On the attractors of an intermediate coupled ocean-atmosphere model

Techniques of numerical bifurcation theory are used to study stationary and periodic solutions of an intermediate coupled model for tropical ocean-atmosphere interaction. The qualitative dynamical behavior is determined for a volume in parameter space spanned by the atmospheric damping length, the coupling parameter, the surface layer feedback strength and the relative adjustment time coefficient. Time integration methods have previously shown much interesting dynamics, including multiple steady states, eastward- or westward-propagating orbits and relaxation oscillations. The present study shows how this dynamics arises in parameter space through the interaction of the different branches of equilibrium solutions and the singularities on these branches. For example, we show that westward-propagating periodic orbits arise through an interaction of two unstable stationary modes and that relaxation oscillations occur through a limit cycle-saddle node interaction. There are several dynamical regimes in the coupled model which are determined by the primary bifurcation structure; this structure depends strongly on the parameters in the model. Although much of the dynamics may be studied in the fast-wave limit, it is shown that ocean wave dynamics introduces additional oscillatory instabilities and how these relate to propagating oscillations.     

副高外围对流雨带中的对流—对称不稳定及锋生的诊断分析

对2009年8月25日西太平洋副热带高压（简称副高）西北外围对流雨带的云图特征进行了分析,利用WRF3.3中尺度模式对对流雨带的发生发展进行了数值模拟,在模拟较成功的基础上,利用模式输出结果分析了对流雨带发生时的对称不稳定、对流不稳定、惯性不稳定以及锋生等。结果表明：副高外围对流雨带由若干具有一定间隔的对流单体构成,单体在随对流层中层气流的移动中逐渐发展直至消亡。对流雨带的西北侧为宽广的带状斜压云系,东南侧为副高控制的晴空区。对流雨带发生于对流层低层（700 hPa以下）的对称不稳定区,700～500 hPa存在对流不稳定和弱的惯性不稳定。随着对流的发展,700～500 hPa的对流不稳定度明显减弱,而惯性不稳定明显加强。对流层低层为倾斜上升区,中高层为垂直上升区,左侧对应下沉气流,呈现明显的倾斜对流和垂直对流的混和特征,体现了对流—对称不稳定的作用。对流层低层（750 hPa以下）锋生的存在提供了对流—对称不稳定能量释放的有利条件。对流雨带与500～800 hPa等厚度线基本平行,而与500 hPa等高线存在明显的交角,雨带中的对流单体随环境气流移动,雨带符合与对称不稳定相联系的带状降水特征。上述结论对实际预报副高外围对流雨带的位置和走向具有指示意义。     

Turbulent mechanisms in stratified fluids

Probability distribution of basic instabilities appearing in stratified flows and point density fluctuations have been studied. Various parameters of the mixing process have been changed in the experiments, to investigate mixing. Detailed flow visualization as well as density measurements have been used in zero-mean-flow laboratory experiments involving grid-stirred turbulent mixing across a density interface and bubble-induced mixing. The overall mixing efficiency of the processes depends on the local Richardson number as well as on the local vorticity. Parameter distributions of low and high mixedness corresponding to different instabilities are presented, showing that dipolar vortices penetrating the interface are the most efficient mixing instabilities.     

Steering of upper ocean currents and fronts by the topographically constrained abyssal circulation

A two-layer theory is used to investigate (1) the steering of upper ocean current pathways by topographically constrained abyssal currents that do not impinge on the bottom topography and (2) its application to upper ocean – topographic coupling via flow instabilities where topographically constrained eddy-driven deep mean flows in turn steer the mean pathways of upper ocean currents and associated fronts. In earlier studies the two-layer theory was applied to ocean models with low vertical resolution (2–6 layers). Here we investigate its relevance to complex ocean general circulation models (OGCMs) with high vertical resolution that are designed to simulate a wide range of ocean processes. The theory can be easily applied to models ranging from idealized to complex OGCMs, provided it is valid for the application. It can also be used in understanding some persistent features seen in observed ocean frontal pathways (over deep water) derived from satellite imagery and other data. To facilitate its application, a more thorough explanation of the theory is presented that emphasizes its range of validity. Three regions of the world ocean are used to investigate its application to eddy-resolving ocean models with high vertical resolution, including one where an assumption of the two-layer theory is violated. Results from the OGCMs with high vertical resolution are compared to those from models with low vertical resolution and to observations. In the Kuroshio region upper ocean – topographic coupling via flow instabilities and a modest seamount complex are used to explain the observed northward mean meander east of Japan where the Kuroshio separates from the coast. The Japan/East Sea (JES) is used to demonstrate the impact of upper ocean – topographic coupling in a relatively weak flow regime. East of South Island, New Zealand, the Southland Current is an observed western boundary current that flows in a direction counter to the demands of Sverdrup flow and counter to the direction simulated in nonlinear global flat bottom and reduced gravity models. A model with high vertical resolution (and topography extending through any number of layers) and a model with low vertical resolution (and vertically compressed but otherwise realistic topography confined to the lowest layer) both simulate a Southland Current in the observed direction with dynamics depending on the configuration of the regional seafloor. However, the dynamics of these simulations are very different because the Campbell Plateau and Chatham Rise east and southeast of New Zealand are rare features of the world ocean where the topography intrudes into the stratified water column over a relatively broad area but lies deeper than the nominal 200 m depth of the continental shelf break, violating a limitation of the two-layer theory. Observations confirm the results from the high vertical resolution model. Overall, the model simulations show increasingly widespread upper ocean – topographic coupling via flow instabilities as the horizontal resolution of the ocean models is increased, but fine resolution of mesoscale variability and the associated flow instabilities are required to obtain sufficient coupling. As a result, this type of coupling is critical in distinguishing between eddy-resolving and eddy-permitting ocean models in regions where it occurs.     

中国东部春季极端降水与同期欧亚大陆地表感热的可能联系

利用1960~2010年ERA-20C再分析资料和中国东部站点降水观测资料,探讨了我国东部春季极端降水与欧亚大陆地表感热通量的联系和可能影响途径。结果发现,当春季欧亚大陆中纬度巴尔喀什湖以西及贝加尔湖以南区域地表感热通量偏弱（强）,我国东部沿海地区地表感热通量偏强（弱）时,我国东部春季极端降水呈现南少（多）北多（少）的反相分布特征。当春季欧亚大陆中纬度关键区地表感热偏弱,低纬度关键区地表感热通量偏强时,春季副热带西风急流偏弱、位置偏北,我国东部北方地区大气斜压不稳定和对流不稳定偏强,北方地区极端降水偏强,而南方地区大气斜压不稳定和对流不稳定偏弱,南方地区极端降水偏弱。当春季欧亚大陆中纬度关键区地表感热偏强,低纬度关键区地表感热通量偏弱,我国东部极端降水的情况大致相反。     

Steering of upper ocean currents and fronts by the topographically constrained abyssal circulation

A two-layer theory is used to investigate (1) the steering of upper ocean current pathways by topographically constrained abyssal currents that do not impinge on the bottom topography and (2) its application to upper ocean – topographic coupling via flow instabilities where topographically constrained eddy-driven deep mean flows in turn steer the mean pathways of upper ocean currents and associated fronts. In earlier studies the two-layer theory was applied to ocean models with low vertical resolution (2–6 layers). Here we investigate its relevance to complex ocean general circulation models (OGCMs) with high vertical resolution that are designed to simulate a wide range of ocean processes. The theory can be easily applied to models ranging from idealized to complex OGCMs, provided it is valid for the application. It can also be used in understanding some persistent features seen in observed ocean frontal pathways (over deep water) derived from satellite imagery and other data. To facilitate its application, a more thorough explanation of the theory is presented that emphasizes its range of validity. Three regions of the world ocean are used to investigate its application to eddy-resolving ocean models with high vertical resolution, including one where an assumption of the two-layer theory is violated. Results from the OGCMs with high vertical resolution are compared to those from models with low vertical resolution and to observations. In the Kuroshio region upper ocean – topographic coupling via flow instabilities and a modest seamount complex are used to explain the observed northward mean meander east of Japan where the Kuroshio separates from the coast. The Japan/East Sea (JES) is used to demonstrate the impact of upper ocean – topographic coupling in a relatively weak flow regime. East of South Island, New Zealand, the Southland Current is an observed western boundary current that flows in a direction counter to the demands of Sverdrup flow and counter to the direction simulated in nonlinear global flat bottom and reduced gravity models. A model with high vertical resolution (and topography extending through any number of layers) and a model with low vertical resolution (and vertically compressed but otherwise realistic topography confined to the lowest layer) both simulate a Southland Current in the observed direction with dynamics depending on the configuration of the regional seafloor. However, the dynamics of these simulations are very different because the Campbell Plateau and Chatham Rise east and southeast of New Zealand are rare features of the world ocean where the topography intrudes into the stratified water column over a relatively broad area but lies deeper than the nominal 200 m depth of the continental shelf break, violating a limitation of the two-layer theory. Observations confirm the results from the high vertical resolution model. Overall, the model simulations show increasingly widespread upper ocean – topographic coupling via flow instabilities as the horizontal resolution of the ocean models is increased, but fine resolution of mesoscale variability and the associated flow instabilities are required to obtain sufficient coupling. As a result, this type of coupling is critical in distinguishing between eddy-resolving and eddy-permitting ocean models in regions where it occurs.     

Instabilities in hurricane-like boundary layers

Recent advances in observational technology have led to a more detailed knowledge of the low-level flow in hurricanes. In particular, quasi-streamwise rolls on a variety of scales have been observed. Some of these rolls have radial wavelengths of 4–10 km, which is comparable to rolls associated with instabilities inherent to Ekman-type boundary layers.The evolution and stability of the swirling boundary layer underneath a hurricane-like vortex is studied using both a nonlinear model and linearized stability analysis. The nonlinear model is an axisymmetric model of incompressible fluid flow, which is used to simulate the development of boundary layers underneath vortices with hurricane-like wind profiles. Axisymmetric rolls appear in these boundary layers, which have some similarities to the observed rolls in hurricanes. The axisymmetric flow is also used as the basic-state for a linearized stability analysis. The analysis technique allows for arbitrary variation in the radial and vertical directions for both the basic-state flow and the perturbations. Thus, the strong radial variations and curvature effects common to strong vortices are part of the analysis. The analysis finds both symmetric and asymmetric instabilities that are similar to those in the nonlinear simulations and in observations. The instabilities acquire some of their energy from the vertical shear associated with a reversal of the radial inflow at the top of the boundary layer, and some of their energy from vertical shear of the azimuthal flow. The radial flow energy conversion tends to increase for flows with less inertial stability and for modes oriented across the low-level shear; the azimuthal flow conversion increases for larger inertial stability and for modes aligned with the low-level shear.     

Criteria for the stability of steady flows induced by diabatic heating

By use of the Liapunov direct method, criteria for the stability of a general steady flow induced by heating are derived for a barotropic model with heating and dissipation. Among these criteria, necessary conditions for the instabilities are identified with the rises of supercritically high speed instability, barotropic instability and some other instabilities.     

Unstable modes of a sheared pycnocline above a stratified layer

Internal waves incident on a sheared ocean pycnocline are studied using analytic and numerical methods. Linear analysis of the unstable modes of a sheared ocean pycnocline is used to demonstrate interactions between internal waves and shear instabilities. A new analytic solution for an asymmetric shear layer over a stratified layer is presented, illustrating modes which couple to internal waves, in addition to the well-known Holmboe modes. The robustness of these solutions is demonstrated using numerical methods for realistic shear profiles. Fully nonlinear numerical simulations illustrate the growth of these modes and demonstrate the excitation of shear instabilities by incident internal waves. The results may have implications for internal wave interactions with the ocean pycnocline and the local generation of internal solitary waves.     

An improved two-time-level split-explicit integration scheme for non-hydrostatic compressible models

Summary A new two-time-level split-explicit time integration scheme for the use in non-hydrostatic compressible modelling is presented. It is demonstrated that the scheme is numerically stable and has a smaller splitting error than other comparable split-explicit schemes. This error is due to the combination of advection and fast-wave terms in the numerical scheme.To outline where the splitting error occurs and how it acts within the splitting mechanism, a short review of existing split-explicit time integration methods is given. An in-depth analysis of the eigenvalues of several two-time-level schemes is performed showing that instabilities are associated with the splitting error term. The term has different signs for forward moving and backward moving waves, causing exponential growing or decaying. This unwanted characteristic is not prevented by a diffusive term in general, but might be counteracted by schemes using an estimate of the fast waves at the midpoint of the time increment.The importance of this fast-waves midpoint estimate leads to the formulation of a class of split-explicit two-time-level schemes. Within this framework any forward-in-time and stable advection scheme might be combined with the fast-waves terms in the splitting algorithm.The new method is implemented in the non-hydrostatic model LM of DWD. Some test cases are presented, indicating that the new scheme has the potential to be used in an operational environment.     

Eddy fluxes and mean flow tendencies in open-ocean baroclinic instability

Linear normal-mode instabilities of a mean flow varying over many internal radii of deformation are considered. Attention is devoted not to the instabilities themselves, but to the second-order effects of such instabilities on the mean flow. These are derived analytically from solutions by Killworth. The effects on symmetric profiles are very different from those on asymmetric profiles. Specifically, the tendencies are much larger in the latter case with the strongest tendency being on the barotropic part of the mean flow; this tendency apparently attempts to make the profile more symmetric.     

Nonlinear evolution of a layered stratified shear flow

We investigate numerically and theoretically the nonlinear evolution of a parallel shear flow at moderate Reynolds number which has embedded within it a mixed layer of intermediate fluid. The two relatively thin strongly stratified density interfaces are centered on the edges of the shear layer. We are particularly interested in the development of primary and secondary instabilities. We present the results of a stability analysis which predicts that such flows may be unstable to stationary vortical disturbances which are a generalization of an inviscid instability first considered by G.I. Taylor. We investigate the behavior of these “Taylor billows” at finite amplitude through two-dimensional numerical simulations. We observe that the braid regions connecting adjacent primary Taylor billows are susceptible to secondary, inherently two-dimensional instabilities. We verify that these secondary instabilities, which take the form of small elliptical vortices, arise due to a local intensification of the spanwise vorticity in the braid region.     

Modeling large-scale instabilities in the Kuroshio extension

Large-scale instabilities of mid-latitude jets (with continuous horizontal and vertical shear) are studied using a long wave approximation, which is valid for disturbances of length scales greater than the internal Rossby radius of deformation. These large-scale instabilities are abundant in the Kuroshio Extension according to observations. Results show westward propagation if the total transport is westward (although the jet near surface is eastward). Large-scale instabilities gain energy from the release of available potential energy, but lose part of the gain to the mean flow by reinforcing the eastward jet near surface. The Reynolds stress tends to be positive north of the jet and negative south of the jet through all depths, which is consistent with observations.     

Is the astronomical forcing a reliable and unique pacemaker for climate? A conceptual model study

There is evidence that ice age cycles are paced by astronomical forcing, suggesting some kind of synchronisation phenomenon. Here, we identify the type of such synchronisation and explore systematically its uniqueness and robustness using a simple paleoclimate model akin to the van der Pol relaxation oscillator and dynamical system theory. As the insolation is quite a complex quasiperiodic signal involving different frequencies, the traditional concepts used to define synchronisation to periodic forcing are no longer applicable. Instead, we explore a different concept of generalised synchronisation in terms of (coexisting) synchronised solutions for the forced system, their basins of attraction and instabilities. We propose a clustering technique to compute the number of synchronised solutions, each of which corresponds to a different paleoclimate history. In this way, we uncover multistable synchronisation (reminiscent of phase- or frequency-locking to individual periodic components of astronomical forcing) at low forcing strength, and monostable or unique synchronisation at stronger forcing. In the multistable regime, different initial conditions may lead to different paleoclimate histories. To study their robustness, we analyse Lyapunov exponents that quantify the rate of convergence towards each synchronised solution (local stability), and basins of attraction that indicate critical levels of external perturbations (global stability). We find that even though synchronised solutions are stable on a long term, there exist short episodes of desynchronisation where nearby climate trajectories diverge temporarily (for about 50 kyr). As the attracting trajectory can sometimes lie close to the boundary of its basin of attraction, a small perturbation could quite easily make climate to jump between different histories, reducing the predictability. Our study brings new insight into paleoclimate dynamics and reveals a possibility for the climate system to wander throughout different climatic histories related to preferential synchronisation regimes on obliquity, precession or combinations of both, all over the history of the Pleistocene.     

线性和非线性正压不稳定

本文从无摩擦的、无辐散的非线性正压涡度方程出发,利用行波解,在相平面上对方程的平衡点分别导得线性和非线性正压不稳定判据,与传统的不稳定判据作了比较分析。还求得了线性和非线性不稳定波的解析解,计算结果表明,若初始时刻两者波幅相等,则以后非线性不稳定波幅的增长值总小于线性不稳定波幅的增长值。非线性效应有使线性不稳定指数型增长减缓的作用。不稳定使得振幅比初始时刻增大一倍所需要的时间,对于线性不稳定大约是6h,对于非线性不稳定大约是18h,后者与实际大气中的观测事实是一致的。     

On the breakdown into turbulence of propagating internal waves

The breakdown of propagating internal waves is studied using linear stability analysis and direct numerical simulations. Sinusoidal wave trains in a uniformly stratified, non-rotating environment are considered. Cases are addressed with differing wave amplitudes and directions of propagation. For large-amplitude waves it is found that the primary instabilities are both two- and three-dimensional. It is also found that there is no qualitative difference in the breakdown process for waves with amplitude slightly below or slightly above the amplitude of incipient overturning. For the parameter regimes considered, the breakdown process could not be attributed to convective or shear instability alone, but a combination of the two. Owing to the growth of instabilities, local patches of statically unstable fluid and also of intense shear form, leading ultimately to local patches of turbulence.     

On the breakdown of the westerlies

The dynamics of the ultra‐long Rossby waves are studied with the aid of a primitive equation numerical model. The investigation is focused on a study of the breakdown of a high‐index circulation. Different idealized flow patterns are used as initial conditions and forecasts are made with the numerical model. The influences of oceans and mountains are studied by incorporating them into the model. The results indicate that barotropic and baroclinic instabilities as well as the structure of the earth's surface are of importance for the development, but the experiments do not clearly indicate which one of these factors is most important.     

Oscillations of the Intertropical Convergence Zone and the genesis of easterly waves Part II: numerical verification

A companion paper (Part I: Toma and Webster 2008), argued that the characteristics of the mean Intertropical Convergence Zone (ITCZ) arise from instabilities associated with the strong cross-equatorial pressure gradient (CEPG) that exists in the eastern Pacific Ocean as a result of the latitudinal sea-surface temperature (SST) gradient. Furthermore, it was argued that instabilities of the mean ITCZ resulted in the in situ development of easterly waves. Thus, in Part I, it was hypothesized that the mean and transient state of eastern Pacific convection was due to local processes and less so to the advection of waves from the North Atlantic Ocean. To test this hypothesis and, at the same time, consider others such as a possible role of the equatorial and subtropical orography in generating local instabilities, a series of controlled numerical experiments are designed using the WRF regional model. The domain of the model was configured to include the western Atlantic Ocean, the Isthmus of Panama and the eastern Pacific Ocean to 155°W. Lateral boundaries were set at 40°N and 40°S, thus containing the mountains of Central America, the Andes and the Sierra Madre of Mexico. In a series of experiments, analysis products were used as boundary conditions that were successively updated four times per day, set as 10-day running average fields or as running mean monthly fields. Finally, the model was run with topography essentially eliminated over the land areas. Although there are differences between the details of the resultant fields, the location of mean convection and the form of the transients remain the same. It is concluded, in support of the theoretical and diagnostic studies of Part I that orographic forcing or waves generated in the North Atlantic Ocean are not the major causes of the mean and transient nature of disturbances in the eastern Pacific.     

2003年江淮梅雨暴雨与湿位涡的关系

统计了2003年发生在江淮地区的梅雨暴雨，根据暴雨中心对流稳定度及降雨性质将暴雨分为4种类型。分析湿位涡与梅雨暴雨中的惯性不稳定、对称不稳定、对流不稳定的关系发现：第1类暴雨往往与对称不稳定有关，第2类暴雨与对流不稳定有关，且这两类暴雨高层多具有强惯性不稳定，降水相对较大；第3、第4类暴雨是稳定性降雨，高层一般不具备惯性不稳定，雨量一般较小。高层的惯性不稳定对降水的加强作用明显。     

Atmospheric Disturbances that Generate Intermittent Turbulence in Nocturnal Boundary Layers

Using the unprecedented observational facilities deployed duringthe 1999 Cooperative Atmosphere-Surface Exchange Study (CASES-99),we found three distinct turbulent events on the night of 18October 1999. These events resulted from a density current,solitary wave, and internal gravity wave, respectively. Our studyfocuses on the turbulence intermittency generated by the solitarywave and internal gravity wave, and intermittent turbulenceepisodes associated with pressure change and wind direction shiftsadjacent to the ground. Both the solitary and internal gravitywaves propagated horizontally and downward. During the passage ofboth the solitary and internal gravity waves, local thermal andshear instabilities were generated as cold air was pushed abovewarm air and wind gusts reached to the ground. These thermal andshear instabilities triggered turbulent mixing events. Inaddition, strong vertical acceleration associated with thesolitary wave led to large non-hydrostatic pressure perturbationsthat were positively correlated with temperature. The directionaldifference between the propagation of the internal gravity waveand the ambient flow led to lateral rolls. These episodic studiesdemonstrate that non-local disturbances are responsible for localthermal and shear instabilities, leading to intermittentturbulence in nocturnal boundary layers. The origin of thesenon-local disturbances needs to be understood to improve mesoscalenumerical model performance.