有地形坡度的非线性Kelvin行波

提出了一个考虑地形坡度的非线性Kelvin行波解的模型，在假定了地形坡度沿山脉走向不变而仅在垂直于山脉走向的方向有改变的情况下，求得了该模型的解析解，这有助于加深对沿海山地捕获波的认识。文中还将该解与经典情形(即侧边界取为垂直刚壁而底面为水平)的解作了比较，发现前者的波速与扰动振幅均较后者要小，这与我国东南沿海武夷山区的沿海山地捕获波的情况相一致。     

切变基流中赤道Kelvin波及纬向对称扰动的稳定性

本文使用赤道β平面下的热带大气Boussinesq近似方程组,分析了纬向切变基流中的赤道Kelvin波以及纬向对称扰动的稳定性。研究结果表明,在纬向基本气流只具有y方向水平切变的情况之下,基本气流在y方向的切变并不能导致Kelvin波发生不稳定,只能导致不同的纬度上对应于Kelvin波传播的相速度有所不同。扰动位势和扰动风速等物理量在y方向的分布特征与基本气流无关。在只考虑垂直切变基流时,要存在稳定的相对于平均基流向东传播的Kelvin波必须要满足Richardson数Ri>2的条件。基本气流在垂直方向的切变也不能导致Kel-vin波发生不稳定,只能导致Kelvin波的相速度发生Doppler频移效应。扰动位势以及扰动速度在y方向的分布特征与基本气流在垂直方向的切变有关。当风的垂直切变大于零时,对流层低层的扰动位势和扰动速度沿y轴的正反方向衰减较快;而当风的垂直切变小于零时,对流层高层的扰动位势和扰动速度沿y轴的正反方向衰减较快。对于沿纬圈方向的对称天气系统,只要风的垂直切变较大,满足Ri<1时,低纬重力惯性内波一定会发生不稳定。而当基本气流的垂直切变较小(Ri>1)时,本文则给出了该扰动发生不稳定的判据条件。只要风的水平切变足够大,大于某一临界值(该临界值与垂直波数m,β因子,静力稳定度N2以及Richardson数Ri有关),在赤道y—z平面上的重力惯性内波也会发生不稳定,从而引起这种沿x轴对称扰动的激发产生与发展。     

线性和非线性地形罗斯贝波

本文在半地转概念下,讨论了线性和非线性地形罗斯贝波的稳定性及其解。指出:线性和非线性稳定性判据形式一致。在线性时,地形东西向及南北向坡度对稳定波动的周期和传播速度有明显影响,其解为周期函数;在不稳定时,解为非周期函数。二级近似时其解为孤立波形式——不稳定时,在地形不同位置可形成东移或西移的孤立波槽或孤立波脊;而在稳定时只形成孤立波槽。三级近似时解出现间断点。     

含大地形的准地转正压模式的孤立波解

该文由修正过的含大地形的准地转正压模式方程出发,考虑青藏高原大地形的实际情况,忽略其东西向地形坡度,再利用约化摄动方法,求其孤立波解,并得到结论:当基本气流无切变时,地形是产生Rossby孤立波的必要因子。     

旋转二维可压缩流动的谱和特征函数——Ⅱ:谱和谱函数结构的分析

本文第一部分(Ⅰ)已给出了线性化旋转二维可压缩流动方程的谱分布,并作了初步分析。本部分(Ⅱ)对这些谱及谱函数作进一步的分析讨论。设基流是低速流,此时可用摄动法求得谱和谱函数,将它们与用差分法所得结果进行比较,表明二者吻合得很好。摄动法中的离散谱初级近似就是无基流时的相应的谱,而连续谱对应的谱函数初级近似则与准地转模式的结果一致。由初级近似和一级修正项可以清楚地说明计算所得的谱和谐函数的许多重要性质。 在低速基流情况下:(1)重力一惯性波为准简谐波,基流和可变的Coriolis参数只给以较小的修正。(2)由于基流在Coriolis力作用下使自由表面有一坡度,Kelvin波必定具有横穿波射线的速度分量,同时顺传和逆传的Kelvin波不再在形态上相似;当基流愈强时上述两性质愈明显;Coriolis参数随空间的变化也改变了顺传和逆传波的相似性,此外,Kelvin波是准非频散的。(3)不为零的基流或科氏参数的变化使慢波离散谱变为非简并的即分立的,它们或者有无穷多个且基流流速为相速的聚点(当基流为常数时),或者只有有限个,甚至不存在;而当基流有切变时则有连续谱。对应于离散谱的谱函数为准简谐波;而对应于连续谱的谐函数则为广义解,但有有限能量。 本问题的谱函数与其伴随算子的谐函数正交,满足同样边界条件     

旋转二维可压缩流动的谱和特征函数 II：谱和谱函数结构的分析

本文第一部分(Ⅰ)已给出了线性化旋转二维可压缩流动方程的谱分布,并作了初步分析。本部分(Ⅱ)对这些谱及谱函数作进一步的分析讨论。设基流是低速流,此时可用摄动法求得谱和谱函数,将它们与用差分法所得结果进行比较,表明二者吻合得很好。摄动法中的离散谱初级近似就是无基流时的相应的谱,而连续谱对应的谱函数初级近似则与准地转模式的结果一致。由初级近似和一级修正项可以清楚地说明计算所得的谱和谐函数的许多重要性质。 在低速基流情况下:(1)重力一惯性波为准简谐波,基流和可变的Coriolis参数只给以较小的修正。(2)由于基流在Coriolis力作用下使自由表面有一坡度,Kelvin波必定具有横穿波射线的速度分量,同时顺传和逆传的Kelvin波不再在形态上相似;当基流愈强时上述两性质愈明显;Coriolis参数随空间的变化也改变了顺传和逆传波的相似性,此外,Kelvin波是准非频散的。(3)不为零的基流或科氏参数的变化使慢波离散谱变为非简并的即分立的,它们或者有无穷多个且基流流速为相速的聚点(当基流为常数时),或者只有有限个,甚至不存在;而当基流有切变时则有连续谱。对应于离散谱的谱函数为准简谐波;而对应于连续谱的谐函数则为广义解,但有有限能量。 本问题的谱函数与其伴随算子的谐函数正交,满足同样边界条件的一切扰动可按本问题的谱函数展开。在低速基流情况下,可用摄动法求解,初级近似下的伴随算子是自伴的。 关于高速基流情况的结果将在本文的第三部分(Ⅲ)发表。     

地形对重力惯性波发展的影响

本文研究了具有南北坡的地形对重力惯性波发展的影响。利用WKB方法，建立了含地形作用的重力惯性波能量方程。研究结果表明:在层结稳定的情况下，当扰动“上坡”（沿地形高度的升度方向传播）时，其能量将减少，即扰动将减弱；当扰动“下坡”（沿地形高度的负升度方向传播）时，其能量将增加，即扰动将发展。如层结为不稳定，情形则相反，即扰动“上坡”时将发展，“下坡”时将减弱。此外，文中对波动的稳定性问题也作了一些讨论。     

赤道两层海洋模式中基本流的切变不稳定性

设计了一个热带赤道β-平面的两层海洋模式,在准长波近似下,应用最大截断模分析赤道波的基本形态,指出无论是正压模或斜压模Kelvin波、Rossby波及基本流所对应的“地形Rossby波”是最基本的波系,在基本流的一定切变条件下,它们之间可以耦合出一类不稳定波。在浅混合层近似和“快波近似”下,正压模和斜压模是可以分离的,因此可以分别分析它们的色散特征,由于它们的特征量不同,在同样波长(扰动的纬向尺度)下,扰动的增长率也不同,通过分析得出在一定参数下,斜压模扰动增长率为正压模的2倍。近似分析表明,混合层中流场的增长要快于温跃层,但温跃层的温度增长要比混合层明显。     

正压大气中非线性重力惯性波的非频散周期解——论Taylor展开的可能性

本文论证了正压大气中非线性重力惯性波的非频散周期解存在性及找到了该波解存在条件。通常来说要得到解析解是困难的,故利用Taylor展开来得到近似解。本文给出了Taylor展开的可能性。然后在Taylor展开允许的情况下,我们得到了近似解的表达式及波速公式,给出了该波动流场与位势高度场的配置结构,并揭示了非线性效应使得波动结构变得不对称。     

简单热带海气耦合模式中的耦合波及其不稳定性（I）

本文建立了一个简单的热带海气耦合模式，模式大气和海洋中包含了Kelvin波和长Rossby波。在赤道β平面近似下，讨论了取耦合系统中最大径向模时，即大气和海洋中只存在Kelvin波时耦合波的性质。结果指出，向东传的耦合Kelvin波可以出现不稳定性，并且由于海气相互作用，在长波部分可以产生向西传的耦合Kelvin波。 耦合Kelvin波的性质与模式中所选用的参数有很大关系，当大气与海洋中自由波的频率相差很大时，耦合波的性质与没有海气相互作用时自由波的性质非常接近；只有当大气与海洋中自由波的频率相差不太大时     

Impacts of the MJO in the Indian Ocean and on the Western Australian coast

The large sea surface temperature variations induced by the Madden-Julian Oscillation (MJO) on the northwest shelf of Australia and the remote influence of the MJO on the subtropical Western Australian coast are explored using the POAMA Ensemble Ocean Data Assimilation System reanalyses (PEODAS) for the period 1980–2010. The focus here is during the November–April extended summer season when the impacts of the MJO on and along the west coast of Australia are greatest. The MJO is well known to force equatorial Kelvin and Rossby waves in the Indian Ocean, and these are well depicted in the PEODAS reanalyses. When the downwelling Kelvin waves (forced by the westerly-convective phase of the MJO) reach the Indonesian region at the eastern boundary of the Indian Ocean, a coastally trapped Kelvin wave appears to propagate southeast along the Indonesian coastline. At the same time, the suppressed convection/easterly phase of the MJO arrives in the eastern Indian Ocean, with increased heat flux into the ocean due to reduced latent heat flux and increased insolation. The coastally trapped Kelvin waves do not appear to get onto the Western Australian coast. Rather, the increased heat flux and Ekman-induced downwelling onto the northwest (NW) coast in the suppressed/easterly phase of the MJO drive an increase in sea surface temperature on the NW Australian shelf. The piling up of warm water and associated sea level rise on the NW shelf is then communicated down the Western Australian coast as a coastally trapped wave, resulting in an increase in the Leeuwin current. Thus we conclude that the MJO signal in sea level along the west coast of Australia does not result from transmission of equatorial waves onto the Western Australian coast, but rather a southward-propagating coastal trapped wave that is directly forced on the NW shelf through Ekman-induced vertical advection and surface heat fluxes in the easterly phase of the MJO. Additionally, subtropical coastal sea level variability is reinforced locally via a teleconnection of the MJO to the local meridional wind off the southwest Australian coast. Considering the capability to predict the MJO to about 4 weeks lead time plus the 2 weeks taken for the MJO signal on the NW shelf to influence sea level at Fremantle, the use of MJO forecasts in management of the Western Australian marine environment should be considered for future application.     

理想海域中台风引起的潮、流及波的分析 Ⅱ.海岸及陆架的影响

采用理想的大陆架地形和台风模型计算了不同方向登陆的台风所激发的海洋响应。结果表明,岸边的潮位变化主要是由于台风引起的强迫振动造成的。而对于登陆型台风来说,在远离台风路径的地方,潮位的变化则是由于边缘波效应。对地平直海岸和二维大陆架,自由边缘波的振幅远小于强迫波的振幅。平行海岸移行台风在岸边产生随台风一起移动的强制波,其中当台风沿着与Kelvin波相同的方向移行时,岸边有陆架波产生,反之则没有陆架波。此外,还讨论了与风暴潮相关的近岸环流。     

Laboratory simulations of coastally trapped waves with rotation, topography and stratification

We describe observations of the generation and propagation of coastally trapped waves in the laboratory and their comparison with theory, over a range of values of several experimental parameters. The topography and stratification used consisted of a sloping continental shelf and vertical continental slope with three-layer stratification that could be approximated by an extended version of the Gill and Clarke model [Gill, A.E., Clarke, A., 1974. Wind-induced upwelling, coastal currents and sea level changes. Deep Sea Res. 21, 325–345]. The latter was modified to accommodate a central mixed layer, curved geometry, and friction on the shelf. This configuration represents coastal geometry with large Burger number. The experiments were successful in realizing coastally trapped waves that were consistent with the theoretical expectations. However, the waves propagated more slowly, and for narrow shelves were damped more rapidly than predicted by the theory. The first was attributed to: (i) the effect of stratification on fluid on the shelf, reducing the topographic Rossby wave effect; (ii) the parameterization of the viscosity. The second difference was attributed to the mechanism of generation: the paddle used did not always generate sinusoidal waves, and the subsequent dispersion resulted in a net loss of amplitude.     

A note on the use of two-layer models of coastally trapped waves

Several aspects of coastally trapped wave behavior in two-layer models and in continuously stratified models are considered. A two-layer model and a uniformly stratified model are compared over a step shelf showing that, although they predict qualitatively different free-wave dispersion properties, some features of their long wave behavior are qualitatively similar. A sharp pycnocline model (a continuously stratified approximation to the two-layer model) is used to show that the presence of a vertical coastal wall (required in most two-layer models) produces substantial changes in the free-wave behavior. With a vertical coastal wall, baroclinic motions may be trapped close to the coast when the bottom there appears locally flat. Without a vertical coastal wall, such near-cost trapping apparently does not occur and the lowest mode of the sharp pycnocline model behaves more like the lowest mode of a uniformly stratified model.     

Propagation of coastal‐trapped waves under an ice cover in Hudson Bay*

Abstract

Three arrays of current‐meter moorings were deployed under landfast sea ice in southeast Hudson Bay for eight weeks in spring 1986. Spectral analysis shows low‐frequency signals with periods of 3 to 11 days. These signals are interpreted as being due to coastal‐trapped waves propagating cyclonically in Hudson Bay; their theoretical dispersion relations and corresponding modal structures are presented for winter stratification and are compared with observations. At a period of 3 days both the modified external Kelvin wave and higher mode continental shelf waves may be important in describing the observed low‐frequency variability, whereas at a period of 10 days the Kelvin wave appears to be the dominant mode. The generation mechanisms for these coastal trapped waves are also investigated. Two sources have been studied: the longshore atmospheric pressure gradient and the average atmospheric pressure over the ice cover in Hudson Bay. Coherence and phase analyses performed with time series of longshore current and atmospheric forcing data reveal that both the average atmospheric pressure and the longshore atmospheric pressure gradient are important in explaining the observed low‐frequency variability, without indicating which one is the most important.     

Coastal trapped waves,with application to the northeast pacific ocean

The dispersion relation is derived for long coastal trapped waves of sub‐inertial frequency that propagate along a single‐step continental shelf in a two‐layer fluid. When the internal (Rossby) deformation radius is smaller than the shelf width, we show that the dispersion relation can be factored exactly, giving two possible modes: i. an internal Kelvin wave modified by topography;

ii. a continental shelf wave modified by the stratification.

A detailed discussion of the eigen‐functions associated with each of these modes is presented. Then the shelf wave dispersion relation is plotted for parameters applicable to the Oregon‐Washington coast. Theoretical values for the periods and wavelengths predicted from these plots are shown to agree favorably with observed values for this region.     

The role of MJO and mid-latitude fronts in the South China Sea summer monsoon onset

Previous studies have suggested that the South China Sea (SCS) summer monsoon onset is concurrent with the arrival of a 30–60-day northward-propagating trough. On the other hand, from a synoptic viewpoint, some studies pointed out that the arrival of a mid-latitude front may be the triggering mechanism of the SCSSM onset. This study attempts to link these two viewpoints and to investigate their relative role in inducing the SCSSM onset. Composites of low-level zonal winds, geopotential heights and temperatures during the 1991–1999 SCSSM onsets based on the European Centre for Medium Range Weather Forecast ERA-40 data indicate that both the Madden and Julian Oscillation (MJO)/Kelvin waves and mid-latitude trough are apparently involved in the onset. The MJO/Kelvin waves play a major role in inducing the large-scale easterly-westerly shift over the central SCS, while the effect of the acceleration of westerlies ahead of the mid-latitude trough is limited to the northern SCS only. Numerical experiments using a regional climate model further demonstrate that the MJO/Kelvin waves control the timing of the onset by changing the background meridional geopotential height gradient over the SCS. When the MJO is at its peak phase over the Maritime continent, it imposes a positive meridional geopotential height gradient over the SCS such that easterly winds are induced, which significantly reduces the strength of a mid-latitude trough. After the equatorial convection has dissipated, a Rossby-wave response is induced, leading to the formation of a northward-moving trough. When this trough moves northward, the meridional geopotential height gradient is reversed and westerly winds are induced. At the same time, if a mid-latitude trough arrives in south China, the westerlies associated with the mid-latitude trough will strengthen because of the background meridional geopotential height gradient, which gives the impression that both the northward-moving trough and mid-latitude trough are in phase and work together to induce the onset.     

On the transient adjustment of a mid-latitude abyssal ocean basin with realistic geometry: the constant depth limit

The early stages in the adjustment of a mid-latitude abyssal basin with realistic geometry are studied using an inverted one and one-half layer model of the Eastern Mediterranean Sea as a natural test basin. The model is forced with a localized sidewall mass source and a compensating distributed mass sink. A flat bottom basin is investigated for comparison with existing theories on abyssal gyral spin-up, and as a precursor to a study with realistic topography. As in existing theories, the early adjustment is dominated by sub-inertial Kelvin and Rossby waves. Obstacles and the varying coastal geometry do not impede the passage of the Kelvin wave, though the circuit time of the main Kelvin wave signal is reduced by an aggregate 6% for the abyssal Eastern Mediterranean basin. The scattering of the Kelvin wave due to small-scale variations in the coastline is also shown not to be significant to the adjustment. The relatively short period of time needed to reach a statistical steady state is attributed to western boundary current formation in response to local Kelvin wave dynamics. Upon cessation of the sidewall forcing, sub-inertial motion controls the spin-down adjustment with basin-scale Rossby waves becoming the most pronounced feature of the flow. Two dynamical issues of particular interest emerge in these simulations: the retardation of Kelvin wave propagation around the abyssal basin and the roles of detrainment and sidewall forcing in the interior vorticity balance. An idealized simulation using an elliptical basin is used to illustrate that the mechanism for Kelvin wave retardation is a geometrically induced dispersion due to large-scale variations in the coastline. A dynamical analysis of the interior circulation shows that detrainment alone does not develop a Sverdrup response. Both the localized sidewall injection and the detrainment are needed to describe the interior dynamics, with both poleward and equatorward flows developing during the adjustment.     

An ocean wind-wave climatology for the Southern Brazilian Shelf. Part II: Variability in space and time

Previously validated model results were used to characterize the wave climate over the Southern Brazilian Shelf (SBS). The low mean significant wave height over the western South Atlantic shelves was shown together with examples of cyclone-induced extreme wave fields and other typical wave conditions. The mean offshore spectra showed a bimodal shape with a predominance of S/SSW and ENE/E waves with distinctive interannual rising periods in wave energy density. Along-shelf wave energy gradients were seen near the coast with higher energy located off capes and coastal projections and energy minima between them. A considerable drop in wave energy suggests the 40 m depth as the mean wave base and consequently the lower limit of the SBS shoreface. The upper shoreface mean wave energy density varied abruptly along the shelf in response to differences in bottom declivities. The large and shallow shoreface was responsible for an intense refraction of the waves and hence very small angles of attack. Additionally, it was shown the sheltering effect caused by capes and coastal projections and a remarkable north/south energy asymmetry between them, caused by a windowing on the wave propagation to the shore. Altogether, it was possible to state that bottom friction plays a major role in wave differentiation along the SBS shoreface, thus suggesting that shelf morphology might indeed be more important to generate wave variability than the offshore wave variation itself.