正压大气环流中的曲面周期波和孤波

大尺度正压大气环流的波动特征对理解气候变化具有重要的意义,而非线性浅水波方程组是描述大尺度正压大气环流的原始控制方程.本文对线性方程的复变函数解,通过二次适当的移植,求得浅水波方程组的发展方程的扰动位势的实变函数解,该实变函数解析解由基流项和波动项两部分组成.其中基流由波数、波速、β效应、变形半径和时间的任意函数共同决定;波动项与β效应有关.分析表明,在大尺度正压大气环流中扰动位势存在曲面的周期波和孤波的现象,周期波与孤波相互调制而呈现不稳定性;当多个周期孤波同时出现时,则彼此独立传播;扰动位势波动项中的时间任意函数对曲面周期孤波的波幅有调制作用,可控制波的产生、发展和消失.所得结果对研究大气波动现象和气候变化具有一定的理论参考价值.     

波纹基底上含不溶性活性剂液滴的铺展稳定性

针对波纹基底上含不溶性活性剂液滴的铺展历程, 采用润滑理论建立了液滴铺展数理模型, 推导出基态和扰动态下液膜厚度和活性剂浓度的演化方程组, 基于非模态稳定性理论分析了液滴铺展的稳定性及参数的影响规律. 研究表明: 扰动量在液滴中心及铺展前沿处很小, 在液膜最薄处达到最大值且活性剂浓度的负扰动现象比较明显; 扰动波数可增强液滴铺展稳定性, 但随扰动波数增加, 该稳定性逐渐下降甚至转变为不稳定. 增加 Marangoni数将导致液滴铺展不稳定性加剧; 增大基底高度具有增强液滴铺展稳定的作用, Peclet数和基底波数取适中值时有利于液滴铺展的稳定性. 关键词： 活性剂液滴 非平整基底 铺展 非模态稳定性     

含活性剂液膜去润湿演化的稳定性特征

针对含非溶性活性剂的液膜在固体基底上的去润湿过程,基于润滑理论建立了基态和扰动态下液膜厚度和表面活性剂浓度的演化模型,应用非模态理论分析了演化过程的稳定性特征,探讨了分子间力对液膜去润湿过程的影响. 研究表明,微扰动波的引入（k=1）有利于液膜去润湿过程的稳定进行,扰动能量逐渐衰减,然而,该效果随着扰动波数的增加而显著改变,k ≥ 2时,液膜演化的稳定性反而恶化,扰动能量被逐步放大,演化呈现出非稳定特征. 增大初始液膜厚度可以有效改善液膜流动的稳定性. 范德华力放大了液膜表面的微扰动,使得液膜演化的稳定性下降;相反,Born斥力和静电斥力具有增强去润湿稳定性的作用. 关键词： 活性剂 去润湿 分离压 稳定性     

粗糙势中耦合布朗粒子的定向输运性能

研究了粗糙棘轮中耦合粒子的定向输运行为,并进一步讨论了阻尼条件下粗糙棘轮的扰动振幅、扰动波数、粒子间的耦合强度及自由长度等因素对耦合布朗粒子质心平均速度及斯托克斯效率的影响.研究发现,合适的粗糙棘轮扰动振幅和扰动波数能促进耦合布朗粒子的定向输运,同时还能增强其斯托克斯效率.此外,合适的耦合强度和自由长度还能使粗糙棘轮的输运性能达到最强.还发现小扰动振幅条件下,通过改变耦合强度和自由长度能够诱导粗糙棘轮的流反转.通过研究更具实际意义的粗糙棘轮,本文所得结论能为实验上理解分子马达的运动行为提供理论指导,还可为纳米量级分子机器的设计及粒子分离技术的实现提供实验启发.     

一种频域-波数域峰值筛选的无源声呐宽带检测方法

在水声信号处理中,传统的无源声呐宽带目标检测在多目标、强干扰的复杂环境中输出信噪比低,使得检测性能急剧下降。针对此问题,提出一种基于均匀线列阵在频域-波数域上宽带信号能量分布特性进行目标检测的方法。该方法首先将阵列信号转换到频域-波数域,利用不同频率下波数主瓣、旁瓣宽度特征以及空间分布特征,设计针对主瓣的判别与分配方法,实现对同一目标不同频率下波数谱主瓣判别,使用主瓣能量累积、主瓣数目累积的方式来形成方位谱,从而进行目标检测。理论分析和仿真结果表明,所提方法只利用对目标检测有突出贡献的波数主瓣,降低了旁瓣的影响,有效提高了无源宽带水声目标的检测能力。海上试验数据处理结果表明,目标输出信噪比相比子带峰值能量检测算法可提高5.58 dB,较传统能量检测可提高8.73 dB,计算时间相比传统能量检测降低46%,验证了所提方法的有效性与实时性。     

大尺度浅水波方程中相互调制的非线性波

基于一般的浅水波方程, 根据大尺度正压大气的特点, 得到无量纲的控制大尺度大气的动力学非线性方程组. 利用多尺度法, 由无量纲的动力学方程组导出了扰动位势的非线性控制方程. 采用椭圆方程构造该扰动位势控制方程的解, 获得了扰动位势和速度的多周期波与冲击波(爆炸波) 并存的解析解. 扰动位势的解表明经向和纬向具有不同周期和波长的周期波, 且都受纬向孤波的调制; 速度的解表明大尺度大气流动存在气旋和反气旋周期性分布的现象. 关键词： 浅水波方程 大尺度正压大气 解析解 非线性波     

垂直排液过程不稳定性的数值模拟

为分析线框排液实验中液膜表面出现的不稳定现象及其成因,针对含有不溶性活性剂的线框液膜排液过程,模拟液膜底部的不稳定现象,分析Marangoni效应、膨胀黏性和扰动波数因素的影响。结果表明：底部扰动在排液开始比较剧烈,而后快速减弱,到排液后期又逐渐增强。排液开始的扰动是由初始扰动引起,而排液后期的扰动与活性剂分布有关。较弱的Marangoni效应可增强表面扰动,而较强的Marangoni效应则减弱底部扰动,使液膜呈刚性,发生表面逆流现象;较高的膨胀黏性减慢液膜排液进程,降低表面速度,且能抑制Marangoni效应引起的逆流现象;波数较大的扰动使液膜在排液初期的扰动变强,但对排液后期的稳定性不产生影响。     

无碰撞电流片低频电磁模不稳定性：MHD模型

利用含无电阻广义Ohm定律的可压缩磁流体力学(MHD)理论，研究了在具有剪切磁场的无碰撞电流片中低频电磁模不稳定性，假定等离子体压力各向同性，推导出了三维扰动传播波模的色散关系.色散关系的数值求解集中在电流片中间平面(z=0)和半厚度边缘(z=1)上，并分别考虑了二维传播和三维传播，以及不同的离子惯性长度情况.主要结果如下：1)对 于二维扰动传播(k_z=0)的波，在z=0平面上，Alfven波增长率最大，不稳定的波 频率 和波数范围也更宽.离中间平面越远，增长率越小，波数区域越小.同时，随着离子惯性长度 的增大，Alfven波不稳定性的增长率变大.2)对于三维扰动传播(k_z≠0)的波， 哨声是 不稳定的.在电流片中间平面上，哨声有明显的增长率；而在离子惯性区外边，哨声的增长 率还变大.3)在电流片中间(z=0)平面上，低频波主要是电流不稳定性激发的.在离中间 平面较远处，电流、密度和压力的梯度不稳定性变得更重要. 关键词： 无碰撞电流片 磁流体力学 色散关系 不稳定性     

可溶性活性剂驱动的液滴铺展稳定性

对含可溶性活性剂的液滴在预置液膜上的非均匀铺展过程,基于润滑理论建立基态和扰动态下的液滴厚度、表面活性剂浓度和内部浓度的演化模型,应用非模态理论分析演化过程的稳定性,探讨活性剂溶解特性及典型参数对液滴演化特征的影响.研究表明:扰动波的引入有利于增强液滴演化的稳定性,且稳定程度与扰动波的波数呈正相关性;然而随扰动波数的持续增大,液滴演化的稳定性逐渐下降,直至失稳;相对于非溶性活性剂,可溶性活性剂减缓了液滴的铺展程度,增强了演化过程的稳定性;预置液膜厚度、Marangoni数、毛细力数及吸附系数的增大,均有利于液滴稳定演化,其中Marangoni效应和毛细力的影响较大,预置液膜厚度则主要增强液滴厚度演化的稳定性.     

分离压作用下波纹状基底上含活性剂液滴铺展稳定性

针对波纹状基底上含不溶性活性剂液滴的铺展过程,引入受活性剂浓度影响的分离压模型,应用非模态稳定性理论分析液滴铺展稳定性.研究表明:与不计及分离压情形相比,分离压作用下的液滴铺展前沿高度明显下降,液滴铺展速率加快;长波扰动有利于增强液滴的演化稳定性,且随扰动波数增大稳定性增强;然而随短波波数增加,液滴演化稳定性逐渐减弱甚至转变为不稳定;较小波数下(k=3)减小引力强度系数α₁和提高斥力强度系数α₂液滴铺展稳定性增强;而较大波数下(k=30)增大α₁和减小α₂有利于液滴铺展稳定性.     

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     

Resonant excitation of rossby waves in the equatorial waveguide and their nonlinear evolution

Nonlinear interactions between the baroclinic Rossby waves trapped in the equatorial waveguide and the barotropic Rossby waves freely propagating across the equator are studied within the two-layer model of the atmosphere, or the ocean. It is shown that a barotropic wave can resonantly excite a pair of baroclinic waves with amplitudes much greater than its proper amplitude. The envelopes of the baroclinic waves obey Ginzburg-Landau-type equations and exhibit nonlinear saturation and formation of characteristic "domain-wall" and "dark-soliton" defects.     

Exact solutions to one-dimensional acoustic fields with temperature gradient and mean flow

An exact solution for one-dimensional acoustic fields in ducts in the presence of an axial mean temperature gradient and mean flow is presented in this paper. The analysis is valid for mean Mach numbers such that the square of the mean Mach number is much less than one. The one-dimensional wave equation for ducts with axial mean temperature gradient and mean flow is derived. By appropriate transformations, the wave equation is reduced to an analytically solvable hypergeometric differential equation for the case of a linear mean temperature profile. The developed solution is applied to investigate the dependence of sound propagation in a duct on factors such as temperature gradient and mean flow. The results obtained using the analytical solution compare very well with the numerical results. The developed solution is also compared with an existing analytical solution.     

Rogue wave dynamics in barotropic relaxing media

In this work, we deal with a nonlinear wave equation, namely the Vakhnenko equation, which models the propagation of nonlinear wave in the barotropic relaxing media. Based on the homoclinic breather limit method, we seek rogue wave solution to the above equation. The results show that rogue wave or giant wave can exist in such a medium.     

Stability characteristic of hypersonic flow over a blunt wedge under freestream pulse wave

To investigate the stability characteristic of hypersonic flow under the action of a freestream pulse wave, a high-order finite difference method was employed to do direction numerical simulation (DNS) of hypersonic unsteady flow over an 8° half-wedge-angle blunt wedge with freestream slow acoustic wave. The evolution of disturbance wave modes in the boundary layer under a pulse wave and a continuous wave are compared, and the wall temperature effect on the hypersonic boundary layer stability for a pulse wave disturbance is discussed. Results show that, both for a pulse wave and a continuous wave in freestream, the disturbance waves inside the nose boundary layer are mainly a fundamental mode; the Fourier amplitude of pressure disturbance mode in the boundary layer for a pulse wave is far less than that for a continuous wave, and the band frequency of the former is wider than that of the latter. All disturbance modes decay rapidly along the streamwise in the nose boundary layer. In the non-nose boundary layer, the dominant mode is transferred from fundamental mode into second harmonic. The transformation of dominant mode for a pulse wave appears much earlier than that for a continuous wave. Different frequency disturbance modes present different changes along streamline in the boundary layer, and the frequency band narrows around the second harmonic mode along the streamwise. Keen competition and the transformation of energy exist among different modes in the boundary layer. Wall temperature modifies the stability characteristic of the hypersonic boundary layer, which presents little effect on the development of fundamental modes and cooling wall could accelerates the growth of the high frequency mode as well as the dominant mode transformation.     

正压流体中具有β效应与地形效应的强迫Rossby孤立波

正压流体中,从有外源的准地转位涡方程出发采用摄动方法和时空伸长变换推导了具有β效应、地形效应和外源的强迫Rossby孤立波方程,得到孤立Rossby波振幅的演变满足带有地形与外源强迫的非齐次 Boussinesq方程的结论. 通过分析孤立Rossby波振幅的演变,指出β效应、地形效应以及外源都是诱导Rossby孤立波产生的重要因素,说明在地形强迫效应和非线性作用相平衡的假定下,Rossby孤立波振幅的演变满足非齐次Boussinesq方程,给出在切变基本气流下地形和正压流体中R     

Acoustic-Gravity Waves in the Atmosphere with a Piecewise-Linear Temperature Profile

We consider the problem of propagation of acoustic-gravity waves in the atmosphere with a constant temperature gradient in the near-surface layer. The assumption of linear temperature dependence on height allowed us to reduce the wave equation to the hypergeometric form, regardless of the compressibility of the medium. The solution of this equation is represented in terms of degenerate hypergeometric functions. To analyze the obtained solution, we consider a two-layer model of a half-bounded atmosphere with a height-independent background temperature in the upper layer. The results are studied in detail under the approximation of an incompressible medium. For the model specified above, we find analytical expressions for the perturbation fields and obtain a characteristic equation whose solution allows us to calculate wave dispersion characteristics at frequencies close to the Brunt-Väisälä frequency for large horizontal scales as compared to the layer thickness.     

Large-Time Behaviors of Solutions to an Inflow Problem in the Half Space for a One-Dimensional System¶of Compressible Viscous Gas

The “inflow problem” for a one-dimensional compressible barotropic flow on the half-line R ₊= (0,+∞) is investigated. Not only classical waves but also the new wave, which is called the “boundary layer solution”, arise. Large time behaviors of the solutions to be expected have been classified in terms of the boundary values by [A. Matsumura, Inflow and outflow problems in the half space for a one-dimensional isentropic model system of compressible viscous gas, to appear in Proceedings of IMS Conference on Differential Equations from Mechanics, Hong Kong, 1999]. In this paper we give the rigorous proofs of the stability theorems on both the boundary layer solution and a superposition of the boundary layer solution and the rarefaction wave. Received: 25 April 2000 / Accepted: 20 April 2001