漫谈非线性共振

 一提到共振,人们就会想到一个故事,一支军队步伐整齐地过一座木桥,由于步伐频率接近桥的固有频率,从而引起共振,导致桥塌掉,造成惨祸。对于一个非线性系统,不但在外力驱动频率接近系统的固有频率时会发生共振(称为主共振),有时强迫频率虽然远离系统的固有频率,但在两频率之间在一定比值时,也会发生共振(称为次共振)。     

外强迫作用下正压大气非线性特征数值模拟

在两种边界条件下用正压大气非线性位势涡度方程模拟了强迫、耗散和非线性共同作用下大气运动的若干特征.在南北两端为齐次边界条件时，单纯的热力强迫下只出现了波状定常解；在只有经向加热和波状地形共同强迫下出现了在两种基本流型之间振荡的准周期解，十分类似于旋转地球上大气运动的纬向和经向流型之间的准周期循环，前者对应于强的西风环流，后者对应于弱西风流型.在周期边界条件下，弱的下垫面加热导致定常解，较强的加热强迫可以得到周期解.尽管下垫面的波状地形也能强迫一个类似的准周期振荡，但弱西风流型是对称的，不像大气中的弱西风流型.因此，在周期边界条件下用低阶截谱模式求出的解析或数值解，不一定适合描述中高纬度大气的非线性动力特征. 关键词： 正压大气 热力强迫 地形起伏 周期解 准周期振荡     

具有固有频率涨落的记忆阻尼线性系统的随机共振

研究了在内噪声、外噪声(固有频率涨落噪声)及周期激励信号共同作用下具有指数型记忆阻尼的广义Langevin方程的共振行为.首先将其转化为等价的三维马尔可夫线性系统,再利用Shapiro-Loginov公式和Laplace变换导出系统响应一阶矩和稳态响应振幅的解析表达式.研究发现,当系统参数满足Routh-Hurwitz稳定条件时,稳态响应振幅随周期激励信号频率、记忆阻尼及外噪声参数的变化存在"真正"随机共振、传统随机共振和广义随机共振,且随机共振随着系统记忆时间的增加而减弱.数值模拟计算结果表明系统响应功率谱与理论结果相符.     

噪声交叉关联强度的时间周期调制对线性过阻尼系统的随机共振的影响

针对由加性、乘性噪声和周期信号共同作用的线性过阻尼系统, 在噪声交叉关联强度受到时间周期调制的情况下,利用随机平均法推导了系统响应的信噪比的解析表达式. 研究发现这类系统比噪声间互不相关或噪声交叉关联强度为常数的线性系统具有更丰富的动力学特性, 系统响应的信噪比随交叉关联调制频率的变化出现周期振荡型随机共振, 噪声的交叉关联参数导致随机共振现象的多样化.噪声交叉关联强度的时间周期调制的引入有利于提高对微弱周期信号检测的灵敏度和实现对周期信号的频率估计. 关键词： 随机共振 周期振荡型共振 噪声交叉关联强度 信噪比     

微孔共振腔吸声机理的直接数值模拟研究

声衬是由大量的微孔共振腔按一定规则排列组成,由于微孔共振腔的小尺寸和流动的复杂性,采用实验和理论方法难以观测其内部及附近的复杂流动情况.本文采用计算气动声学方法对不同频率和声强声波入射下的二维微孔共振腔的吸声过程进行了直接数值模拟.结果表明: (1)腔口处粘性耗散和涡脱落现象是其吸声的书要形式;(2)在不同的频率和声强入射下,微孔共振腔的吸声过程表现出三种不同的模式,分别为无涡脱落、规则涡脱落和不规则涡脱落;(3)微孔共振腔的吸声性能在入射波为共振腔固有频率时最好.     

脉冲激励下超音速混合层涡结构的演化机理

采用大涡模拟方法对脉冲激励作用下的超音速混合层流场进行数值模拟,所得结果清晰展示了流场中涡结构的独特生长机理.基于涡核位置提取方法,对超音速混合层流场中涡结构的空间尺寸和瞬时对流速度等动态特性进行了定量计算.通过分析流场中涡结构的动态特性在不同频率脉冲激励下的变化,揭示出受脉冲激励超音速混合层流场中涡结构的演化机理:涡结构的生长不再是依靠相邻涡-涡结构之间的配对与融合,而是通过涡核外围的一串小涡旋结构被依次吸进涡核来实现,且受激励流场中各个涡结构的空间尺寸变化较小;流场中的涡结构数量与脉冲频率成正比例关系,而涡结构的空间尺寸与脉冲频率成反比例关系;涡结构的平均对流速度随脉冲频率的增大而减小.针对受脉冲激励超音速混合层,给出了能够表征涡结构特性与脉冲激励参数之间关系的方程式,即受激励流场中涡结构的平均对流速度与脉冲周期的乘积近似等于流场中涡结构的空间尺寸(涡结构平均直径).     

具有频率涨落的简谐力激励下线性谐振子的随机共振

针对线性谐振子受到具有频率涨落的简谐力激励的情况, 计算出系统响应的一阶矩解析表达式.研究发现系统的输出响应以固有频率振动, 响应振幅随简谐激励力频率的变化出现"真实"随机共振,随固有频率的变化出现抑制和 共振两种现象.     

采用FFT-POD的非定常流动控制频谱和能谱特性研究

对数值模拟的不同频率下非定常激励的扩压通道流场采用POD方法分析,对取得的各级模态系数进行频谱分析,对不同变量的能谱进行对比分析,研究非定常激励对流场的控制机理。分析表明:非定常信号能够强制与流场发生共振作用,低阶模态共振作用较强,随之会出现衰减现象;同时流场的"固有频率"不会被改变,只会暂时抑制或加强,流场中的"保护"机制同样如此;动能谱显示非定常激励使流场中代表大涡的2、3阶动能份额增大,同时也增大了流场的第一阶模态拟涡能份额,从而使流场小尺度脉动能量和平直流动能减少。     

中国东部2012年夏季降水及年代际转型的可能信号分析

针对2012年夏季中国东部降水"南旱北涝"的异常特征, 对比分析了近50年不同年代中国东部降水的分布型及海洋和环流等影响因素, 并讨论了2012年中国东部夏季降水异常作为中国东部降水年代际转型信号的可能性. 研究结果表明: 1961—1978年期间, 北太平洋年代际涛动(PDO)处于冷位相, 东亚夏季风偏强, 西太平洋副热带高压(副高)偏弱, 北方地区冷空气活动偏弱, 从而有利于南方水汽北上, 造成中国北方地区夏季降水异常偏多; 1979—1992年间则呈相反的特征, 造成1970年代末期中国东部夏季降水发生了一次年代际尺度的调整. 2010年代后期以来, PDO由暖位相向冷位向转变, 2012年北太平洋海温异常偏暖, 西太平洋海温由异常偏暖状态转变为正常略偏冷状态, 东亚夏季风由弱变强, 副高由强变弱, 北方冷系统活动减弱, 这些特征均与1961—1978年时段的情况类似, 支持2012年作为中国东部夏季降水发生年代际调整的前期信号的可能性. 近10年PDO, 东亚夏季风(EASM), 副高(WPSH)和贝湖高压(BH)四种指数夏季平均值的演变则进一步说明 了2012年的这种异常特征不仅是年际尺度的振荡, 更可能是前期演化基础上的一种量变到质变的调整. 关键词： 年代际 降水 北太平洋年代际涛动 东亚夏季风     

信号调制下色噪声间关联的周期调制对单模激光随机共振的影响

在色噪声间的关联程度受时间周期调制的激光系统中,研究噪声受信号调制情况下的随机共振.用线性化近似的方法计算了光强关联函数及信噪比.具体讨论信噪比随噪声强度、噪声自关联时间、信号频率以及时间周期调制频率的变化关系.发现一种新的随机共振：信噪比随时间周期调制频率的变化出现周期振荡型随机共振;发现广义随机共振：信噪比随抽运噪声自关联时间的变化、随信号频率的变化出现随机共振;同时也存在典型的信噪比随噪声强度的变化而出现的随机共振.而信噪比随量子噪声自关联时间的变化表现为抑制. 关键词： 信号调制 时间周期调制 噪声间关联程度 周期振荡型随机共振     

A discontinuous/continuous low order finite element shallow water model on the sphere

We study the applicability of a new finite element in atmosphere and ocean modeling. The finite element under investigation combines a second order continuous representation for the scalar field with a first order discontinuous representation for the velocity field and is therefore different from continuous and discontinuous Galerkin finite element approaches. The specific choice of low order approximation spaces is attractive because it satisfies the Ladyzhenskaya–Babuska–Brezzi condition and is, at the same time, able to represent the crucially important geostrophic balance.The finite element is used to solve the viscous and inviscid shallow water equations on a rotating sphere. We introduce the spherical geometry via a stereographic projection. The projection leads to a manageable number of additional terms, the associated scaling factors can be exactly represented by second order polynomials.We perform numerical experiments considering steady and unsteady zonal flow, flow over topography, and an unstable zonal jet stream. For ocean applications, the wind driven Stommel gyre is simulated. The experiments are performed on icosahedral geodesic grids and analyzed with respect to convergence rates, conservation properties, and energy and enstrophy spectra. The results match quite well with results published in the literature and encourage further investigation of this type of element for three-dimensional atmosphere/ocean modeling.     

黑潮及其延伸区海表温度变化特征与大气环流相关性的初步分析

为了研究黑潮海表温度的时间变化特征, 以预测黑潮海表温度变化趋势, 本文利用哈德莱中心1941-2009年海表温度 资料定义了一个黑潮温度指数KI, 来表征吐噶喇海峡以东黑潮及其延伸区的海温变化. 由小波分析得到, KI具有准3、 7年的年际振荡特征和准20年的年代际变化特征, 此外KI还具有明显的季节锁相特征. KI与太平洋年代际振荡(PDO)及厄尔尼诺-南方涛动(ENSO)有很好的滞后相关性. 通过美国国家环境预报中心/大气研究中心再分析资料合成分析发现KI为正异常时, 赤道东太平洋海温异常变暖(即厄尔尼诺发生), 哈德莱环流加强, 使得西风动量的输 送增强, 造成阿留申低压加深(PDO为暖相), 进而冷却黑潮延伸区的海表温度并使黑潮延伸区向东延伸, 这一"ENSO-PDO-黑潮海温变化"的过程具有滞后性, 从而使得ENSO指数、PDO指数可以作为黑潮温度变化的前兆因子, 对于预测黑潮海温变化及周边气候均具有一定的意义.     

Radiative forcing of aerosols and gases over tropical ocean and its impact on the global atmospheric environment: GCM investigations during INDOEX campaigns

Radiative forcings due to aerosols and the pollutant gases accumulated as haze which are transported from nearby continent to the tropical ocean are essentially important elements of the world climate system. Vertical transport of aerosols and gaseous species takes place within the deep convective cloud clusters of the inter-tropical convergence zone and subsequently these are distributed by the upper atmospheric zonal wind flow, thereby have impact on the global atmospheric environment. The comprehensive global atmospheric models have shown capability of simulating the climate of the atmosphere with proper forcing. We have deduced the radiative forcing, optical depth and the global energy balance components by a global atmospheric model. The results are validated well with INDOEX and other available observational findings.     

Effects of typhoon "KAI-TAK" on deep ocean ambient noise in the South China Sea

By investigating the effects on deep ocean ambient noise of typhoon "KAI-TAK" which passed the north area of the South China Sea,it is shown that the wind speed,the rainfall intensity and the long wave swell caused by typhoon affect the ocean ambient noise significantly.The correlation between the ocean ambient noise and the wind speed during the typhoon is much better than that in the non-typhoon period in the same Beaufort scale.Analysis of the correlation between the 415 h ocean ambient noise measured data and wind speed shows that,when the frequency is greater than 300 Hz,the correlation coefficient between the ocean ambient noise and the wind speed is greater than 0.5,achieving a moderate correlation;when the frequency is greater than 630 Hz,the correlation coefficient is between 0.8 and 0.9,achieving a high degree of correlation.The correlation between the ocean ambient noise and the wind speed is better than that between the ocean ambient noise and the significant wave height when the frequency is greater than 300 Hz.The correlation between the ocean ambient noise and the wind speed in infrasonic band from 10 Hz to 20 Hz is poor in the South China Sea,because the shipping is busy in this sea area and the ocean ambient noise is contaminated by the ship noise even during the typhoon.     

热带海洋与中低纬大气相互作用的信息传输特征分析

基于传递熵概念和方法定义气象场的信息源特征度、信息汇特征度和信息传输平衡特征度.使用海表温度和高度场资料计算海气相互作用过程中的信息传递.侧重分析赤道中东太平洋(20?S-20?N,170?E-100?W)与热带地区、北半球和南半球中高纬度地区大气之间的信息传递,给出信息传递的区域和全球分布特征;并提取海表温度指数和高度场指数分析赤道中东太平洋与大气信息传递特征的季节变化和年代际变化.研究结果表明,海洋信息源主要分布在热带地区,大气信息汇主要分布在中纬度地区,从热带地区到中纬度地区,海洋对大气的强迫作用在减弱,而大气对海洋的强迫作用在增强;不同区域不同层次的高度场对赤道中东太平洋海表温度有着不同的响应,热带中东太平洋上空高度场最大延迟为4个月.欧亚大陆中部上空和北美大陆上空高度场均随时间延迟呈现波动性变化:欧亚大陆中部上空高度场随时间延迟呈现增强的趋势,而北美大陆上空高度场随时间延迟呈现减弱的趋势.海表温度指数对热带中东太平洋上空850 hPa和欧亚大陆中部上空500 hPa高度场指数的传递熵以2000 s最弱,而海表温度指数对北美大陆上空700 hPa高度场指数的传递熵以2000 s最强.表明不同年代际背景下不同区域大气对赤道中东太平洋海表温度异常的响应是不同的.然而不同季节的响应却十分相似:冬季最强,秋季次之,春季再次,夏季最弱.     

台风“启德”对南海深海海洋环境噪声特性的影响研究

研究台风“启德”经过南海北部对南海深海海洋环境噪声的影响,表明台风导致的风速增减、降雨强弱以及形成的长波涌浪均会影响海洋环境噪声级的大小变化,海洋环境噪声显著受到台风的影响。相同风级下,台风期间海洋环境噪声级与风速的相关性明显好于非台风期间。分析测量的415 h海洋环境噪声数据与风速、波高的相关性,频率大于300 Hz时,海洋环境噪声级与风速的互相关系数大于0.5,达到中度相关;频率大于630 Hz时,互相关系数介于0.8和0.9之间,达到高度相关;频率大于300 Hz时,海洋环境噪声级与风速的相关性好于海洋环境噪声级与波高的相关性。南海海洋环境噪声10~20 Hz的次声频与风速的相关性差,是因为南海航运繁忙,该频段的海洋环境噪声会受到航船噪声的影响,即使台风期间也不例外。      

Low-frequency variability of the atmospheric circulation: a comparison of statistical properties in both hemispheres and extreme seasons

Summary A statistical investigation is presented of the main variables characterizing the tropospheric general circulation in both hemispheres and extreme seasons, Winter and Summer. This gives us the opportunity of comparing four distinct realizations of the planetary circulation, as a function of different orographic and thermal forcing conditions. Our approach is made possible by the availability of 6 years of global daily analyses prepared by ECMWF (European Centre for Medium-range Weather Forecast). The variables taken into account are the zonal geostrophic wind, the zonal thermal wind and various large-scale wave components, averaged over the tropospheric depth between 1000 and 200 hPa. The mean properties of the analysed quantities in each hemisphere and season are compared and their principal characteristics are discussed. The probability density estimates for the same variables, filtered in order to eliminate the seasonal cycle and the high-frequency ?noise?, are then presented. The distributions are examined, in particular, with respect of their unimodal or multimodal nature and with reference to the recent discussions in the literature on the bimodality which has been found for some indicators of planetary wave activity in the Northern Hemisphere Winter. Our results indicate the presence of nonunimodally distributed wave and zonal flow components in both hemispheres and extreme seasons. The most frequent occurrence of nonunimodal behaviour is found for those wave components which exhibit an almost vanishing zonal phase speed and a larger ?response? to orographic forcing. Paper presented at the IV Congresso del Gruppo Nazionale per la Fisica dell'Atmosfera e dell'Oceano, June 22–24, 1987, Rome.     

Dynamic behavior of a freely-propagating turbulent premixed flame under global stretch-rate oscillations

Dynamic features of a freely propagating turbulent premixed flame under global stretch rate oscillations were investigated by utilizing a jet-type low-swirl burner equipped with a high-speed valve on the swirl jet line. The bulk flow velocity, equivalence ratio and the nominal mean swirl number were 5 m/s, 0.80 and 1.23, respectively. Seven velocity forcing amplitudes, from 0.09 to 0.55, were examined with a single forcing frequency of 50 Hz. Three kinds of optical measurements, OH-PLIF, OH^* chemiluminescence and PIV, were conducted. All the data were measured or post-processed in a phase-locked manner to obtain phase-resolved information. The global transverse stretch rate showed in-phase oscillations centering around 60 (1/s). The oscillation amplitude of the stretch rate grew with the increment of the forcing amplitude. The turbulent flame structure in the core flow region varied largely in axial direction in response to the flowfield oscillations. The flame brush thickness and the flame surface area oscillated with a phase shift to the stretch rate oscillations. These two properties showed a maximum and minimum values in the increasing and decreasing stretch periods, respectively, for all the forcing amplitudes. Despite large variations in flame brush thickness at different phase angles, the normalized profiles collapse onto a consistent curve. This suggests that the self-similarity sustains in this dynamic flame. The global OH^* fluctuation response (i.e. response of global heat-release rate fluctuation) showed a linear dependency to the forcing velocity oscillation amplitudes. The flame surface area fluctuation response showed a linear tendency as well with a slope similar to that of the global OH^* fluctuation. This indicated that the flame surface area variations play a critical role in the global flame response.     

Upwelling induced by periodic wind stress

Summary In this paper we exhibit analytical solutions for the upwelling and the coastal currents induced by periodic wind stress. We present solutions for an infinite deep ocean and for a shallow ocean. There is upwelling only when the period of the forcing is longer than the inertial period,i.e. f>ω. When the period of the forcing is shorter than the inertial period,i.e. f<ω, there is not upwelling, but propagating waves are excited. Paper presented at the IV Congresso del Gruppo Nazionale per la Fisica dell'Atmosfera e dell'Oceano, June 22–24, 1987, Rome