Shallow-water waves on a rotating ocean due to oscillatory surface stresses

The initial-value problem of shallow-water waves due to an oscillatory surface stress distribution on a homogeneous rotating ocean is solved by the method of integral transforms. For the wave integral, an asymptotic analysis is given which is uniform across the line produced by the coalescing of the pole and the stationary point of the wave spectrum; the result, unlike previous findings, is non-singular when the circular frequency of oscillation equals the Coriolis parameter. Some limiting cases of interest are deduced and the asymptotic envelope of the progressive waves at the surface is illustrated graphically.     

正弦振荡来流下柔性立管涡激振动发展过程

在风浪流的作用下,海洋浮式结构物将带动悬链线立管在水中作周期性往复运动,从而在立管运动方向上产生相对振荡来流,这种振荡来流将激励立管悬垂段发生“间歇性” 的涡激振动. 在海洋工程水池中对一个4m 长的立管微段进行模型试验研究,以探索相对振荡来流作用下立管涡激振动产生的机理及其发展的物理过程. 试验通过振荡装置带动模型作正弦运动来模拟不同最大约化速度U_Rmax、不同KC（Keulegan-Carpenternumber）的相对振荡来流,利用光纤应变片测量立管涡激振动响应. 结合模态分析方法处理试验数据得到位移响应时历,继而提出相对振荡来流下柔性立管涡激振动发展的3 个阶段:建立阶段、锁定阶段以及衰减阶段. 并进一步总结了最大约化速度U_Rmax,KC 对涡激振动发展过程的影响规律. 最终获得不同最大约化速度U_Rmax下,涡激振动各发展阶段随KC 所占时间分布比例图.      

On the need of nonlinear control for efficient model-based wake stabilization

The mitigation of oscillatory vortex shedding behind a cylinder is chosen as a well-investigated benchmark problem to compare model-based feedback flow control approaches. The flow is sensed by a single velocity signal in the wake and is manipulated via a single volume force actuator. A low-dimensional proper orthogonal decomposition Galerkin model is adopted as a control-oriented fluid flow representation. An extended Kalman filter is used as an effective means for online dynamic state estimation. Investigated strategies of linear and nonlinear controller design include pole placement, linear parameter-varying, input–output linearization, Lyapunov-based backstepping, and nonlinear model predictive control. These strategies are applicable to a large class of flows with oscillatory dynamics and to experimental conditions, where variants have already been used. Controllers are evaluated and compared based on their application to the full plant, that is, to the direct numerical simulation of the wake, emulating an experiment with a single hot-wire sensor. Overall, nonlinear closed-loop control is shown to be distinctly superior to linear approaches. As is often the case, physics dictates a similarity of successful control commands, irrespective of the design approach, and differentiates these controllers, as a group, from less successful approaches.     

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利用有限元软件,通过对撑竿跳高过程的大变形动力学数值模拟,得到了不同材料 撑竿的变形过程、跳高成绩,以及能量的转化效率指标. 通过截面尺寸设计,预测了不同材 料撑竿所能达到的最大高度. 最后以布勃卡的体能参数为标准,为其设计能越过最大高度的 等截面和变截面碳纤维复合材料撑竿.     

半浮区热毛细对流的不稳定性与转捩

近二十年来,微重力流体开展了半浮区液桥热毛细对流的不稳定性与转捩的研究．文中给出了热毛细振荡对流发生的临界参数,分析了液桥几何位形（尺度比,体积比）、物理参数及传热参数对临界Ｍａｘａｎｇｏｎｉ的影响．报导了有关的地面模拟实验,微重力实验以及本问题的线性稳定性分析、能量分析和数值模拟结果,并介绍了定常轴对称热毛细对流通过非定常振荡热毛细对流到湍流的转捩过程和三种热毛细振荡对流的产生机理．     

Pattern analysis of viscous oscillation in a shear flow induced by an exothermic reaction

An investigation is made of oscillatory phenomenon induced by an exothermic reaction. This oscillatory phenomenon occurs in a very thin mixing layer between two miscible and reacting fluids. A qualitative model based on the interaction among reaction, molecular momentum transfer, molecular heat transfer, molecular mass transfer and forced convective transfer was proposed by Kuroda and Ogawa [1994. Nonlinear waves in a shear flow with a diffusive exothermic reaction and its qualitative reasoning. Chem. Eng. Sci. 49(16), 2699-2708]. It is experimentally shown in the present study that the oscillatory patterns change in the flow direction. In the upstream area where oscillatory patterns are nearly straight stripes, effects of viscosity on those stripes are investigated. In the downstream area where stripes are wavy and disordered, fractal analysis is introduced to investigate the relationship between the transition of oscillatory flow patterns and process factors, i.e. the viscosity ratio, the entire viscosity, flow rate and the flow rate ratio. Fractal analysis is also applied to temperature oscillation, and it is confirmed that the characteristic patterns of oscillation become obscure as the entire viscosity increases. The entire viscosity is an important factor for controlling both oscillatory patterns of flow and temperature in this reactive flow system.     

镓铟锡液滴撞击泡沫金属表面的运动学特性研究

常温下为液态的镓铟锡合金以其优异的导热性能在具有特殊要求的传热领域有着重要的应用价值,与传统流动介质相比较大的表面张力使得其产生的流动现象必有所区别.本文研究镓铟锡所形成的液滴撞击泡沫金属表面后所产生的铺展、回缩及回弹现象.采用高速相机拍摄液滴投影轮廓随液滴运动的变化过程,并通过图像处理获得不同撞击速度、底板表面孔径下的液滴铺展系数、中心位置轮廓高度以及液滴回弹后在空中的振动特性.研究结果表明:具有较高表面张力的镓铟锡液滴的铺展系数随无量纲时间的变化在铺展初始阶段仍满足常规流体的1/2次幂关系,只在铺展后期与底板的无量纲孔径有关系;液滴的最大铺展系数在较小无量纲孔径底板大于在光滑镍板,且随底板无量纲孔径增大而逐渐减小;在回弹过程,由于底板孔隙结构的存在使得液滴回弹后在空中的振动呈现3种形态:规则的横向和纵向振动、带旋转的横向和纵向振动以及旋转振动;最后,通过对振动频率的拟合和分析,进一步拓展了传统振动频率理论公式在非规则振动过程预测中的应用.      

Heat transfer performance for batch oscillatory flow mixing

Experimental heat transfer data is presented for two batch operations of oscillatory flow mixing. In one case fluid is oscillated within a baffled tube and in the second case baffles are oscillated within a process fluid. For both situations the heat transfer coefficient depends on the intensity of oscillation, and the energy performance of each configuration corresponds to that of an equivalent net turbulent flow in a pipe or a batch stirred vessel. The results indicate that oscillatory flow batch mixing is as energy efficient as other conventional mixing configurations and the heat transfer performance indicates that each oscillatory flow mixing configuration could be satisfactorily used as a batch reactor system.     

Oscillating Convection of Nanofluid in Porous Medium

In this paper, oscillatory convection in a horizontal layer of nanofluid in porous medium is studied. For porous medium, Darcy model is applied. A linear stability theory and normal mode analysis method is used to find the solution confined between two free boundaries. The onset criterion for oscillatory convection is derived analytically and graphically. Regimes of oscillatory and non-oscillatory convection for various parameters are derived. The effects of Lewis number, concentration Rayleigh number, Prandtl?CDarcy number (Vadasz Number) and modified diffusivity ratio on the oscillatory convection are investigated graphically. We examine the validity of ??PES?? and concluded that ??PES?? is not valid for the problem.     

Dynamic analysis of the earth pole oscillation process

In the framework of classical mechanics, we perform an amplitude-frequency analysis of a small-parameter model of the Earth pole diurnal oscillations under the action of luni-solar gravitational-tidal torques. The Euler–Liouville dynamic equations with irregular perturbations taken into account are used to obtain the structural properties of diurnal oscillations of the Earth pole coordinates. The results of the Earth pole motion simulation are compared with the high-precision data of VLBI observations on a short time interval.     

The Impact of Footprints of Large-Scale Outer Structures on the Near-Wall Layer in the Presence of Drag-Reducing Spanwise Wall Motion

This study is motivated by the observation that the drag-reduction effectiveness achieved by the imposition of oscillatory spanwise wall motion declines with Reynolds number. The question thus posed is whether the decline is linked to the increasingly strong influence of large-scale outer structures in the log layer on the near-wall turbulence, in general, and the streak strength in the viscosity-affected layer, in particular – a process referred to as modulation. This question is addressed via an extensive statistical analysis of DNS data for a channel flow at a friction Reynolds number 1020, subjected to oscillatory spanwise wall motion at a nominal wall-scaled period of 100. The analysis rests on a separation of turbulent scales by means of the Empirical Mode Decomposition. This method is used to derive conditional statistics of small-scale motions and skin friction subject to prescribed intensity of large-scale motions – referred to as footprinting. It is shown that the large-scale fluctuations are responsible, directly on their own, for roughly 30% to the skin friction. Positive large-scale fluctuations are also shown to be the cause of a major amplification of small-scale streaks, relative to weak attenuation by negative fluctuations. This highly asymmetric process is likely to be indirectly influential on the drag-reduction process, although it is not possible to identify this indirect effect in quantitative terms as part of the present analysis.     

半浮区液桥热毛细振荡流

采用非定常、三维直接数值模拟方法研究大Pr数半浮区液桥热毛细对流从定常流向振荡流的过渡过程．文中详细描述了热毛细振荡流的起振和振荡特征,给出了液桥横截面上振荡流的流场和温度分布．在地面引力场条件下计算的结果与地面实验的结果进行比较,得出液桥水平截面上的流场和温度分布图样以一定的速度旋转,自由表面固定点处流体的环向流速正、负交替变化的一致结论．     

Non-conservative oscillatory systems with periodic solutions

This note extends the work of previous authors to the closed orbits of non-linear oscillatory systems. The simple phase plane analysis is used.     

Coarsening Fronts

We characterize the spatial spreading of the coarsening process in the Allen–Cahn equation in terms of the propagation of a nonlinear modulated front. Unstable periodic patterns of the Allen–Cahn equation are invaded by a front, propagating in an oscillatory fashion, and leaving behind the homogeneous, stable equilibrium. During one cycle of the oscillatory propagation, two layers of the periodic pattern are annihilated. Galerkin approximations and the Conley index for ill-posed spatial dynamics are used to show existence of modulated fronts for all parameter values. In the limit of small amplitude patterns or large wave speeds, we establish uniqueness and asymptotic stability of the modulated fronts. We show that the minimal speed of propagation can be characterized by a dichotomy which depends on the existence of pulled fronts. The main tools here are an Evans function type construction for the infinite-dimensional ill-posed dynamics and an analysis of the complex dispersion relation based on Sturm–Liouville theory.     

The onset of convection in a nanofluid saturated porous layer using Darcy model with cross diffusion

Linear and nonlinear stability analysis for the onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is studied. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The modified Darcy equation that includes the time derivative term is used to model the momentum equation. In conjunction with the Brownian motion, the nanoparticle fraction becomes stratified, hence the viscosity and the conductivity are stratified. The nanofluid is assumed to be diluted and this enables the porous medium to be treated as a weakly heterogeneous medium with variation, in the vertical direction, of conductivity and viscosity. The critical Rayleigh number, wave number for stationary and oscillatory mode and frequency of oscillations are obtained analytically using linear theory and the non-linear analysis is made with minimal representation of the truncated Fourier series analysis involving only two terms. The effect of various parameters on the stationary and oscillatory convection is shown pictorially. We also study the effect of time on transient Nusselt number and Sherwood number which is found to be oscillatory when time is small. However, when time becomes very large both the transient Nusselt value and Sherwood value approaches to their steady state values.     

Thermo-rheological behavior of model protein–polysaccharide mixtures

The use of mixtures of pea protein isolate (PPI) and κ-carrageenan (κ-C) is increasing rapidly with the aim of increasing the stability and viscosity of food products. Recent works have studied their textural and thermal properties but few have studied the influence of the temperature and concentration on the rheological behavior of model systems. In the present work, we study the thermo-rheological properties in the linear and non-linear viscoelastic regimes, in both shear and extensional flows, of mixtures of PPI and κ-C with the aim of obtaining a model for the temperature-induced gelation of complex mixtures of globular vegetable proteins under linear and non-linear deformations. We analyzed the influence of temperature and protein-to-polysaccharide ratios and showed that there are strong changes in the mechanical properties. In shear flows, small-amplitude oscillatory shear was used to study the linear regime and large-amplitude oscillatory shear was used for the non-linear regime. In extensional flows, studies were carried out via the analysis of the dynamics of capillary thinning and breakup process in a filament-thinning rheometer.     

Magneto-convection in an anisotropic porous layer with Soret effect

Thermal instability in an electrically conducting two component Boussinesq fluid-saturated-porous medium has been investigated, in the presence of Soret coefficient. The porous medium is confined between two horizontal surfaces, and subjected to a constant vertical magnetic field. Flow in the porous medium is characterized by generalized Darcy model, which includes the time derivative term. Performing linear and non-linear stability analysis, the effect of magnetic field on the stability of flow through porous medium has been investigated. The normal mode method is used in linear stability analysis, while a weak non-linear analysis based on a minimal representation of double Fourier series method is used in non-linear analysis. The critical Rayleigh number, wave number for stationary and oscillatory modes, and frequency of oscillations are obtained analytically using linear theory. Effects of various parameters on stationary, oscillatory and finite amplitude convection, rate of heat and mass transfer have been obtained analytically and presented graphically.     

Shape analysis and damped oscillatory solutions for a class of nonlinear wave equation with quintic term简

This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi- tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi- mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so- lutions. It can be seen that the error is infinitesimal decreasing in the exponential form.     

The convective instability of Maxwell fluid-saturated porous layer using a thermal non-equilibrium model

A linear stability analysis is carried out to study viscoelastic fluid convection in a horizontal porous layer heated from below and cooled from above when the solid and fluid phases are not in a local thermal equilibrium. The modified Darcy–Brinkman–Maxwell model is used for the momentum equation and two-field model is used for the energy equation each representing the solid and fluid phases separately. The conditions for the onset of stationary and oscillatory convection are obtained analytically. Linear stability analysis suggests that, there is a competition between the processes of viscoelasticity and thermal diffusion that causes the first convective instability to be oscillatory rather than stationary. Elasticity is found to destabilize the system. Besides, the effects of Darcy number, thermal non-equilibrium and the Darcy–Prandtl number on the stability of the system are analyzed in detail.     

Thermal instability in a rotating anisotropic porous layer saturated by a viscoelastic fluid

Linear and non-linear thermal instability in a rotating anisotropic porous medium, saturated with viscoelastic fluid, has been investigated for free-free surfaces. The linear theory is being related to the normal mode method and non-linear analysis is based on minimal representation of the truncated Fourier series analysis containing only two terms. The extended Darcy model, which includes the time derivative and Coriolis terms has been employed in the momentum equation. The criteria for both stationary and oscillatory convection is derived analytically. The rotation inhibits the onset of convection in both stationary and oscillatory modes. A weak non-linear theory based on the truncated representation of Fourier series method is used to find the thermal Nusselt number. The transient behaviour of the Nusselt number is also investigated by solving the finite amplitude equations using a numerical method. The results obtained during the analysis have been presented graphically.