The impact of nonlinear stability and instability on the validity of the tangent linear model

l.Intr0ducti0nTheequationsgoverningthemotionsoftheatmosphereandoceanaren0nlinear0nes.Itisdiffcultandcomplicatedtodealwiththenonlinearproblem.Sothetangentlinearmodel(TLM),whichisobtainedbylinearizingthenonlinearmodelinthevicinityofthebasicflow.iswidelyutilizedinthetheoreticalresearchandpracticalimplementationintheatmosphericandoceanicsciences.First-TLMcanbeusedtoestimatetheev0luti0nofsmallPerturbati0nsinaf0recastmodel.Second,itisadoptedinextendedKalmanfilterinthedataassimilation(Evensen,l99…     

Nonlinear stability analysis of the zonal flows at middle and high latitudes

An attempt has been made to apply Arnol’d type nonlinear stability criteria to the diagnostic study of the persistence (stability) or breakdown (instability) of the atmospheric flows. In the case of the blocking high, the cut-off low and the zonal flow, the relationships of the geostrophic stream function versus the po-tential vorticity of the observed atmosphere are analyzed, which indicates that Arnol'd second type nonlinear stability theorem is more relevant to the observed atmosphere than the first one. For both the sta-ble and unstable zonal flows, Arnol’d second type nonlinear stability criteria are applied to the diagnosis. The primary results show that our analyses correspond well to the evolution of the atmospheric motions. The synoptically stable zonal flows satisfy Arnol'd second type nonlinear stability criteria; while the synoptically unstable ones violate the nonlinear stability criteria.     

Wave-Mean Flow Interaction: the Role of Continuous-Spectrum Disturbances

Traditionally, “eddy feeds zonal flow” in the atmosphere is considered as a result of decaying unstable waves. We show that disturbances made of non-modal solutions-the continuous-spectrum disturbances-can also effectively transport zonal angular momentum and interact with the zonal basic flow. These disturbances, though stable, eventually decay, losing their energy to strengthen the westerly jets in the atmosphere.Calculations with observational data illustrate that the atmospheric zonal flow is maintained primarily by continuous-spectrum disturbances rather than by unstable waves. Angular momentum transport by continuous-spectrum disturbances is one order of magnitude larger than that by all kinds of normal modes (referred as discrete-spectrum disturbances) including unstable waves.     

不稳定边界层下地形重力内波

水槽实验及线性理论研究表明,当低层大气处于近中性或不稳定时,如果地形引起的动力扰动足够强,地形扰动可在上部稳定层结中激发出重力内波,波动反过来影响低层流场,引起动量输送。低层大气处于近中性或不稳定时,地形波同样对大气运动可产生波阻,这应引起模式工作者的重视。最后讨论了大气粘性对中性或不稳定层结下地形波的影响。     

大气中大尺度振动的不稳定

这篇文章同时考虑了基本气流的垂直分布和水平分布来讨论大尺度扰动的不稳定度。讨论了不稳定扰动发生的必要规准,并进一步讨论了扰动的发展或阻尼对大气环流的作用。     

Roles of Synoptic to Quasi-Monthly Disturbances in Generating Two Pre-Summer Heavy Rainfall Episodes over South China

In this study,power spectral analysis and bandpass filtering of daily meteorological fields are performed to explore the roles of synoptic to quasi-monthly disturbances in influencing the generation of pre-summer heavy rainfall over South China.Two heavy rainfall episodes are selected during the months of April-June 2008-15,which represent the collaboration between the synoptic and quasi-biweekly disturbances and the synoptic and quasi-monthly disturbances,respectively.Results show that the first heavy rainfall episode takes place in a southwesterly anomalous flow associated with an anticyclonic anomaly over the South China Sea(SCS)at the quasi-biweekly scale with 15.1%variance contributions,and at the synoptic scale in a convergence zone between southwesterly and northeasterly anomalous flows associated with a southeastward-moving anticyclonic anomaly on the leeside of the Yungui Plateau and an eastwardpropagating anticyclonic anomaly from higher latitudes with 35.2%variance contribution.In contrast,the second heavy rainfall episode takes place in southwest-to-westerly anomalies converging with northwest-to-westerly anomalies at the quasi-monthly scale with 23.2%variance contributions to the total rainfall variance,which are associated with an anticyclonic anomaly over the SCS and an eastward-propagating cyclonic anomaly over North China,respectively.At the synoptic scale,it occurs in south-to-southwesterly anomalies converging with a cyclonic anomaly on the downstream of the Yungui Plateau with 49.3%variance contributions.In both cases,the lower-tropospheric mean south-to-southwesterly flows provide ample moisture supply and potentially unstable conditions;it is the above synoptic,quasi-biweekly or quasimonthly disturbances that determine the general period and distribution of persistent heavy rainfall over South China.     

Nonlinear feature of the abrupt transitions between multiple equilibria states of an ecosystem model

Based on a five-variable theoretical ecosystem model, the stability of equilibrium state and the nonlinear feature of the transition between a grassland state and a desert state are investigated. The approach of the conditional nonlinear optimal perturbations (CNOPs), which are the nonlinear generalization of the linear singular vectors (LSVs), is adopted. The numerical results indicate that the linearly stable grassland and desert states are nonlinearly unstable to large enough initial perturbations on the condition that the moisture index $\mu$ satisfies 0.3126<μ<0.3504. The perturbations represent some kind of anthropogenic influence and natural factors. The results obtained by CNOPs, LSVs and Lyapunov vectors (LVs) are compared to analyze the nonlinear feature of the transition between the grassland state and the desert state. Besides this, it is shown that the five-variable model is superior to the three-variable model in providing more visible signals when the transitions occur.     

Instability of internal waves near a critical level

The three-dimensional stability problem is investigated for a family of velocity and density profiles similar in form to those expected for large-amplitude internal gravity waves near a critical level. These profiles exhibit regions of high shear and stable stratification alternating with regions of weak shear and unstable stratification. Analytical solutions are given for inviscid, neutral modes that are similar to those found under neutral conditions with stable stratification. Neutral modes form closed streamline patterns centered at locations of maximal shear, and are not strongly influenced by nearby regions of unstable stratification. Unstable modes are computed numerically. It is shown that the instability mechanism for these wave-like flows fundamentally three-dimensional in character and exhibits both shear and convective dynamics. For flows with parameter values below the neutral curves, unstable modes oriented in the streamwise direction undergo shear instability, while modes oriented orthogonally are convectively unstable. In addition to their intrinsic physical relevance, the results of this study have important implications for the physics and the numerical modeling of breaking internal gravity waves. Two-dimensional models will bias the breaking dynamics by eliminating the possibility for convection oriented in the transverse plane.     

论层结和风场对小尺度扰动发展的非线性影响

本文考虑了小尺度扰动发展时,扰动场和平均场(环境)间的非线性相互作用后,分析了大气层结和盛行风对扰动发展的影响。分析结果指出,在层结是中性或不稳定分布时,扰动总能够得到发展;在稳定层结的情况下,只要某一临界条件满足,扰动也能发展。一般来说,盛行风将抑制扰动的发展;但对某些类型的风速廓线,盛行风对扰动的发展也能起到积极的作用。     

Multiscale Combined Action and Disturbance Characteristics of Pre-summer Extreme Precipitation Events over South China

The dominant frequency modes of pre-summer extreme precipitation events(EPEs) over South China(SC) between1998 and 2018 were investigated. The 67 identified EPEs were all characterized by the 3–8-d(synoptic) frequency band.However, multiscale combined modes of the synoptic and three low-frequency bands [10–20-d(quasi-biweekly, QBW);15–40-d(quasi-monthly, QM); and 20–60-d(intraseasonal)] accounted for the majority(63%) of the EPEs, and the precipitation intensity on the peak wet day was larger th...     

Phillips模式的斜压不稳定的非线性饱和问题:能量情形

A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model-the case of energy-is studied within the context of Arnold's second stability theorem. Analytic upper bounds on the energy of wavy disturbances are obtained. For one unstable region in the parameter plane, the result here is a second-order correction in ε to Shepherd's; For another unstable region, the analytic upper bound on the energy of wavy disturbances offers an effective constraint on wavy (nonzonal) disturbances φ'i at any time.     

An instability mechanism in the atmosphere over a water body

Summary ?The previously unexplored mechanism of the hydrodynamic instability of the atmospheric boundary layer over a water body is theoretically investigated. In air, stratified with respect to moisture, vertical motions produce variations in specific humidity (mixing ratio) near the interface surface. This, in turn, causes variation in evaporation from the water surface and horizontal thermal inhomogeneities result on the surface which, under certain conditions, can strengthen the initial vertical motions. In this paper the linear problem of the stability of the system under consideration is solved. Boundaries of the unstable region in the space of physical parameters are defined, and specific values of growth rates of disturbances are investigated. The results show the possibility of the development of disturbances with horizontal scales of several hundred metres for a period of about one hour even for the stable stratified atmospheric layer over a water surface and in the absence of destabilizing shears of velocity. The horizontal sizes of the most rapidly growing modes, as a rule, are an order of magnitude larger than the vertical ones. Received November 17, 1998; revised November 20, 2001     

Interaction between an eddy and a zonal jet : Part II. Two-and-a-half-layer model

In a two-and-a-half-layer quasi-geostrophic model, a process study is conducted on the interaction between a vortex and a zonal jet, both with constant potential vorticity. The vortex is a stable anticyclone, initially located north of the eastward jet. The potential vorticity of the jet is allowed to have various vertical structures, while the vortex is concentrated in only one layer. The flow parameters are set to values characteristic of the Azores region.First, the jet is stable. Weak vortices steadily drift north of the jet without crossing it while strong vortices can cross the jet and tear off a cyclone with which they pair as a heton (baroclinic dipole). This heton often breaks later in the shear exerted by the jet; the two vortices finally drift apart. When crossed by deep anticyclones, the jet develops meanders with 375 km wavelength. These results exhibit a noticeable similarity with the one-and-a-half-layer case studied in Part I.Secondly, the jet is allowed to be linearly unstable. In the absence of the vortex, it develops meanders with 175 km wavelength and 25-day e-folding time on the β-plane. For various vertical structures of the jet, baroclinic instability is shown to barely affect jet–vortex interaction if the linear growth rate of unstable waves is smaller than 1/(14 days). Further simulations with a linearly unstable, nonlinearly equilibrated jet evidence its strong temporal variability when crossed by a deep vortex on the β-plane. In particular, long waves can dominate the spectrum for a few months after jet crossing by the vortex. Again in this process, the deep vortex couples with a surface cyclone and both drift southwestward.     

非纬向基本气流的斜压不稳定

本文用分层两层模式研究了在一般非纬向基本气流情况下的斜压不稳定。通过比较分析,给出了基本气流对斜压不稳定的影响,结果表明,在非纬向基本气流情况下,更有利于出现斜压不稳定。 将非纬向基本气流的斜压不稳定理论用于高纬度地区的大气运动,说明了高纬度地区常见的小扰动强烈发展,是切变基本气流所驱动的一种“涡旋波”的斜压不稳定。     

Discrete Spectra and Continuous Spectrum of the Barotropic Quasi-Geostrophic Model-A Calculation of Meteorological Data

l.Intr0ducti0nMaintenance,developmentanddecay0fmiddlelatitudeatmosphericdisturbancesarecentraltotheunderstandingofsynopticweatherprocessesandshort-termclimatevariability.FrontogenesisandsurgeofcoldwavesaretypicallyassociatedwithrapiddevelopmentoffavorablyconfiguredsmalldisturbancesintheuppertroPOsphere.Thesedisturbancesfurtheractasinteractivetransientforcingtocauselowfrequencyvariabilities.Theyalsoaffectthein-tensityofwesterliesandtheequator-to-P0letemPeraturegradientoftheatmosphere.Studieso…     

Note on the Symmetric Stability of Quasi－Homogeneous and Incompressible Rotating Ocean

The general property of zonally symmetric stability of quasi-homogeneous and incompressible rotating ocean can be determined by a nondimensional parameter Rs which is similar to the Richardson number in Howard’s paper. The results indicate that the rotating effect leads to stabilize the basic flows and the horizontal shear effect leads to destabilize the basic flows. In addition, the most unstable growth rate is obtained and the semicircle and semiellipse theorem about the distributions of the unstable phase velocity are given in this paper.     

Structures of dynamically unstable shear flows and their implications for shallow internal gravity waves

Summary In this study, the response of a dynamically unstable shear flow with a critical level to periodic forcing is presented. An energy argument is proposed to explain the upshear tilt of updrafts associated with disturbances in two-dimensional stably stratified flows. In a dynamically unstable flow, the energy equation requires an upshear tilt of the perturbation streamfunction and vertical velocity whereU _z is positive. A stability model is constructed using an iteration method. An upshear tilt of the vertical velocity and the streamfunction fields is evident in a dynamically unstable flow, which is required by energy conversion from the basic shear to the growing perturbation wave energy according to the energy argument. The momentum flux profile indicates that the basic flow is decreased (increased) above (below) the critical level. Thus, the shear instability tends to smooth the shear layer. Following the energy argument, a downshear tilt of the updraft is produced in an unstably stratified flow since the perturbation wave energy is negative. The wave energy budget indicates that the disturbance is caused by a thermal instability modified by a shear flow since the potential energy grows faster than the kinetic energy.With 4 Figures     

Diffusion cloud chamber operation and the background gas effect

Key design and operational aspects for thermal diffusion cloud chamber (TDCC) applications are discussed in the context of a two-dimensional solution to the mass and energy balances describing diffusion through a stagnant background gas. The important issue of buoyancy-driven convective disturbances and their impact upon nucleation measurements made using a diffusion cloud chamber are discussed. A new derivation of the relation that predicts the upper limit of total pressure allowed for stable (the absence of buoyancy-driven convective disturbances) operation of the diffusion cloud chamber is presented. For the first time, this limit of stable operation can be predicted prior to making experimental measurements. Nucleation data obtained in our laboratory are examined in the context of this predicted limit of stable operation. New nucleation data are presented for 1-pentanol using helium as a background gas. Only data corresponding to stable operation in the cloud chamber is used in the analysis. The effect of background gas on nucleation we have reported previously is confirmed for 1-pentanol, as well as for all the other alcohols that have been investigated in our laboratory.     

On formation of convective roll vortices by internal gravity waves: A theoretical study

Summary The linearized atmospheric equations system is solved analytically in a two layer model. The solutions show that the thermal disturbance located at the interface can induce internal gravity wave, which propagates downstream in the stable layer and brings about flow disturbances in the lower unstable layer. Motion of roll vortices with flow pattern similar to that found in the convective cloud street forms in the lower part of the upper layer and the upper part of the lower layer. If proper content of water vapor exists the cloud lines presenting small angle with the mean wind appear at the top of the lower layer. The effects of the wind speed and the temperature structures of the atmosphere in the lower convective layer and the overlying stable layer on the characteristics of the roll vortices are also discussed in this study.With 7 Figures