Dynamics of algae blooming: effects of budget allocation and time delay

Algal blooms are increasing in coastal waters worldwide. The study on the features of algal pollution in water bodies and the ways to eliminate them is of vital importance. Preventing, treating, and monitoring algal blooms can be an unanticipated cost for a water system. To tame algal bloom in a lake, the government provides funds through budget allocation. In this paper, we propose a mathematical model to investigate the effect of budget allocation on the control of algal bloom in a lake. We assume that the growth of budget follows logistic law and also increases in proportion to the algal density in the lake. A part of the budget is utilized for the control of inflow of nutrients, while the remaining is used in the removal of algae from the lake. Our results show that algal bloom can be mitigated from the lake by reducing the inflow rate of nutrients to a very low value, which can be achieved for very high efficacy of budget allocation for the control of nutrients inflow from outside sources. Also, increasing the efficacy of budget allocation for the removal of algae helps to control the algal bloom. Further, more budget should be used on the control of nutrient’s inflow than on the removal of algae, as the presence of nutrients in high concentration will immediately proliferate the growth of algae. Moreover, the combined effects of controlling the inflow of nutrients and removing algae at high rates will result in nutrients and algae-free aquatic environment. Further, we modify the model by considering a discrete time delay involved in the increment of budget due to increased density of algae in the lake. We observe that chaotic oscillations may arise via equilibrium destabilization on increasing the values of time delay. We apply basic tools of nonlinear dynamics such as Poincaré section and maximum Lyapunov exponent to confirm the chaotic behavior of the system.

     

白洋淀内水体的流动特征研究

研究了风对白洋淀内水体循环流动的影响，研究指出：(1)风应力可看作是水体循环 的主要驱动力. (2)在风应力的作用下，水体表层的流动主方向与风的方向一致，下层水体 的流动方向与表层方向相逆或近似相逆. (3)表层以下水体流动复杂，次表层水平流动有明 显的双涡结构. (4)淀底地形对水体垂向流动影响很大，垂向速度变化复杂，垂向上有双涡 流动现象. 从动力学角度研究了淀内水体流动的情况.     

敞开式大跨空间桁架结构风荷载分布特性研究

敞开式空间结构的桁架由于直接受气流作用,其流场空间分布复杂,风荷载确定困难,且风洞试验受模型缩尺比限制难于获取桁架结构上的气动力．借助数值风洞技术,利用高性能计算平台,本文数值求解了敞开式桁架结构的空间流场及风荷载分布．敞开式空间桁架结构整体风荷载表现为水平向为主,竖向不显著的特点,该点与封闭式桁架结构整体通常表现出竖向较强吸力作用明显不同．敞开式空间桁架结构整体风荷载对风向角表现并不敏感,其原因在于敞开式空间桁架的流场多处分离且相互干扰严重,其整体特征紊流不易在某个风向角下特别占优．     

高雷诺数湍流风场大涡模拟的并行直接求解方法

在环境流体力学中,风场是风沙流、风雪流等自然环境特性问题研究的动力源和基础. 通常采用壁湍流模型进行风场大涡模拟(large eddy simulation, LES)计算,但受到计算规模的限制使得 高雷诺数风场的模拟计算难以实现. 并行计算技术是解决大规模高雷诺数风场大涡模拟的关键技术之一. 在不可压湍流风场的LES模拟中,压力泊松方程的并行计算技术是进行规模并行计算的困难点. 根据风场流动模拟计算的特点,采用水平网格等距而垂直于地面网格非等距,在解决规模并行计算中求解压力泊松方程的难点问题时,利用FFT解耦三维泊松方程使其变为垂向的一维三对角方程, 并利用可并行的三对角方程PDD求解技术,可建立三维泊松方程的直接并行求解技术. 结合其它容易并行的动量方程计算,本文建立风场LES模拟的并行直接求解方法(parallel direct method-LES, PDM-LES). 在超级计算机上对新方法进行并行效率测试,并行计算效率达到90${\%}$. 新的方法可用于进行湍流风场大涡模拟的大规模并行计算. 计算结果表明,湍流风场瞬时速度分布近壁面存在条带状的拟序结构,平均场的速度分布符合速度对数律特性,风场湍流特性基本合理.      

The effects of surface injection through a perforated square cylinder on some aerodynamic parameters

The surface pressure distribution and the vortex shedding frequency were investigated for the flow around perforated horizontal and diagonal square cylinders with surface injection through various surfaces. For this purpose, surface pressure measurements on each square cylinder (horizontal and diagonal) and vortex shedding frequency measurements in the wake region were performed at three different Reynolds numbers in a wind tunnel. The parameters considered were injection coefficient, position of perforated surface (i.e., top, rear, top-rear and all), pressure coefficient, drag coefficient, and the Strouhal number. The results showed that pressure coefficient distribution, drag coefficient, and the Strouhal number were influenced by the position of the perforated surface and by the injection coefficient. The surface injections through the top-rear, rear and all surfaces of a diagonal square cylinder reduce the drag coefficient for the all Reynolds numbers, while the injection through all surfaces only reduces the drag coefficient of a horizontal square cylinder. The other aerodynamic parameter Strouhal number can also be controlled by injection through certain surfaces of a horizontal square cylinder.     

The effects of toxin-producing phytoplankton and environmental fluctuations on the planktonic blooms

Toxin-producing phytoplankton (TPP) and environmental fluctuations are important factors influencing the real aquatic ecosystems. Whether planktonic blooms are related to these factors is an interesting problem. In this paper, based on bottom-up mechanism, we first propose a nutrient–phytoplankton (NP) model with TPP under environmental fluctuations and study the extinction and persistence in mean. We also investigate the existence of ergodic stationary distribution. Taking into account seasonal variation, then we extend the NP model into a non-autonomous stochastic model and investigate the existence of periodic solution. Combined with the published data, we numerically illustrate the obtained results. From theoretical analysis and numerical simulations, periodic oscillatory succession of planktonic blooms can be seen clearly, which suggests that toxin-producing phytoplankton and environmental fluctuations play a key role in the termination of algal blooms.     

Wind tunnel measurements of the preferential concentration of inertial droplets in homogeneous isotropic turbulence

We describe an experimental setup aimed at studying turbulent-induced droplet collisions in a laboratory setting. Our goal is to reproduce conditions relevant to warm-rain formation in clouds. In these conditions, the trajectories of small inertial droplets are strongly influenced by the background air turbulence, and collisions can potentially explain the droplet growth rates and spectrum broadening observed in this type of clouds. Warm-rain formation is currently under strong scrutiny because it is an important source of uncertainty in atmospheric models. A grid at the entrance of a horizontal wind tunnel produces homogeneous isotropic turbulence at a Re _λ in the range of 400–500. Water droplets are injected from the nodes of the turbulence-inducing grid at a volume fraction (?) of 2.7?×?10^?5 and with sizes of 10–200?μm. A complex manifold-injection system was developed to obtain uniform water droplet seeding, in terms of both water content and size distribution. We characterize the resulting droplet-laden turbulent flow, and the statistics of droplet pairs are measured and analyzed. We found that the radial distribution function (RDF), a measure of preferential concentration of droplets that plays a key role in collision kernel models, has a large peak at distances below the Kolmogorov microscale of the turbulence. At very long separations, comparable with the integral length scale of the turbulence, these RDFs show a slow decay to the average probability given by the mean droplet number density. Consistent with this result, conditional analysis shows an increased local concentration of droplets within the inertial length scale (≈ 10–100 Kolmogorov lengths). These results are in good agreement with previous experiments that found clustering of inertial droplets with St?≈ 1 at scales on the order of 10η. Ultimately, our results support the hypothesis that turbulence-induced preferential concentration and enhanced settling can lead to significant increases in the collision probability for inertial droplets in the range 10–50?μm.     

Dynamic wind loads and wake characteristics of a wind turbine model in an atmospheric boundary layer wind

An experimental study was conducted to characterize the dynamic wind loads and evolution of the unsteady vortex and turbulent flow structures in the near wake of a horizontal axis wind turbine model placed in an atmospheric boundary layer wind tunnel. In addition to measuring dynamic wind loads (i.e., aerodynamic forces and bending moments) acting on the wind turbine model by using a high-sensitive force-moment sensor unit, a high-resolution digital particle image velocimetry (PIV) system was used to achieve flow field measurements to quantify the characteristics of the turbulent vortex flow in the near wake of the wind turbine model. Besides conducting “free-run” PIV measurements to determine the ensemble-averaged statistics of the flow quantities such as mean velocity, Reynolds stress, and turbulence kinetic energy (TKE) distributions in the wake flow, “phase-locked” PIV measurements were also performed to elucidate further details about evolution of the unsteady vortex structures in the wake flow in relation to the position of the rotating turbine blades. The effects of the tip-speed-ratio of the wind turbine model on the dynamic wind loads and wake flow characteristics were quantified in the terms of the variations of the aerodynamic thrust and bending moment coefficients of the wind turbine model, the evolution of the helical tip vortices and the unsteady vortices shedding from the blade roots and turbine nacelle, the deceleration of the incoming airflows after passing the rotation disk of the turbine blades, the TKE and Reynolds stress distributions in the near wake of the wind turbine model. The detailed flow field measurements were correlated with the dynamic wind load measurements to elucidate underlying physics in order to gain further insight into the characteristics of the dynamic wind loads and turbulent vortex flows in the wakes of wind turbines for the optimal design of the wind turbines operating in atmospheric boundary layer winds.     

顶部重力加砂颗粒速度场及浓度场的实验研究

对砂尘环境试验设备顶部重力加砂气固两相流的颗粒速度场及浓度场进行了研究．利用中国科学院寒区旱区环境与工程研究所室内风沙环境风洞，采用激光数字式粒子成像测速技术(DPIV)，得到顺风向距加砂口不同水平距离截面位置颗粒相速度及空间分布规律．表明在顺风向距加砂口水平距离约3m左右处的位置，颗粒相速度才接近风洞风速，且粒子基本均匀扩散开，从而证明了国外砂尘实验设备的不合理性、为我国自行研制大型砂尘环境试验设备，确定加砂／尘方法及试验段参数等提供了依据．     

雷暴冲击风风洞设计及流场测试

鉴于雷暴冲击风试验装置的特殊性以及与低速直流风洞的共通性,参考低速直流风洞的设计方法设计完成了试验装置的洞体结构,并制作了具有调节功能的平板来模拟地面.通过调节平板,该装置能够同时改变冲击风强度、直径、射流高度、入射倾角等冲击风参数.试验测得稳态条件下射流口下竖向风速分布,以及沿竖向分布和水平分布的水平风速,研究了水平距离、高度及冲击风参数的影响.研究结果表明:最大水平风速出现的高度与其水平位置有关;射流速度V_(jet)与射流直径D_(jet)在一定范围内对试验结果影响不大;射流高度h与入射倾角α对冲击风的流场有明显影响.     

Determination of real-time predictors of the wind turbine wake meandering

The present work proposes an experimental methodology to characterize the unsteady properties of a wind turbine wake, called meandering, and particularly its ability to follow the large-scale motions induced by large turbulent eddies contained in the approach flow. The measurements were made in an atmospheric boundary layer wind tunnel. The wind turbine model is based on the actuator disc concept. One part of the work has been dedicated to the development of a methodology for horizontal wake tracking by mean of a transverse hot wire rake, whose dynamic response is adequate for spectral analysis. Spectral coherence analysis shows that the horizontal position of the wake correlates well with the upstream transverse velocity, especially for wavelength larger than three times the diameter of the disc but less so for smaller scales. Therefore, it is concluded that the wake is actually a rather passive tracer of the large surrounding turbulent structures. The influence of the rotor size and downstream distance on the wake meandering is studied. The fluctuations of the lateral force and the yawing torque affecting the wind turbine model are also measured and correlated with the wake meandering. Two approach flow configurations are then tested: an undisturbed incoming flow (modelled atmospheric boundary layer) and a disturbed incoming flow, with a wind turbine model located upstream. Results showed that the meandering process is amplified by the presence of the upstream wake. It is shown that the coherence between the lateral force fluctuations and the horizontal wake position is significant up to length scales larger than twice the wind turbine model diameter. This leads to the conclusion that the lateral force is a better candidate than the upstream transverse velocity to predict in real time the meandering process, for either undisturbed (wake free) or disturbed incoming atmospheric flows.     

Fractal analysis of atomizing liquid flows

The work reported in this paper questions the relevance of using fractal concept to study liquid primary atomization process by characterizing the shape of the continuous liquid flow from the nozzle exit to the end of the atomization process. First, three fractal methods were tested on synthetic images in order to define the best adapted protocol to the objective of the study. It appeared that the Euclidean distance mapping was the best appropriate method. Second, this technique was applied to analyze series of images of atomizing liquid flows obtained for several working conditions. This application demonstrates that atomizing liquid flows are fractal objects and that primary atomization can be reasonably seen as fractal processes. The appropriateness of fractal concept was also demonstrated by the fact that fractal characteristics such as textural or structural fractal dimension and inner cutoff scale are physically representative of the process investigated here.     

风沙两相流PIV测量算法研究

在风沙两相流图像特征的基础上，提出了一种基于模式识别动态聚类方法中$K$-均值 算法的数字面具(Digital Mask)自动生成算法来求解风沙两相流动. 简化了传统生成Digital Mask过程中手动设置参数的操作，减少了人为误差，为批量处理风沙两相流PIV图像提供 了一种安全快捷的方法. 并将该算法应用于风沙两相流的PIV实际测量，分别得到了不同流 动状态下的气流、沙粒以及风沙气固两相流的速度场.     

Effect of thermal diffusion and electrostatic force on evolution of wind-blown sand flow

A theoretical model is suggested to mathematically describe the effect of thermal diffusion from a sand-bed on evolution of a wind-blown sand flow.An upward wind field is engendered by the thermal diffusion and the coupling interaction among the horizontal and upward wind flow,saltating grains,and a kind of electrostatic force exerted on the grains are considered in this theoretical model.The numerical results show that the effect of the thermal diffusion on the evolution process of wind-blown grain flow is quite obvious and very similar to the effect of the electrostatic force on the evolution.Not only the time for the entire system to reach a steady state(called the duration time),the transport rate of grains,the mass-flux profiles and the trajectory of saltating grains are affected by the thermal diffusion and the electrostatic force exerted on saltating grains, but also the wind profiles and the temperature profiles at the steady state are affected by the wind-blown sand flow.     

不同风场下TNT炸药爆炸烟云的扩散模型及特性

为获取不同风场下TNT爆炸烟云扩散时空分布规律与高度变化模型,本文理论描述了爆炸烟云扩散过程与机理,开展了不同水平风速下烟云扩散的计算流体力学（computational fluid dynamics, CFD）仿真和外场时空分布实验,建立了不同水平风速下烟云高度随时间变化模型及烟云最终高度计算模型,分析了烟云扩散过程中形态、温度、密度、速度变化规律。研究结果显示:CFD方法仿真烟云分布结果与实验结果基本一致,大气稳定且无风条件下烟云高度随时间呈指数0.5的幂函数关系,最终高度与爆炸当量可拟合为指数0.47的幂函数模型;水平风会加快烟云与空气混合的速度,导致幂函数模型中指数参数随风速变大而呈线性减小规律,风速越大烟云上升速度衰减越快、上升时间越短、最终高度越低。     

Analysis of sand particles’ lift-off and incident velocities in wind-blown sand flux

In the research of windblown sand movement,the lift-off and incident velocities of saltating sand particles play a significant role in bridging the spatial and temporal scales from single sand particle’s motion to windblown sand flux.In this paper,we achieved wind tunnel measurements of the movement of sand particles near sand bed through improving the wind tunnel experimental scheme of paticle image velocimetry(PIV) and data processing method.And then the influence of observation height on the probability distributions of lift-off and incident velocities of sand particles was analyzed.The results demonstrate that the observation height has no obvious influence on the distribution pattern of the lift-off and incident velocities of sand particles,i.e.,the probability distribution of horizontal and vertical velocities of lift-off and incident sand particles follow a Gaussian distribution and a negative exponential distribution,respectively.However,it influences the center of the Gaussian distribution,the decay constant and the amplitude of the negative exponential distribution.     

Two-phase flow distributors for fuel cell flow channels

All existing proton exchange membrane （PEM） fuel cell gas flow fields have been designed on the basis of single-phase gas flow distribution. The presence of liquid water in the flow causes non-uniform gas distribution, leading to poor cell performance. This paper demonstrates that a gas flow restrictor/distributor, as is commonly used in two-phase flow to stabilize multiphase transport lines and multiphase reactors, can improve the gas flow distribution by significantly reducing gas real-distribution caused by either non-uniform water formation in parallel flow channels or flow instability associated with negative-slope pressure drop characteristic of two-phase horizontal flow systems.     

An implicit three‐dimensional numerical model to simulate transport processes in coastal water bodies

A three‐dimensional baroclinic numerical model has been developed to compute water levels and water particle velocity distributions in coastal waters. The numerical model consists of hydrodynamic, transport and turbulence model components. In the hydrodynamic model component, the Navier–Stokes equations are solved with the hydrostatic pressure distribution assumption and the Boussinesq approximation. The transport model component consists of the pollutant transport model and the water temperature and salinity transport models. In this component, the three‐dimensional convective diffusion equations are solved for each of the three quantities. In the turbulence model, a two‐equation k–ϵ formulation is solved to calculate the kinetic energy of the turbulence and its rate of dissipation, which provides the variable vertical turbulent eddy viscosity. Horizontal eddy viscosities can be simulated by the Smagorinsky algebraic sub grid scale turbulence model. The solution method is a composite finite difference–finite element method. In the horizontal plane, finite difference approximations, and in the vertical plane, finite element shape functions are used. The governing equations are solved implicitly in the Cartesian co‐ordinate system. The horizontal mesh sizes can be variable. To increase the vertical resolution, grid clustering can be applied. In the treatment of coastal land boundaries, the flooding and drying processes can be considered. The developed numerical model predictions are compared with the analytical solutions of the steady wind driven circulatory flow in a closed basin and of the uni‐nodal standing oscillation. Furthermore, model predictions are verified by the experiments performed on the wind driven turbulent flow of an homogeneous fluid and by the hydraulic model studies conducted on the forced flushing of marinas in enclosed seas. Copyright © 2000 John Wiley & Sons, Ltd.