Establishment and adjustment of monsoon-driven circulation in the South China Sea

The South China Sea (SCS) is one of the large marginal seas of the western Pacific Ocean. In comparison with open oceans, the SCS circulation has obviously transient characteristics due to its small basin-scale and semi-annually reversed monsoon forcing. …     

Multi-scale variability of the tropical Indian Ocean circulation system revealed by recent observations

The tropical Indian Ocean circulation system includes the equatorial and near-equatorial circulations, the marginal sea circulation, and eddies. The dynamic processes of these circulation systems show significant multi-scale variability associated with the Indian Monsoon and the Indian Ocean dipole. This paper summarizes the research progress over recent years on the tropical Indian Ocean circulation system based on the large-scale hydrological observations and numerical simulations by the South China Sea Institute of Oceanology(SCSIO), Chinese Academy of Sciences. Results show that:(1) the wind-driven Kelvin and Rossby waves and eastern boundary-reflected Rossby waves regulate the formation and evolution of the Equatorial Undercurrent and the Equatorial Intermediate Current;(2) the equatorial wind-driven dynamics are the main factor controlling the inter-annual variability of the thermocline in the eastern Indian Ocean upwelling;(3) the equatorial waves transport large amounts of energy into the Bay of Bengal in forms of coastal Kelvin and reflected free Rossby waves. Several unresolved issues within the tropical Indian Ocean are discussed:(i) the potential effects of the momentum balance and the basin resonance on the variability of the equatorial circulation system, and(ii) the potential contribution of wind-driven dynamics to the life cycle of the eastern Indian Ocean upwelling. This paper also briefly introduces the international Indian Ocean investigation project of the SCSIO, which will advance the study of the multi-scale variability of the tropical Indian Ocean circulation system, and provide a theoretical and data basis to support marine environmental security for the countries around the Maritime Silk Road.     

正压大气模式下具有β效应与地形效应的Rossby孤立波

正压大气模式下,采用摄动方法和时空伸长变换推导了具有β效应、地形效应和耗散的mKdV-Burgers方程,得到Rossby孤立波振幅的演变满足带有β效应,地形与耗散的mKdV-Burgersm方程的结论.说明β效应、地形效应是诱导Rossby孤立波的重要因素.     

Amplification and energy transformation of the magnetized Rossby waves in the ionosphere with an inhomogeneous zonal wind. I. A theory

The generation and further dynamics of the planetary magnetized Rossby waves and inertial waves in a dissipative ionosphere in the presence of a smooth inhomogeneous zonal wind (shear flow) have been studied. The magnetized Rossby waves are caused by the interaction with the spatially inhomogeneous geomagnetic field and represent the ionospheric manifestations of usual tropospheric Rossby waves. The effective linear mechanism of amplification and mutual transformation of the Rossby and inertial waves has been revealed. For shear flows, the operators of linear problems are not self-adjoint, and the corresponding eigenfunctions are non-orthogonal; therefore, a canonical modal approach is of little use in studying such motions. It becomes necessary to apply the so-called nonmodal mathematical analysis, which has actively been developed for the last years. The nonmodal approach makes it possible to reveal that the transformation of wave-like disturbances in shear flows is caused by the nonorthogonality of eigenfunctions in the problem of linear dynamics. Thus, there appear a new degree of the system freedom and a new way of disturbance evolution in the medium.     

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.     

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.     

具有非线性地形的正压流体中孤立Rossby波的mKdV方程

正压流体中,采用摄动方法将准地转位涡方程推导出地形效应的mKdV方程,得到Rossby波振幅的演变满足地形效应的mKdV方程的结论,说明地形效应是诱导Rossby孤立波的重要因素.     

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.     

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.     

Magnetic Rossby waves in a stably stratified layer near the surface of the Earth's outer core

Abstract

The stratification profile of the Earth's magnetofluid outer core is unknown, but there have been suggestions that its upper part may be stably stratified. Braginsky (1984) suggested that the magnetic analog of Rossby (planetary) waves in this stable layer (the ‘H’ layer) may be responsible for a portion of the short-period secular variation. In this study, we adopt a thin shell model to examine the dynamics of the H layer. The stable stratification justifies the thin-layer approximations, which greatly simplify the analysis. The governing equations are then the Laplace's tidal equations modified by the Lorentz force terms, and the magnetic induction equation. We linearize the Lorentz force in the Laplace's tidal equations and the advection term in the magnetic induction equation, assuming a zeroth order dipole field as representative of the magnetic field near the insulating core-mantle boundary. An analytical β-plane solution shows that a magnetic field can release the equatorial trapping that non-magnetic Rossby waves exhibit. A numerical solution to the full spherical equations confirms that a sufficiently strong magnetic field can break the equatorial waveguide. Both solutions are highly dissipative, which is a consequence of our necessary neglect of the induction term in comparison with the advection and diffusion terms in the magnetic induction equation in the thin-layer limit. However, were one to relax the thin-layer approximations and allow a radial dependence of the solutions, one would find magnetic Rossby waves less damped (through the inclusion of the induction term). For the magnetic field strength appropriate for the H layer, the real parts of the eigenfrequencies do not change appreciably from their non-magnetic values. We estimate a phase velocity of the lowest modes that is rather rapid compared with the core fluid speed typically presumed from the secular variation.     

On resonant over-reflection of waves by jets

It is well known that internal or Rossby waves propagating across a jet can be amplified, a phenomenon usually referred to as over-reflection. In some cases, over-reflection can be infinitely strong – physically, this means that the reflected and transmitted waves can exist without an incident one, i.e. they are spontaneously emitted by the mean flow. In this article, it is shown that infinitely strong over-reflection (resonant over-reflection) occurs for gravity-wave scattering by ageostrophic jets in a rotating barotropic ocean and Rossby-wave scattering by a two-jet configuration on the quasigeostrophic beta-plane. It is further demonstrated that, generally, a resonantly over-reflected wave is always marginal to instability, i.e. either an increase or a decrease of its wavenumber transforms it into an unstable eigenmode localised near the jet.     

Shear flow driven magnetized planetary wave structures in the ionosphere

The generation and further linear and nonlinear dynamics of planetary ultra-low-frequency (ULF) waves are investigated in the rotating dissipative ionosphere in the presence of inhomogeneous zonal wind (shear flow). Planetary ULF magnetized Rossby type waves appear as a result of interaction of the medium with the spatially inhomogeneous geomagnetic field. An effective linear mechanism responsible for the intensification and mutual transformation of large scale magnetized Rossby type and small scale inertial waves is found. For shear flows, the operators of the linear problem are not self-conjugate, and therefore the eigenfunctions of the problem may not be orthogonal and can hardly be studied by the canonical modal approach. Hence, it becomes necessary to use the so-called nonmodal mathematical analysis. The nonmodal analysis shows that the transformation of wave disturbances in shear flows is due to the non-orthogonality of eigenfunctions of the problem in the conditions of linear dynamics. Using numerical modeling, the peculiar features of the interaction of waves with the background flow as well as the mutual transformation of wave disturbances are illustrated in the ionosphere. It has been shown that the shear flow driven wave perturbations effectively extract an energy of the shear flow increasing the own energy and amplitude. These perturbations undergo self-organization in the form of the nonlinear solitary vortex structures due to nonlinear twisting of the perturbation’s front. Depending on the features of the velocity profiles of the shear flows the nonlinear vortex structures can be either monopole vortices or vortex streets and vortex chains.     

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.     

Barotropic waves along an eastern continental shelf

Abstract

An analysis is presented of the propagation of barotropic non-divergent oscillations along the western side of an ocean basin along which the persistent circulation in the basin is strongly intensified and laterally sheared. Because the Rossby number of a western boundary current is near unity, the properties of these waves are strongly affected by the steady circulation pattern. It is shown that for relatively long wavelengths, these waves can travel along the shelf in both directions; however, for a small range of short wavelengths they can only propagate northward and are unstable. Along the southeastern coast of North America, the unstable waves have wavelengths of order 150 km and periods of order 10 days. However, these waves can become stable oscillations in the deeper water northeast of Cape Hatteras. These oscillations are a possible explanation of the initiation of Gulf Stream meanders along the continental rise.     

Convection driven by centrifugal bouyancy in a rotating annulus

Abstract

Drift rates and amplitudes of convection columns driven by centrifugal bouyancy in a cylindrical fluid annulus rotating about a vertical axis have been measured by thermistor probes. Conical top and bottom boundaries of the annular fluid region are responsible for the prograde Rossby wave like dynamics of the convection columns. A constant positive temperature difference between the outer and the inner cylindrical boundaries is generated by the circulation of thermostatically controled water. Mercury and water have been used as converting fluids. The measurements extend the earlier visual observations of Busse and Carrigan (1974) and provide quantitative data for an eventual comparison with nonlinear theories of thermal Rossby waves. The measured drift frequencies are in general agreement with linear theory. Of particular interest is the decline of the amplitude of convection with increasing Rayleigh number in a region beyond the onset of convection.     

非对称型强飓风中的准平衡流特征分析Ⅱ:波动结构

利用非对称波分量分解和小波分析的方法,对准平衡动力模型下非对称强飓风内中尺度波动的空间结构和时间序列特征进行分析.结果表明,平衡流场中1波扰动占主要地位且具有涡旋Rossby波的典型结构特征,准平衡流各波数下扰动的空间分布反映了中尺度波动的混合性质;模式大气和准平衡垂直运动的全局功率谱中,超过信度检验的强波动信号中不仅包含分别表征重力波和涡旋Rossby波的高频和低频波动信号,还存在表征具有物理性质不可分特性的混合涡旋Rossby-重力波的中频波动.混合波的出现建立了不同频段波动之间的能量交换通道,其信号的变化对飓风系统的强弱变化具有一定的指示作用.非平衡垂直运动的波动强信号则主要集中在高频和低频区域,反映了在飓风强度变化情况下,与高频重力波有关的快波调整过程所引起的垂直扰动的振荡和传播.强垂直风切变对飓风内中尺度波动的切向和径向传播具有重要影响,当环境垂直风切变很强时,准平衡1波扰动在径向和切向方向上均呈"驻波"形态,随着环境垂直风切变的减弱,1波扰动以混合波波速逆基本气流传播.     

On the generation of baroclinic rossby waves in the presence of a semi-circular boundary

Abstract

An analytical model is constructed for the generation of baroclinic Rossby waves by a vorticity source in the presence of a semi-circular boundary. The vorticity source is used to represent the effect of the Agulhas retroflection to the south of Southern Africa. The displacement of the interface between the two layers of the model ocean consists of quantized waves near the coast and a train of Rossby waves drifting westward further offshore.     

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.     

On the reynolds stress and lateral eddy viscosity due to transient oceanic Rossby waves

Summary From numerical solutions of a wind-driven homogeneous ocean model, anegative lateral eddy viscosity of the order 10⁴ cm² sec^–1 is inferred from the large-scale time-dependent currents in the interior of an enclosed shallow basin. The transient Rossby waves in this region produce a systematic convergence of eddy momentum at the latitude of the maximum average eastward current, and thus effect a transfer of zonal momentum from the large-scale eddies to the mean flow. In this sense they are analogous to the Rossby waves in the atmospheric general circulation, and it is speculated that such waves may help to maintain the mean zonal ocean currents. Although this negative viscosity induced by the large-scale transients is relatively small compared with the prescribed lateral viscosity of 10⁸ cm² sec^–1 and should be given a quite different physical interpretation, it is evidently an important viscous effect for the mean flow in the interior of the basin. The prescribed viscosity, on the other hand, is effective in controlling the model's simulated sub-grid scale dissipation, which occurs almost entirely in the nearby steady boundary currents.     

Field theoretical techniques in statistical fluid dynamics: With application to nonlinear wave dynamics

Abstract

A derivation of two-point Markovian closure is presented in classical statistical field theory formalism. It is emphasized that the procedures used in this derivation are equivalent to those employed in the quantum statistical field theory derivation of the Boltzmann equation. Application of these techniques to the study of two-dimensional flow on a β-plane yields a quasi-homogeneous, quasi-stationary transport equation and a renormalized dispersion relation for Rossby waves