On the stability of vortex streets in a stratified fluid

On the basis of the perturbation theory developed previously by the authors for localized hydrodynamic vortices, the influence of a specified jet flow and of the structure of individual vortices on the stability of the Karman street is investigated. It is shown that, for a street of vortices with a power law of decrease in the azimuthal velocity, the jet flow suppresses instability only with respect to perturbations with wavelengths from a certain range determined by the parameters of the flow. At the same time, for streets formed from vortices with a Gaussian profile of the azimuthal velocity, even in the absence of a specified flow, there is a certain region of the street’s parameters in which the street is stable against perturbations of all scales. Thus, for the purposes of modeling quasi-two-dimensional flows in a stratified fluid by a sequence of localized vortices, which is discussed in this study, vortices with a Gaussian profile of the azimuthal velocity turn out to be preferable. The results of this study are consistent with numerous experiments on the structure of a quasi-two-dimensional wake behind a body in a stratified fluid at large Reynolds and Froude numbers.     

A three-dimensional wake impingement model and applications on tandem oscillating foils

Potential flow based vortex numerical methods have been widely used in aerodynamics and hydrodynamics. In these methods, vortices shed from lifting bodies are traced by using vortex filaments or dipole panels. When the wake elements encounter a downstream body, such as a rudder behind a propeller or a stator behind a rotor, a treatment is necessary to divert the wake elements to pass by the body. This treatment is vital to make wake simulations realistic and to satisfy the non-penetration condition during wake body interaction. It also helps to avoid pure numerical disturbances such as when a vortex filament or an edge of a dipole panel passes through the collection point of a body element; this is a singularity for induced velocity and it will introduce a large numerical disturbance. This necessary treatment for three-dimensional problems with geometrical complexity has not been found to date. In this study, a wake impingement model was developed to divert wake elements to slip over the body surface, model the vortex/body interaction, and predict forces on fluctuating components. The model was also tested on configurations of oscillating foils in tandem with an existing panel method code. Simulation results with the wake impingement model are shown to be in closer agreement with limited published experimental data than those without the model. With the established wake impingement model, force fluctuations on the after body due to the wake vortex impingement were investigated based on a series of simulations. The series varied several parameters including distance between two foils, oscillating frequency, span, rear foil pitch angle, swap angle and vertical position.     

The mesoscale atmospheric vortex as a manifestation of the Novorossiysk bora

The WRF-ARW regional atmosphere circulation model has been used to reproduce a few episodes of cold intrusion and the Novorossiysk bora accompanied by the formation of the mesoscale cyclonic vortex over the Black sea, which can be clearly observed from satellite images of cloudiness. It has been shown that the vortex development is associated with the specific features of air flow around the northwestern edge of the Caucasus Mountains. We have estimated the vertical vorticity associated with the alongshore horizontal gradient of temperature. We have considered the field structure of wind velocity and temperature of the axisymmetric quasi-two-dimensional vortex generated in the coastal zone and displaced seaward after separating from the coast. With the background northerly wind, the coastal cyclonic circulation is not accompanied by the vortex separation from the coast. The specific feature of the development of the cyclonic vortex is the southeastern wind with velocities of up to 10 m/s in the Caucasus coastal area from Sochi to Sukhum.     

Numerical model of currents generated by sources and sinks in a circular rotating channel

This paper presents the results of numerical calculations using shallow water equations for the currents in the laboratory experiments with a rotating circular channel. An axial symmetric function of mass source is introduced into the equations for the depth of the layer to model experimental sources and sinks of fluid, which induces opposing zonal flows together with the Coriolis force. Different configurations and amplitudes of mass sources lead to the appearance of vortex motions in the channel with different circular motions in the vortices and azimuthal displacements of their centers along the channel. Diagrams of regimes are presented in the parameters of relative angular velocities of the mean zonal flow and vortex transport around the axis of the system rotation. The differences of the theory and real experiments with currents of finite depth in a channel are discussed.     

中国“海洋一号”卫星图像上的冯·卡门大气涡街现象与动力分析

利用中国"海洋一号(HY-1B)"卫星海洋水色水温扫描仪(COCTS)和美国Terra卫星中分辨率成像光谱仪(MODIS)等观测数据对2011年3月2日济州岛东南海域的冯·卡门(von Kármán)大气涡街现象进行了观测和动力分析。COCTS和MODIS观测得到大气涡街涡列距离和涡旋间距比(h/a)均值分别为0.32和0.35;在大气涡街发生海域存在低风速海面风涡旋和海面温度暖舌;济州岛的大气垂直结构存在一逆温层。利用COCTS和MODIS伪彩色合成图观测时间差异,计算得到涡旋移动速率为12.2 m/s,而分别利用它们各自的几何观测参数(h/a),结合涡街动力模型计算得到涡旋移动速率分别为12.8 m/s和12.3 m/s。利用上述观测结果计算得到大气涡街个例的脱落频率为1.24×10-4 s-1,脱落周期为134 min,其中雷诺数范围为60~75,涡街运动学黏性系数范围为2 200~2 750,弗劳德数为0.10,罗斯比数为0.43。分析结果表明中国"海洋一号"卫星数据可用于冯·卡门大气涡街等海洋大气现象的定量化研究。     

A numerical study on the formation and variation of a clockwise-circulation during winter in the Yellow Sea

In the Yellow Sea, the north-westerly wind dominates in winter and the existence of horizontal clockwise circulation has been suggested (Yanagi and Takahashi, 1993). The formation and variation mechanisms of this clockwise circulation is investigated using the wind forced numerical model which has a simplified basin configuration of the Yellow Sea. The model results show that two vortices (an anticlockwise vortex off Chinese coast and a clockwise vortex off Korean coast) are generated by the uniform north-westerly wind. Both vortices propagate along the shelf slope as the first mode shelf waves. An anti-clockwise vortex can not grow because it does not balance to the wind forcing. On the other hand, a clockwise vortex can grow and it reaches to the equilibrium condition at the northern part of the Yellow Sea, because this circulation can balance to the wind forcing. The time scale to become into the equilibrium condition is about 2 days. From this fact, it is ascertained that a clockwise circulation in the basin is generated periodically according to the variable wind forcing with 4 days period. The steady part of the current field exists with the fluctuating one which is induced by the periodical north-westerly wind.     

海洋中长生命反气旋涡在地形上的演变以及涡旋的合并现象

通过对海洋中长生命反气旋涡在Ｇａｕｓｓ型孤立地形上演变的研究,发现地形对长生命反气旋涡的发展和传播有相当重要的影响。在无地形作用的情况下,仅有反气旋涡能够存在于向西的均匀基流中,这个涡是长生命的,并且在西移过程中有明显的向西倾斜。然而当其上游存在一个孤立地形时,可以发现这个涡有一个向东的倾斜,它的强度将增强且向西的移速会增加,其规迹象陀螺的运动。另一方面,当两个强度相同的反气旋涡同时存在时,这两个     

Flow Separation and Vortex Dynamics in Waves Propagating over A Submerged Quartercircular Breakwater

The interactions of cnoidal waves with a submerged quartercircular breakwater are investigated by a Reynolds-Averaged Navier–Stokes (RANS) flow solver with a Volume of Fluid (VOF) surface capturing scheme (RANS-VOF) model. The vertical variation of the instantaneous velocity indicates that flow separation occurs at the boundary layer near the breakwater. The temporal evolution of the velocity and vorticity fields demonstrates vortex generation and shedding around the submerged quartercircular breakwater due to the flow separation. An empirical relationship between the vortex intensity and a few hydrodynamic parameters is proposed based on parametric analysis. In addition, the instantaneous and time-averaged vorticity fields reveal a pair of vortices of opposite signs at the breakwater which are expected to have significant effect on sediment entrainment, suspension, and transportation, therefore, scour on the leeside of the breakwater.     

Effect of the Planetary Boundary Layer Horizontal Inhomogeneity in the Two-Dimensional Fluid Motion Model

The generalized two-dimensional vortex equation is derived for an incompressible viscous fluid in a rotating system for a vertically averaged flow taking into account the variability of the boundary layer characteristics. The resulting equation contains parameters and their spatial derivatives determined by the second moments of functions describing the vertical profiles of the flow components. Numerical experiments demonstrate the influence of the boundary-layer horizontal inhomogeneity on the evolution of the vorticity field of a pair of atmospheric vortices.     

Structure of a pair of anticyclonic vortices in northern part of the South China Sea in autumn of 1994

A pair of remarkable meso-scale anticyclonic vortices, one formed closely to another, inthe northern part of the South China Sea during the period from the later August to early September of 1994 were documented by the in situ observation data. Their spatial structures were examined in detail from the horizontal and two nearly perpendicular/vertical angles of view. It was shown that the horizontal scales of these two vortices were around 100, 50 km, and their vertical scales were about 500, 1000 m, respectively. Two "warm core" structures associated with these two vortices were found in their horizontal and vertical analyses. The closer spacing of these two vortices (namely, 60 km), which was smaller than the Rossby radius of deformation, suggested that they might merge with each other during their next evolution stages and form into a larger vortex eventually.     

On the onset of the instability of a three-dimensional jet in a stratified fluid

The onset of a three-dimensional jet flow in a stratified fluid is studied with the aid of a direct numerical simulation. An initially cylindrical jet with a Gaussian velocity profile is considered in a fluid with stable linear density stratification. The results indicate that, if an initial small perturbation of the velocity field has a wide spectrum, an exponential growth of the isolated quasi-two-dimensional mode occurs and its spectral maximum is shifted toward smaller wave numbers in comparison with the maximum of the helical mode of the instability of a nonstratified jet. The growth rate is proportional to Ri^0.5, where Ri is the global Richardson number. The onset of the instability leads to the formation of the flow’s vortex structure, which consists of a collection of different-polarity quasi-two-dimensional vortices located in a horizontal plane near the longitudinal axis of the jet. At sufficiently long times (Nt > 100, where N is the buoyancy frequency and t is time), the growth of instability reaches the saturation stage and further fluctuations in velocity and density decay under the effect of viscous diffusion. At this stage, the flow becomes self-similar and the time dependences of the transverse and vertical widths of the jet are consistent with the asymptotic behaviors of integral parameters of the flow that are observed experimentally in the far stratified wake. The results suggest that the onset of the instability of a quasitwo-dimensional mode can play the determining role in the dynamics of flow in the far stratified wake.     

A simple model of propulsive oscillating foils

The design of thrusters inspired by the locomotion of fishes is currently investigated in many research centres for unmanned underwater vehicles. Fast fishes propel themselves in water through the rhythmic motion of their tail. Propulsion is achieved by means of the periodic shedding of vortex structures by the edges of the tail. Thrust is produced because the vortices give rise to a steady jet of fluid which leaves the tail in the direction which is opposite to the forward motion of the fish. Assuming that the fish tail can be modelled by a two-dimensional plate in steady forward motion and oscillating with a combination of harmonic heaving and pitching movements, Brown and Michael’s model is presently used to determine the dynamics of the vortex structures shed by plate edges. Numerical simulations have been carried out to investigate the effects on the flow field of varying the physical parameters of the phenomenon. The knowledge of the strength and trajectory of the vortex structures shed by the plate allows the characteristics of the jet producing the thrust to be quantified.     

On the nature of oceanic eddies shed by the Island of Gran Canaria

We use hydrographic and buoy data to compare the initial temperature fields and Lagrangian evolution of water parcels in two vortices generated by the southward flowing Canary Current passing around the island of Gran Canaria Island. One vortex is anticyclonic, shed in June 1998 as the result of an incident current of about 0.05 m s⁻¹, and the second one is cyclonic, shed in June 2005 with the impinging current estimated as 0.03 m s⁻¹. The two vortices exhibit contrasting characteristics yet display some important similarities. The isopycnals are depressed in the core of the anticyclonic vortex, at least down to a depth of 700 m, whilst they dome up in the core of the cyclonic vortex but only down to 450 m. In the top 300 m the depression/doming of the isotherms is similar for both vortices, with a maximum vertical displacement of the isotherm of about 80 m, which correspond to temperature anomalies of some 2.5 °C at a given depth. A simple method is developed to obtain the initial orbital velocity field from the temperature data, from which we estimate peak values of 0.7 and 0.5 m s⁻¹ for the anticyclonic and cyclonic vortices, respectively. The buoys, three for the anticyclonic vortex and two for the cyclonic one, were drougued at 100 m depth, below the surface mixed layer, and their initial velocities are consistent with the above values. In both vortices, the buoys revolve either within a central core, where the rotation rate remains stable and large for several weeks, or in an outer ring, where the rotation rate is significantly smaller and displays large radial fluctuations. Within the inner core the anticyclonic vortex has significant inward radial velocity, while the cyclonic vortex has near-zero radial mean motions. The cyclonic vortex rotates more slowly than the anticyclonic, their initial periods being 4.5 and 2.5 days, respectively. A simple axisymmetric model with radial diffusion (coefficient K_h≅25 m² s⁻¹) and advection reproduces the observations reasonably well, the diffusive effect being more important than that resulting from the observed radial advection. The model also supports the hypothesis that the rotation rate of cyclonic vortices is less than that of anticyclonic vortices, as otherwise they would become inertially unstable. Both the buoys data and sea surface temperature images confirm that the vortices evolve from youth to maturity, as the cores shrink and the outer rings expands, and then to a decay stage, as the core rotation rates decrease, though frequent interactions with other mesoscale structures result in more accelerated aging. Despite these interaction they last many months as coherent structures south of the Canary Islands.     

长江口南港底部边界层特征的观测与分析

对长江口2002年和2003年共4个潮周期的数据进行了分析,通过流速对数剖面公式计算边界层参数,并对各个潮周期内的边界层参数的变化规律进行了分析,同时也对悬沙输送可能对垂向水流结构以及边界层参数造成的影响进行了探讨。结果表明,悬沙的时间分布特征对温度、盐度、水体密度的分布格局有重要影响,主要表现在水体的Rf值普遍较高,分层稳定。此外,悬沙也可影响边界层参数,从而对水流结构产生影响。由于水体的层化作用,使层间的摩擦阻力增大,相当于在垂向上产生不同内边界层,因而影响了流速在垂向上的变化。     

Turbulence-plankton interactions: a new cartoon

Climate change redistributes turbulence in both space and time, adding urgency to understanding of turbulence effects. Many analytic and analog models used to simulate and assess effects of turbulence on plankton rely on simple Couette flow. There shear rates are constant and spatially uniform, and hence so is vorticity. Over the last decade, however, turbulence research within fluid dynamics has focused on the structure of dissipative vortices in space and time. Vorticity gradients, finite net diffusion of vorticity and small radii of curvature of streamlines are ubiquitous features of turbulent vortices at dissipation scales but are explicitly excluded from simple, steady Couette flows. All of these flow components contribute instabilities that cause rotation of particles and so are important to simulate in future laboratory devices designed to assess effects of turbulence on nutrient uptake, particle coagulation, motility and predator‐prey encounter in the plankton. The Burgers vortex retains these signature features of turbulence and provides a simplified “cartoon” of vortex structure and dynamics that nevertheless obeys the Navier‐Stokes equations. Moreover, this idealization closely resembles many dissipative vortices observed in both the laboratory and the field as well as in direct numerical simulations of turbulence. It is simple enough to allow both simulation in numerical models and fabrication of analog devices that selectively reproduce its features. Exercise of such numerical and analog models promises additional insights into mechanisms of turbulence effects on passive trajectories and local accumulations of both living and nonliving particles, into solute exchange with living and nonliving particles and into more subtle influences on sensory processes and swimming trajectories of plankton, including demersal organisms and settling larvae in turbulent bottom boundary layers. The literature on biological consequences of vortical turbulence has focused primarily on the smallest, Kolmogorov‐scale vortices of length scale η. Theoretical dissipation spectra and direct numerical simulation, however, indicate that typical dissipative vortices with radii of 7η to 8η, peak azimuthal speeds of order 1 cm s^?1 and lifetimes of order 10 s or longer (and much longer for moderate pelagic turbulence intensities) deserve new attention in studies of biological effects of turbulence.     

The effect of cyclone-anticyclone asymmetry at small Rossby numbers

Cyclone-anticyclone asymmetry in a rotating fluid results in vortices with cyclonic rotation being attenuated more rapidly than vortices with anticyclonic rotation due to the Ekman bottom friction. To explain this effect, some authors invoked rather complex integral (averaged along the vertical) models with the parametrization of nonlinear friction. A simple analytical model, free of the procedure of formal averaging and based on a separate consideration of the equations for external flow in the nonviscous region and internal flow in the boundary layer, is investigated in this work. The corresponding equations are written in the so-called geostrophic momentum approximation, which makes it possible to take into account the nonlinear advective mass transport in the boundary layer at small Rossby numbers. The nonlinear equation of the hyperbolic type for the tangential velocity, which describes the process of attenuation of an axisymmetric vortex, is obtained from the condition of total mass conservation. Based on the solutions to this equation, it was shown that distinctions in the character of vortex attenuation are caused by deviations from the geostrophic regime in the nonviscous region. It was established that the concentration (compression) of anticyclonic vortices and the extension of cyclonic ones take place in the process of attenuation.     

Large-scale turbulence under a solitary wave

The structure of large-scale turbulence under a broken solitary wave on a 1 in 50 plane slope was studied. Three-component velocity measurements were taken at different heights above a smooth bed in the middle surf zone using an acoustic Doppler velocimeter. The measured data showed that turbulent velocity components were well correlated in the middle part of the water column. The velocity correlations could be produced by an oblique vortex similar to the obliquely descending eddy observed previously by other investigators. The vertical distributions of the relative values of the components of the Reynolds stress tensor showed that the structure of turbulence evolved continuously between the free surface and the bottom. The evolution was related to transition from two-dimensional to three-dimensional flow structures and the effect of the solid bottom on flow structures. Time histories of measured turbulent kinetic energy and turbulence stresses showed episodic turbulent events near the free surface but more sporadic turbulence in the lower layer. Large or intense turbulent events were found to have short duration and time lag relative to the wave crest point. These events also maintained good correlations between the turbulence velocity components close to the bottom.Instantaneous turbulent velocity fields were measured near the bottom at the same cross-shore location by using a stereoscopic particle image velocimetry system. These measurements showed that the near-bed flow field was characterized by large-scale, coherent flow structures that were the sources of most of the turbulent kinetic energy and turbulence stresses. The types of organized flow structures observed included vortices and downbursts of turbulence descending directly from above, lateral spreading of turbulent fluid along the bed, and formation of vortices in shear layers between fluid streams. A common feature of the organized flow structures near the bed was the large turbulence velocities in the longitudinal and transverse directions, which reflected the influence of a solid bottom on the breaking-wave-generated turbulence arriving at the bed.     

基于客观方法的海洋三维涡旋核心线提取

涡旋核心线是海洋中尺度涡旋结构的重要组成要素,涡旋核心线提取和可视化对于切入中尺度涡三维结构研究、开展海洋物质能量垂直运输分析具有重要意义。本文基于客观参考框架和准则,提出了使用客观化的流场参数得到区域,并提取其山谷线作为涡旋核心线的方法,实现了对海洋三维结构中尺度涡旋核心线的提取和可视化。首先,引入了最优局部参考系,使速度、速度梯度等测度转换为在运动的参考系下保持不变的客观量,提升了在海洋科学实践中的可靠性和实用性。其次,针对含有垂向速度的海洋三维流场数据,计算其空间雅可比矩阵,展示了涡旋核心区域的三维结构,实现了海洋涡旋研究从二维到三维的提升。最后,分别在多个半径大小播撒流线种子点,分析不同旋转方向的涡旋,对已提取的涡旋核心线实验结果进行验证,证明了客观海洋三维涡旋核心线提取方法的有效性及可行性。     

Structure and resilience of overwintering habitats of Calanus finmarchicus in the Eastern Norwegian Sea

Very high concentrations of overwintering Calanus finmarchicus were found in the eastern Lofoten Basin of the Norwegian Sea close to the shelf break in January 2001–2002. A coupled 3D hydrodynamic and ecological model was used to study the formation of this deep overwintering aggregation and its stability. The ecological model includes nutrients, phytoplankton and microzooplankton in addition to a stage-structured model of C. finmarchicus. Using a Eulerian approach, the model was initiated with an overwintering stock evenly distributed in the oceanic regions of the Norwegian Sea, i.e. where depths>600 m. Spawning and development of the new generation take place in response to vertical mixing and phytoplankton development. Animals are assumed to begin their descent to overwintering depths of 700–1000 m as late stage Vs. Model results show that, in late summer, high concentrations of animals were found at overwintering depths near the shelf break north of the North Sea, off the northeastern Vøring Plateau and in the eastern Lofoten Basin along the slope of the Barents Sea shelf. They remained there for months due to deep eddies and southward, deep currents along the Norwegian shelf. The simulation experiments indicate that the combined effect of deep anticyclonic circulation and vertical migration behavior of the animals may explain the high concentrations of overwintering C. finmarchicus found in field surveys in the Eastern Lofoten Basin, close to the shelf break.