有界大洋对纬向风强迫的响应及共振

为揭示北太平洋主、次要气候模态即太平洋年代际振荡(PDO)和北太平洋流涡振荡(NPGO)的形成机理及其振荡周期与大洋水平尺度之间的联系,采用中纬β通道中的约化重力准平衡线性大洋模型,解析求解了纬向风强迫下的大洋流场响应,讨论了其中的共振问题.1)有界大洋的响应形态分别类似于冬季PDO和NPGO的流场模.2)响应形态分别表现为在大洋西海岸以东,前者有一个椭圆状流涡,后者有南北两个旋转方向相反的流涡并构成流涡偶;在整个大洋,前者有一个洋盆尺度环流,后者在大洋南北分别有两个旋转方向相反的洋盆尺度环流;在中纬度西风急流异常位置偏北和偏南,则能分别强迫出以上的两种情况.3)大洋流场对纬向风场强迫的响应频率(周期)与纬向风强迫频率(周期)相同,但大洋响应要滞后于纬向风的强迫;而响应流场即流函数的强度则与纬向风强迫的大小成正比.当纬向风强迫频率(周期)与该大洋固有频率(周期)相同时,二者会有共振发生,此时大洋响应最为强烈;而二者频率(周期)相差较远时,响应则不大.摩擦越小共振就越强,共振的个数也越多.有界大洋东西向的长度对其固有频率(周期)即共振频率(周期)有明显影响,并起着决定作用;当该长度减小时,相邻两个共振周期的间隔会增大.海洋大气间的两两非线性相互作用,使得随机风场的振荡包含了从极低频到高频的各种成分;通过该共振,可从中挑选出与大洋固有频率相同或相近的共振频率,在该频率上流场对风场的响应最为强烈,从而也就锁定了PDO和NPGO的周期.最终结论为:非线性相互作用、风场对流场的强迫、共振是造成PDO和NPGO的三个关键因子;该解析解的性质为时变的共振Rossby波.     

The chaotic layer of a nonlinear resonance under low-frequency perturbation

Conditions whereby the chaotic layer of a nonlinear resonance is described in terms of low-frequency separatrix mapping are discussed. In this case, the accurate estimation of the size of the layer requires the arrangement of resonances at its edge to be known. The resonance picture is constructed using the separatrix mapping invariants of the first three orders. The variation of the layer size with the mapping amplitude is traced with the criterion for resonance overlapping. Results obtained by direct calculation and by invariants analysis are compared. Issues that remain to be solved are noted.     

Solar forcing of the stream flow of a continental scale South American river

Solar forcing on climate has been reported in several studies although the evidence so far remains inconclusive. Here, we analyze the stream flow of one of the largest rivers in the world, the Paraná in southeastern South America. For the last century, we find a strong correlation with the sunspot number, in multidecadal time scales, and with larger solar activity corresponding to larger stream flow. The correlation coefficient is r=0.78, significant to a 99% level. In shorter time scales we find a strong correlation with El Ni?o. These results are a step toward flood prediction, which might have great social and economic impacts.     

Dynamics of Turing patterns under spatiotemporal forcing

We study, both theoretically and experimentally, the dynamical response of Turing patterns to a spatiotemporal forcing in the form of a traveling-wave modulation of a control parameter. We show that from strictly spatial resonance, it is possible to induce new, generic dynamical behaviors, including temporally modulated traveling waves and localized traveling solitonlike solutions. The latter make contact with the soliton solutions of Coullet [Phys. Rev. Lett. 56, 724 (1986)]] and generalize them. The stability diagram for the different propagating modes in the Lengyel-Epstein model is determined numerically. Direct observations of the predicted solutions in experiments carried out with light modulations in the photosensitive chlorine dioxide-iodine-malonic acid reaction are also reported.     

Spatially synchronous extinction of species under external forcing

More than 99% of the species that ever existed on the surface of the Earth are now extinct and their extinction on a global scale has been a puzzle. One may think that a species under an external threat may survive in some isolated locations leading to the revival of the species. Using a general model we show that, under a common external forcing, the species with a quadratic saturation term first undergoes spatial synchronization and then extinction. The effect can be observed even when the external forcing acts only on some locations provided the dynamics contains a synchronizing term. Absence of the quadratic saturation term can help the species to avoid extinction.     

Chaos in a driven pendulum under asymmetric forcing

An analysis of the stochastic layer in a pendulum driven by an asymmetric high-frequency perturbation of fairly general form is continued. Analytical expressions are found for the amplitudes of secondary harmonics, and their contributions to the amplitude of the separatrix map responsible for onset of dynamical chaos are evaluated. Additional evidence is presented of the previously established fact that the secondary harmonics completely determine the stochasticl-ayer width when the primary frequencies lie in certain intervals. The mechanism of the onset of chaos in the vicinity of zeros of Melnikov integrals is shown to be substantially different as compared to the previously analyzed case of symmetric perturbation.     

Dynamics of Hamiltonian systems under piecewise linear forcing

A two-parameter family of smooth Hamiltonian systems perturbed by a piecewise linear force is analyzed. The systems are represented both as maps and as dynamical systems. Currently available analytical and numerical results concerning the onset of chaos and global diffusion in such systems are reviewed. Dynamical behavior that has no analogs in the class of systems with analytic Hamiltonians is described. A comparison with the well-studied dynamics of a driven pendulum is presented, and essential differences in dynamics between smooth and analytic systems are highlighted.     

Evolution of wave turbulence under "gusty" forcing

We consider nonlinear evolution of a random wave field under gusty forcing, fluctuating around a constant mean. Here the classical wave turbulence theory that assumes a proximity to stationarity is not applicable. We show by direct numerical simulation that the self-similarity of wave field evolution survives under fluctuating forcing. The wave field statistical characteristics averaged over fluctuations of forcing evolve as if there were a certain constant "effective wind." The results justify the use of the kinetic equations with forcing averaged over gusts as a good first approximation.     

Bifurcations of a lattice gas flow under external forcing

We study the behavior of a Frisch-Hasslacher-Pomeau lattice gas automaton under the effect of a spatially periodic forcing. It is shown that the lattice gas dynamics reproduces the steady-state features of the bifurcation pattern predicted by a properly truncated model of the Navier-Stokes equations. In addition, we show that the dynamical evolution of the instabilities driving the bifurcation can be modeled by supplementing the truncated Navier-Stokes equation with a random force chosen on the basis of the automaton noise.     

Nonlinear fast growth of water waves under wind forcing

In the wind-driven wave regime, the Miles mechanism gives an estimate of the growth rate of the waves under the effect of wind. We consider the case where this growth rate, normalised with respect to the frequency of the carrier wave, is of the order of the wave steepness. Using the method of multiple scales, we calculate the terms which appear in the nonlinear Schrödinger (NLS) equation in this regime of fast-growing waves. We define a coordinate transformation which maps the forced NLS equation into the standard NLS with constant coefficients, that has a number of known analytical soliton solutions. Among these solutions, the Peregrine and the Akhmediev solitons show an enhancement of both their lifetime and maximum amplitude which is in qualitative agreement with the results of tank experiments and numerical simulations of dispersive focusing under the action of wind.     

Dynamics of a deformable self-propelled particle under external forcing

We investigate dynamics of a deformable self-propelled particle under external fields in two dimensions based on the time-evolution equations for the center of mass and a tensor variable characterizing deformations. We consider two kinds of external force. One is a gravitational force which enters additively in the time-evolution equation for the center of mass. The other is an electric force supposing that a dipole moment is induced in the particle. This force is added to the equation for the deformation tensor. It is shown that a rich variety of dynamics appears by changing the strength of the forces and the migration velocity of a self-propelled particle. A theoretical analysis is carried out to clarify the dynamics and the bifurcations.     

Phenomenology of two-dimensional stably stratified turbulence under large-scale forcing

In this paper, we characterise the scaling of energy spectra, and the interscale transfer of energy and enstrophy, for strongly, moderately and weakly stably stratified two-dimensional (2D) turbulence, restricted in a vertical plane, under large-scale random forcing. In the strongly stratified case, a large-scale vertically sheared horizontal flow (VSHF) coexists with small scale turbulence. The VSHF consists of internal gravity waves and the turbulent flow has a kinetic energy (KE) spectrum that follows an approximate k^?3 scaling with zero KE flux and a robust positive enstrophy flux. The spectrum of the turbulent potential energy (PE) also approximately follows a k^?3 power-law and its flux is directed to small scales. For moderate stratification, there is no VSHF and the KE of the turbulent flow exhibits Bolgiano–Obukhov scaling that transitions from a shallow k^?11/5 form at large scales, to a steeper approximate k^?3 scaling at small scales. The entire range of scales shows a strong forward enstrophy flux, and interestingly, large (small) scales show an inverse (forward) KE flux. The PE flux in this regime is directed to small scales, and the PE spectrum is characterised by an approximate k^?1.64 scaling. Finally, for weak stratification, KE is transferred upscale and its spectrum closely follows a k^?2.5 scaling, while PE exhibits a forward transfer and its spectrum shows an approximate k^?1.6 power-law. For all stratification strengths, the total energy always flows from large to small scales and almost all the spectral indicies are well explained by accounting for the scale-dependent nature of the corresponding flux.     

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).     

Entrainment of a spatially extended nonlinear structure under selective forcing

The response of a nonlinear state to a variable forcing periodic in space is studied in an extended dynamical system consisting of a liquid crystal layer driven to convection. Both the statics and the dynamics of the entrainment and the locking effects are analyzed. The dynamics of the evolution are controlled by topological singularities that allow a diffusion of the phase. The mechanisms involved are related to the role of the defects in systems undergoing spontaneous symmetry breakings.