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1.
The barotropic instability is traditionally viewed as an initial-value problem wherein wave perturbations of a laterally sheared flow in a homogeneous uniformly rotating fluid that temporally grows into vortices. The vortices are capable of mixing fluid on the continental shelf with fluid above the continental slope and adjacent deep-sea region. However, the instability can also be viewed as a boundary-value problem. For example, a laterally sheared coastal flow is perturbed at some location, creating perturbations that grow spatially downstream. This process leads to a time periodic flow that exhibits instability in space. This article first examines the linear barotropic instability problem with real frequency and complex wavenumber. It is shown that there exists a frequency band within which a spatially growing wave is present. It is then postulated that far downstream the spatially unstable flow emerges into a chain of identically axisymmetric vortices. Conservation of mass, momentum and energy fluxes are applied to determine the diameter, spacing and the speed of translation of the vortices. 相似文献
2.
本文在基态位涡（Potential Vorticity,PV）径向分布和基态涡旋强度对热带气旋（Tropical Cyclone,TC）类涡旋系统稳定性特征影响的研究基础上,结合理想试验和数值模拟诊断分析基态PV径向分布对扰动增长和系统结构变化的影响.基于线性正压浅水模型,设计三种典型基态PV中空结构下基态涡旋强度对系统稳定性影响的敏感性试验.结果表明：基态涡旋的强度主要影响稳定性的强弱,强度越强,不稳定增长率越大,而基态PV径向分布对系统最不稳定波动性质起着决定作用.分析不同波数下扰动的发展及不同波数间扰动的相互作用可知,对于宽且实的PV环,系统稳定性主要取决于低波数不稳定,且最不稳定波数扰动的发展具有明显的优势地位;对于窄且空的PV环,系统稳定性主要取决于高波数不稳定,且多个高波数下增长最快模态的不稳定增长率值十分接近.利用模态线性叠加法讨论扰动增长对系统结构变化的影响表明：最不稳定波数的扰动发展对系统结构变化有关键影响,而多个波数的扰动不稳定增长相当时,不同波数的扰动发生相互作用从而影响系统结构变化.最后,利用实际个例模拟资料分析基态PV径向分布及其变化对TC结构和强度的影响表明：TC内核区出现的多边形眼墙结构与当前时刻基态PV径向分布所决定的最不稳定波数有很好的对应关系,同时基态PV径向分布变化所反映出的系统动力稳定性强弱与TC强度发展阶段具有很好的相关性. 相似文献
3.
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. 相似文献
4.
Delayed baroclinic response of the Antarctic circumpolar current to surface wind stress 总被引：2，自引：0，他引：2
The Antarctic Circumpolar Current (ACC) responds to the surface windstress via two processes, i.e., the instant barotropic process and the delayed baroclinic process. This study focuses on the baroclinic instability mechanism in ACC, which was less reported in the literatures. Results show that the strengthening of surface zonal windstress causes the enhanced tilting of the isopycnal surface, leading to more intense baroclinic instability. Simultaneously, the mesoscale eddies resulting from the baro- clinic instability facilitate the transformation of mean potential energy to eddy energy, which causes the remarkable decrease of the ACC volume transport with the 2-year lag time. This delayed negative cor- relation between the ACC transport and the zonal windstress may account for the steadiness of the ACC transport during last two decades. 相似文献
5.
Dmitry V. Stepanov 《Ocean Dynamics》2018,68(10):1353-1370
Based on an eddy-permitting numerical model, the mesoscale variability in the East-Sakhalin Current is investigated during the winter-spring period. Analysis of necessary conditions for the development of baroclinic instability showed that the nearshore component of the East-Sakhalin Current is potentially baroclinic unstable in the first half-year. The simulated circulation uncovered a generation of anticyclonic eddies on the eastern Sakhalin shelf. It was established that a spatial scale of these eddies and the first baroclinic Rossby radius of deformation are values of the same order; a lifetime of these eddies varies from 4 to 6 weeks, given the Rossby number varies from 0.05 to 0.2. Analysis of the rate of eddy energy conversion on the eastern Sakhalin shelf showed that the generation of the revealed mesoscale eddies results from, mainly, baroclinic instability, whereas barotropic instability can be both favoring and preventing to the generation of these eddies. 相似文献
6.
Charles A. Lin 《地球物理与天体物理流体动力学》2013,107(4):227-259
Abstract A high vertical resolution model is used to examine the instability of a baroclinic zonal flow and a finite amplitude topographically forced wave. Two families of unstable modes are found, consisting of zonally propagating most unstable modes, and stationary unstable modes. The former have time scale and spatial structure similar to baroclinic synoptic disturbances, but are localized in space due to interaction with the zonally asymmetric forcing. These modes transport heat efficiently in both the zonal and meridional directions. The second family of stationary unstable modes has characteristics of modes of low frequency variability of the atmosphere. They have time scales of 10 days and longer, and are of planetary scale with an equivalent barotropic vertical structure. The horizontal structure resembles blocking flows. They are maintained by available potential energy of the basic wave, and have large zonal heat fluxes. The results for both families of modes are interpreted in terms of an interaction between forcing and baroclinic instability to create favoured regions for eddy development. Applications to baroclinic planetary waves are also considered. 相似文献
7.
Abstract we report the results of experiments on the spin-up of two layers of immiscible fluid with a free upper surface in a rotating cylinder over a wide range of internal Froude numbers. Observations of the evolution of the velocity field by particle tracking indicates that spin-up of the azimuthal velocity in the upper layer take much longer than in a homogeneous fluid. Initially, spin-up occurs at a rate comparable to that of homogeneous fluid but, at high internal Froude number, a second phase follows in which the remaining lative motion decays much more slowly. Quantitative comparison of these measurements to the theory of Pedlosky (1967) shows good agreement. Visualization of the interface displacement during spin-up detected the presence of transient azimuthal variations in the interface elevation over a wide range of Froude (F), Ekman (E), and Rossby (ε) number. nalysis of the occurrence of the asymmetric variations using the parameter space (Q, F), where Q = E 1/2/ε, suggested by the baroclinic instability theory and experiments of Hart (1972), showed that the flow was stable for Q > 0.06 with no discernable dependence on F. This result, together with the prediction of Pedlosky's theory that radial gradient of potential vorticity in the two layers have opposite signs, suggests at the baroclinic instability mechanism was responsible for the asymmetries. The location and timing of these instabilities may account for the discrepancies between the observations and the Pedlosky (1967) theory. 相似文献
8.
Abstract The linear stability of a non-divergent barotropic parallel shear flow in a zonal and a non-zonal channel on the β plane was examined numerically. When the channel is non-zonal, the governing equation is slightly modified from the Orr-Sommerfeld equation. Numerical solutions were obtained by solving the discretized linear perturbation equation as an eigenvalue problem of a matrix. When the channel is zonal and lateral viscosity is neglected the problem is reduced to the ordinary barotropic instability problem described by Kuo's (1949) equation. The discrepancy between the stability properties of westward and eastward flows, which have been indicated by earlier studies, was reconfirmed. It has also been suggested that the unstable modes are closely related to the continuous modes discretized by a finite differential approximation. When the channel is non-zonal, the properties of unstable modes were quite different from those of the zonal problem in that: (1) The phase speed of the unstable modes can exceed the maximum value of the basic flow speed; (2) The unstable modes are not accompanied by their conjugate mode; and (3) The basic flow without an inflection point can be unstable. The dispersion relation and the spatial structure of the unstable modes suggested that, irrespective of the orientation of the channel, they have close relation to the neutral modes (Rossby channel modes) which are the solutions in the absence of a basic shear flow. The features mentioned above are not dependent on whether or not the flow velocity at the boundary is zero. 相似文献
9.
本文基于正压浅水模型,分析基态位涡（Potential Vorticity：PV）结构对热带气旋（Tropical Cyclone：TC）类涡旋系统稳定性及其波动特征的影响.通过引入基态PV结构参数：宽度δ（眼墙内外边界涡度发生陡变的半径长度之比）和中空度γ（眼心相对涡度与内核区域平均相对涡度之比）,设计具有相同基流最大切向风速和最大风速半径的170组不同基态PV环结构的敏感性试验,并讨论了不同基态PV结构下涡旋系统最不稳定波数（the most unstable wavenumber：MUWN）和系统最不稳定模态（the most unstable mode of System：MUMS）的特征频率及其不稳定增长率的大小.结果指出：当PV环较宽,系统表现为低波数最不稳定,相应的MUMS为低频波且增长率小;当PV环较窄,系统表现为高波数不稳定,且PV环越实最不稳定波数越高;当PV环窄且空时,MUMS均为中高频波动,且不稳定增长率随PV环的宽度变窄和中空度变空而明显增大.分析典型PV结构下系统演变特征可知,当PV环较宽,MUMS表现为具有平衡约束的低频波动的线性不稳定特征;当PV环趋向窄且空时,MUMS的平衡性约束趋向弱化,同时不稳定增长表现为明显的指数型增长.进一步讨论系统内部非对称结构的形成和传播机制发现,对于弱不稳定的PV环来说,低波数波最不稳定的特征波动具有典型涡旋Rossby波特征;而对于强不稳定的PV环来说,高波数不稳定的特征波动混合波性质明显. 相似文献
10.
Generation of cyclonic vortices in the middle layer of flow around a large mountain like Tibet and Rocky was investigated by means of a 3-D nonhydrostatic meteorological prognostic model. Special attention was paid to the effects of the earth’s rotation and stratification on the vortices detached successively from the slope of a high and large horizontal scale mountain. It was found the successive formation and detachment of such ‘von Karman-like vortices’ occurred in the flow regime at high Rossby numbers Ro and low Froude numbers Fr. It was successfully divided by the criterion of baroclinic instability. This means that if the condition is unstable baroclinically, a lee vortex is destabilized into a three-dimensional one, while under baroclinically stable conditions the lee vortex with vertical axis retains its standing structure and remains long lasting in the middle layer. 相似文献
11.
This work addresses the linear dynamics underlying the formation of density interfaces at the periphery of energetic vortices, well outside the vortex core, both in the radial and axial directions. We compute numerically the unstable modes of an anticyclonic Gaussian vortex lens in a continuously stratified rotating fluid. The most unstable mode is a slow mode, associated with a critical layer instability located at the vortex periphery. Although the most unstable disturbance has a characteristic vertical scale which is comparable to the vortex height, interestingly, the critical levels of the successively fastest growing modes are closely spaced at intervals along the axial direction that are much smaller than the vortex height. 相似文献
12.
A cross-sectional model of an idealised constant depth gulf with a sill at its entrance, connected to a deep ocean, is used
to examine the barotropic and baroclinic response of the region to wind forcing. The role of the oceanic boundary condition
is also considered. Calculations show that in the case of a tall sill, where the pycnocline intersects the sill, the baroclinic
response of the gulf is similar to that of a lake, and internal waves cannot radiate energy out of the gulf. The barotropic
response shows free surface oscillations, with nodes located close to the centre of the oceanic basin and entrance to the
gulf, with associated barotropic resonant periods. As the sill height is reduced, baroclinic wave energy is radiated from
the gulf into the ocean, and the form of the baroclinic response changes from a standing wave (tall sill) as in a lake to
a progressive wave (no sill). The location of sea surface elevation nodes and resonant periods changes as the sill height
is reduced. Calculations of the barotropic resonant periods with and without stratification could not determine if they were
influenced by the presence of stratification, although published analytical theory suggests that they should be able to when
energy is lost from the gulf by internal wave radiation. This inability to detect changes in barotropic resonant period due
to stratification effects is due to the small change in resonant frequency produced by baroclinic effects, as shown by analytical
results, and the broad peak nature of the computed resonant frequency. In the case of a closed offshore boundary (an offshore
island), there is a stronger and narrower energy peak at the resonant frequency than when a barotropic radiation condition
is applied. However, the influence of stratification upon the resonant frequency could not be accurately determined. Although
the offshore boundary was well removed from the gulf to such an extent that any baroclinic waves reflected from it could not
reach the gulf within the integration period, it did, however, slightly influence the gulf baroclinic response due to its
influence on the barotropic response. 相似文献
13.
Two prognostic experiments taking into account real atmospheric forcing for 2006 and 2011 were carried out based on the eddy-resolving numerical model with a horizontal resolution of 1.6 km for the Black Sea. The main dynamic features such as the Rim Current, the Sevastopol, and Batumi anticyclones are reproduced in both experiments. The model results are confirmed via observation data. We accomplished the analysis of simulated circulation and energetics. The results demonstrate that both the vertical viscosity and vertical diffusion along with the energy inflow from the wind have been the main contributors to the annual and seasonal budgets of kinetic and potential energies of the Black Sea circulation. It is shown that two regimes of the Black Sea general circulation are implemented depending on a magnitude of wind contribution to the kinetic energy in winter. Intensive mesoscale eddy formation was observed along the Anatolian, Caucasian, and Crimean coasts. The analysis of the Black Sea circulation and eddy energetics allowed us to conclude that the generation and development of the mesoscale coastal eddies is associated with the barotropic instability in case of intensive coastal currents and is associated with both the barotropic and baroclinic instability in case of weak coastal currents. 相似文献
14.
Geostrophic adjustment of frontal anomalies in a rotating continuously stratified fluid is studied in the standard framework of strictly rectilinear fronts and jets. Lagrangian approach to this problem is developed allowing to analyze, in a conceptually and technically simple way, both major problems of the nonlinear adjustment: the existence of a smooth adjusted state for a given set of initial conditions and the attainability of the adjusted state during the adjustment process. Dynamical splitting into balanced (adjusted state) and unbalanced (inertia-gravity waves) motions becomes transparent in the Lagrangian approach. Conditions of existence of the balanced state in the unbounded domain are established. It is shown that nonexistence of a smooth adjusted state in the vertically bounded domains is generic and a parallel with the classical scenario of deformation frontogenesis is developed. Small perturbations around smooth adjusted states are then studied with special emphasis on the wave-trapping inside the jet/front. Trapped modes with horizontal scales comparable to the width of the jet are explicitly constructed for a barotropic jet and their evolution is studied with the help of the WKB-approximation for weakly baroclinic jets. Modifications of the standard scenario of adjustment due to subinertial (quasi-) trapped modes and implications for data analysis are discussed. 相似文献
15.
Using a new functional analysis tool, multiscale window transform(MWT), and the MWT-based localized multiscale energetics analysis and canonical transfer theory, this study reconstructs the Kuroshio system on three scale windows, namely,the mean flow window, the interannual-scale(low-frequency) window, and the transient eddy window, and investigates the climatological characteristics of the intricate nonlinear interactions among these windows. Significant upscale energy transfer is observed east of Taiwan, where the mean Kuroshio current extracts kinetic energy from both the interannual and eddy windows.It is found that the canonical transfer from the interannual variability is an intrinsic source that drives the eddy activities in this region. The multiscale variabilities of the Kuroshio in the East China Sea(ECS) are mainly controlled by the interaction between the mean flow and the eddies.The mean flow undergoes mixed instabilities(i.e., both barotropic and baroclinic instabilities) in the southern ECS, while it is barotropically stable but baroclinically unstable to the north. The multiscale interactions are found to be most intense south of Japan, where strong mixed instabilities occur; both the canonical transfers from the mean flow and the interannual scale are important mechanisms to fuel the eddies. It is also found that the interannual-scale energy mainly comes from the barotropically unstable jet, rather than the upscale energy transfer from the high frequency eddies. 相似文献
16.
Two-layer equatorial primitive equations for the free troposphere in the presence of a thin atmospheric boundary layer and thermal dissipation are developed here. An asymptotic theory for the resonant nonlinear interaction of long equatorial baroclinic and barotropic Rossby waves is derived in the presence of such dissipation. In this model, a self-consistent asymptotic derivation establishes that boundary layer flows are generated by meridional pressure gradients in the lower troposphere and give rise to degenerate equatorial Ekman friction. That is to say, the asymptotic model has the property that the dissipation matrix has one eigenvalue which is nearly zero: therefore the dynamics rapidly dissipates flows with pressure at the base of the troposphere and creates barotropic/baroclinic spin up/spin down. The simplified asymptotic equations for the amplitudes of the dissipative equatorial barotropic and baroclinic waves are studied by linear theory and integrated numerically. The results indicate that although the dissipation slightly weakens the tropics to midlatitude connection, strong localized wave packets are nonetheless able to exchange energy between barotropic and baroclinic waves on intraseasonal timescales in the presence of baroclinic mean shear. Interesting dissipation balanced wave-mean flow states are discovered through numerical simulations. In general, the boundary layer dissipation is very efficient for flows in which the barotropic and baroclinic components are of the same sign at the base of the free troposphere whereas the boundary layer dissipation is less efficient for flows whose barotropic and baroclinic components are of opposite sign at the base of the free troposphere. 相似文献
17.
Abstract Analysis of a two-layer, flat-bottom, steady-wind driven, eddy-resolving general circulation model reveals a distinct separation in frequency of baroclinic and barotropic motion in the region distant from the model Gulf Stream. The far-field motions at periods less (greater) than about 100 days are predominantly barotropic (baroclinic), unlike the near-field, eddy-generating, free-jet region which contains barotropic and baroclinic energy throughout the modei frequency range. The far-field barotropic energy produces a peak in the model sea-level spectra between 25 and 50 days with a magnitude comparable to energy levels observed in spectra of sea level from oceanic island tide gauges. The far-field barotropic motion is clearly composed of large-scale, resonant, barotropic normal modes drive by mesoscale activity of the turbulent, free-jet region. Oceanic mesoscale turbulence may therefore provide for planetary normal modes an excitation mechanism distinct from atmospheric forcing. The open-ocean, barotropic, model response is very similar to that of a fluctuating-wind driven model, which suggests that atmospheric and intrinsic forcing of mid-ocean eddies may be of comparable importance. 相似文献
18.
W. R. Young 《地球物理与天体物理流体动力学》2013,107(1-4):35-61
Abstract Various interactions between small numbers (two and four) of baroclinic, geostrophic point vortices in a two-layer system are studied with attention to the qualitative changes in behavior which occur as size of the deformation radius is varied. A particularly interesting interaction, which illustrates the richness of baroclinic vortex dynamics, is a collision between two hetons. (A heton is a vortex pair in which the constituent vortices have opposite signs and are in opposite layers. The “breadth” of a heton is the distance between its constituent vortices. A translating heton transports heat.) When two hetons, which initially have different breadths, collide, the result is either an exchange of partners, or a “slip-through” collision in which the initial structures are preserved. It is shown here that the outcome is always an exchange, provided the deformation radius is sufficiently small. This strongly contrasts with a collision between pairs of classical, one-layer vortices in which no exchange occurs if the initial ratio of the breadths is sufficiently extreme. Finally the transport of passive fluid by a translating baroclinic pair is investigated. A pair of vortices in the top layer transports no lower layer fluid if the distance between the vortices is less than 1.72 deformation radii. By contrast, the size of the region trapped by a heton increases without bound as the spacing between the vortices increases. 相似文献
19.
By means of barotropic model, the characteristic and initial value problems are investigated to reveal the local two-dimensional
barotropic instability of the nonuniform current to the dynamic mechanism of the formation of the Yangtze-Huaihe River severe
storm in July 1991. Analytical theory and numerical experiment show that (i) the unstable developing modes are chiefly the
two periods of about 44 d and 10 d, which are fundamentally consistent with that of the precipitation change of the Yangtze-Huaihe
River. (ii) The growth rate of the local perturbation is dominated by the meridional wave numbern = 1–5 and zonal wave numberk = 1–12, i.e. the severe storm over the Yangtze-Huaihe River results from the interaction of the systems at different latitudes
and waves of different scales, (iii) The perturbation over the Yangtze-Huaihe River possesses the property of local intensification,
which slowly migrates westward over the lower and middle reaches of the Yangtze-Huaihe River. (iv) The growth rate of the
instability, especially the propagation velocity of the perturbation, is sensitive to the external parameters ū and α.
Project supported by the National Natural Science Foundation of China. 相似文献
20.
Peter D. Killworth 《地球物理与天体物理流体动力学》2013,107(4):235-258
Abstract The stability of an isolated one-layer reduced gravity front is examined. It is shown that the system is unstable to long-wave disturbances provided merely that a simple condition on the depth profile is satisfied far from the front. The instability does not require the extremum of potential vorticity needed by quasi-geostrophic theory. The instability releases mean kinetic and mean potential energy from the system, but lacking a second layer cannot truly be termed baroclinic instability. 相似文献