the Merid-ional Overturning Circulation (MOC). During the past 50 years, in the Norther…     

北太平洋海表面高度的年际变化及其机制

利用15年（1993～2007年）月平均的海表面高度（SSH）异常资料,分析了北太平洋海表面高度的年际变化的时空结构,并研究了热通量和风应力两个因子对其的强迫作用.结果表明,北太平洋年际时间尺度SSH变化的大值区在黑潮延伸区和西太平洋暖池区.EOF分解第一模态的空间结构沿纬向呈带状分布,第二模态为沿经向呈带状分布.热通量强迫作用在中纬度的东北太平洋可以解释SSH年际变化40%以上.风应力对SSH的作用包括正压和斜压两个方面.正压Sverdrup平衡模型模拟的SSH年际变化较弱,仅能解释高纬度副极地环流西部的20%~40%.由大尺度风应力强迫的第一阶斜压Rossby波模型可以解释热带地区的20%~60%,中纬度中部的20%~40%,以及阿拉斯加环流东部和副极地环流西部的20%~60%.风应力强迫的一阶斜压Rossby波模型对SSH的强迫机理又可分为局地风应力强迫和西传Rossby波作用.其中,风应力的局地强迫作用（Ekman抽吸）在东北太平洋、白令海以及热带中部有显著的预报技巧,可以解释SSH年际变异的40%以上.Rossby波的传播作用在中纬度海域的副热带环流中西部和夏威夷岛以东起着重要作用,可解释20%~60%.     

Reflection of equatorial Kelvin waves at eastern ocean boundaries Part II: Pacific and Atlantic Oceans

The effect of viscosity, non linearities, incident wave period and realistic eastern coastline geometry on energy fluxes are investigated using a shallow water model with a spatial resolution of 1/4 degree in both meridional and zonal directions. Equatorial and mid-latitude responses are considered. It is found that (1) the influence of the coastline geometry and the incident wave period is more important for the westward energy flux than for the poleward flux, and (2) the effect of the inclination of the eastern ocean boundary on the poleward energy flux, for the Pacific and Atlantic Oceans, decline as the period of the incident wave increases. Furthermore, the model simulations suggest that the poleward energy fluxes from meridional boundaries give plausible results for motions of seasonal and annual periods. For comparatively shorter periods, a realistic coastline geometry has to be included for more accurate results. It is recommended that any numerical model involving the reflection of baroclinic Rossby waves (of intraseasonal, seasonal or annual periods) on the eastern Pacific or Atlantic Oceans, should consider the effect of the coastline geometry in order to improve the accuracy of the results.     

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...