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.     

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.     

Laboratory, numerical, and theoretical modeling of the flow in a far wake in a stratified fluid

The far-wake flow past a sphere towed in a fluid with high Reynolds and Froude numbers and with a pycnocline-form salt-density stratification is studied in a laboratory experiment based on particle image velocimetry and in numerical and theoretical modeling. In the configuration under consideration, the axis of sphere towing is located under a pycnocline. Flow parameters, the profiles of density and average velocity, and the initial field of velocity fluctuation in numerical modeling are specified from the data of the laboratory experiment. The fields of fluid velocity at different times and the time dependences of integral parameters of wake flow, such as the average velocity at the axis and the transverse width of the flow, are obtained. The results of numerical modeling are in good qualitative and quantitative agreement with the data of the laboratory experiment. The results of the laboratory experiment and numerical modeling are compared to the predictions of a quasi-linear and quasi-two-dimensional theoretical model. The time evolution of both the average velocity at the axis and the transverse width of the wake is obtained with the model and is in good agreement with the experimental data. The results of numerical modeling also show that, under the effect of velocity fluctuation in the wake, internal waves whose spatial period is equal to the characteristic period of the wake’s vortex structure are excited efficiently in the pycnocline.     

Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle: Part II: Cnoidal waves

Vortex generation and evolution due to flow separation around a submerged rectangular obstacle under incoming cnoidal waves is investigated both experimentally and numerically. The Particle Image Velocimetry (PIV) technique is used in the measurement. Based on the PIV data, a characteristic velocity, phrased in terms of incoming wave height, phase speed, dimension of the obstacle, and a local Reynolds number are proposed to describe the intensity of vortex. The numerical model, which solves the two dimensional Reynolds Averaged Navier Stokes (RANS) equations, is used to further study the effects of wave period on the vortex intensity. Measurements for the mean and turbulent velocity fields further indicate that the time history of the intensity of fluid turbulence is closely related to that of the vortex intensity.     

波流耦合下桩周珊瑚砂冲刷机理研究

针对我国南海某岛礁珊瑚砂地基上的圆形桩基础,采用N-S方程k-ε模型、双向耦合方式跟踪流场中颗粒运动轨迹的方法,对桩周珊瑚砂的冲刷规律进行了求解,分析了桩体周围流体的速度场以及桩体表面剪应力场的分布规律,同时对桩周珊瑚砂冲刷坑的形成过程进行了模拟。计算结果表明,在桩体周围形成的马蹄形漩涡和桩柱后方的尾涡作用下,桩周土体出现了较为明显的冲刷现象,涡旋的释放显著地影响着珊瑚砂地基上桩基的冲刷坑形状;而且,由于珊瑚砂颗粒密度较石英砂小,水动力作用下桩周冲刷坑更容易形成,所以实际工程中需要考虑有效的防护措施。     

Analytical Solutions to the Flow Field Induced by Uniformly Moving Multiple Helical Vortex Filaments

This paper presents analytic solutions for the flow field of inviscid fluid induced by uniformly and rigidly moving multiple helical vortex filaments in a cylindrical pipe. The relative coordinate system is set on the moving vortex filaments. The analytical solutions of the flow field are obtained on the assumption that the relative velocity field induced is time-independent and helically symmetrical. If the radius of the cylindrical pipe approaches infinity, these solutions are also available for tmbounded space. The results show that both the absolute velocity field and pressure field are periodical in time, and may reduce to time-independent when the helical vortex filaments are immobile or slip along the filaments themselves. Furthermore, the solution of velocity field is reduced to Okulov‘s formula for the case of a single static vortex filament in a cylindrical pipe. The calculated locations of pressure peak and valley on the pipe wall agree with experimental results.     

Large-scale turbulence under a solitary wave: Part 2: Forms and evolution of coherent structures

The instantaneous turbulent velocity field produced by a broken solitary wave propagating on a 1 in 50 plane slope was measured in the longitudinal transverse plane in the middle part of the water column and near the bottom using a stereoscopic particle image velocimetry system. These measurements showed that large-scale turbulence first arrived in the form of a downburst of turbulent fluid. In the middle of the water column, the downbursts arrived shortly after the wave crest had passed. Each downburst was accompanied by two counter-rotating vortices. The latter grew rapidly in size to become a prominent feature of the flow field. Each vortex had a typical length scale of 1/2 to 1 water depth, and carried most of the turbulent kinetic energy in the region between the vortices. Near the bottom, the counter-rotating vortices were not as well defined and covered only a small plane area compared to the entire flow structure. The turbulent fluid descending from above diverged at the bed and the resulting flow structure developed an elongated shape as the source of down-flow travelled onshore with the broken wave. It was found that the transverse spacing between adjacent downbursts ranged from 2 to 5 times the local still water depth. Since vortices cannot end in the interior of the fluid, the counter-rotating vortices must extend to the free surface in the form of a vortex loop. It was suggested that these vortex loops were produced by bending and stretching of primary vorticity generated in the wave breaking process, possibly as a result of three-dimensional water surface deformation. The vortex loops were then carried downward by the falling water from the broken wave.     

Vertical structure of the quasi-two-dimensional velocity field of a viscous incompressible flow and the problem of nonlinear friction

An approximate theory is constructed to describe quasi-two-dimensional viscous incompressible flows. This theory takes into account a weak circulation in the vertical plane and the related divergence of the two-dimensional velocity field. The role of the nonlinear terms that are due to the interaction between the vortex and potential components of velocity and the possibility of taking into account the corresponding effects in the context of the concept of bottom friction are analyzed. It is shown that the nonlinear character of friction is a consequence of the three-dimensional character of flow, which results in the effective interaction of vortices with vertical and horizontal axes. An approximation of the effect of this interaction in quasi-two-dimensional equations is obtained with the use of the coefficient of nonlinear friction. The results based on this approximation are compared to the data of laboratory experiments on the excitation of a spatially periodic fluid flow.     

Laboratory model of the Obukhov geostrophic vortex

The results of laboratory modeling of geostrophic adjustment in a shallow-water layer in rotating paraboloid are presented. According to the Rossby-Obukhov theory, this process excites nonstationary wave and stationary vortex (geostrophic) components of motion in a rotating fluid. In our experiments, the wave and vortex components were excited by extracting a preliminarily imbedded hemisphere (which made the initial distribution of the depth of the fluid inhomogeneous) from the central area of a rotating vessel with a parabolic base. Under this excitation technique, a prominent cyclonic eddy is formed in the central portion; the structure of this eddy is satisfactorily described within the linear theory of adjustment. Along with the shallow-water experiments, the published experimental data on modeling geostrophic adjustment in a two-layer medium are analyzed. A simple analytic solution to the corresponding problem of the adjustment theory is obtained, and this solution agrees with the experiment.     

海底矿石软管中水力输送数值模拟研究

海底矿石在软管中的水力输送是深海采矿的重要过程。采用计算流体动力学—离散元耦合的计算方法（CFD-DEM）,对矿石颗粒在软管中的输送进行数值模拟,重点关注矿石颗粒的运动、分布规律以及管壁受到的颗粒作用力,分析输送速度和输送浓度（入射颗粒的体积分数）对输送过程的影响规律,探索管道中易发生堵塞、易受颗粒磨损的区域。结果表明,软管中颗粒的动力学特性与管道倾角、输送速度和输送浓度有关。颗粒主要沿管道截面底部推移,倾角较大的上升段出现处于悬移状态的颗粒;管道横截面内颗粒运动速度从上至下递减,截面中心处颗粒的速度接近输送速度。输送过程中颗粒的局部浓度（该区域颗粒与固液两相流的体积比）始终大于输送浓度,局部平均速度始终小于输送速度。上升段颗粒体积分数大于下降段,颗粒速度小于下降段。管道拱顶和谷底位置管壁所受颗粒作用力最明显,管壁最可能受颗粒磨损。     

动波浪壁圆柱绕流三维数值模拟

利用计算流体力学软件Fluent开展了三维动波浪壁圆柱绕流的数值模拟,建立了三维运动波浪壁圆柱模型,通过C语言自编程序实现波浪壁面的运动控制,并保证壁面变形时网格的高质量。在来流速度u=0.125 m/s、雷诺数Re=12 500的情况下,开展了动波浪壁波动速度w=0、0.062 5、0.125、0.187 5 m/s四个工况的计算分析,并比较了不同波动速度对流场结构、升力、阻力特性的影响。结果表明:动波浪壁圆柱能有效抑制流动的分离,消除交替脱落的尾涡,从而消除周期振荡的升力;在消除卡门涡街的同时,圆柱后驻点处的涡量值随波动速度增加而增加,其原因在于波形移动加大了壁面流体的速度,从而减小了圆柱前后的压力差,减小了阻力;随着波动速度的增大,平均阻力系数呈明显下降趋势,当波动速度为来流速度的1.5倍时,平均阻力系数相对于光滑圆柱下降了53.76%。     

利用旋转平台模拟双河口羽流相互作用的研究

本文通过旋转平台实验室实验的方法,探讨了双河口情况下两个羽流将如何发生相互作用。在研究中,提出了一种新颖的技术对河口羽流的各切面流场进行测量,来获得河口羽流多个平面的速度场及涡度场,并基于此模拟了双河口羽流系统的准三维结构。通过对不同入流速度下的双河口羽流流场演变过程和内部结构进行了一系列对比研究,以期揭示上游河流的入流如何影响下游河口涡旋的形成及在羽流相互作用情形下各个羽流的演变。实验结果表明:随着上游入流流量的增加,上游羽流形成的沿岸流对下游河口涡旋沿岸迁移的促进和离岸输运的抑制作用将更加显著。特别是在上游入流流量等于或大于下游入流流量的情况下,下游羽流河口涡旋的体积增长明显较单一河口情况放缓。在上游入流流量较大的情况下,下游原有河口涡旋被推向更下游位置,在远离河口的位置形成另一个河口涡旋。在垂直方向上,我们可以观察到高上游入流流量条件下的下游河口涡旋的深度较小,更有利于形成三层流体的情况。本研究对多河口近海流域的营养盐及污染物的输运情况等社会和生态问题的研究有着重要的意义。     

Effects of mass and damping ratios on VIV of a circular cylinder

In this study the basic characteristics of the dynamic response and vortex shedding from an elastically mounted circular cylinder in laminar flow is numerically investigated. The Reynolds number ranges from 80 to 160, a regime that is fully laminar. The governing equations of fluid flow are cast in terms of vorticity. The two-dimensional vorticity transport equation is solved using a vortex method. Effects of important parameters on the system response and vortex shedding are investigated; these include: mass ratio, damping ratio, Reynolds number and reduced velocity. The numerical results show that a decrease in either the mass ratio or damping ratio of the system can lead to an increase in both the oscillation amplitude and the reduced velocity range over which lock-in occurs. The results also suggest that the mass-damping parameter may characterize the system response adequately, although the effect of changing mass ratio appears to be a little more profound compared to damping ratio. Vorticity contour plots suggest that the vortex shedding occurs in the 2S mode, although a wake structure similar to the C(2S) mode appears at distances 15–20 diameters downstream in the lock-in region. The simulation results are in good agreement with previously published data.     

Propagation of water waves over permeable rippled beds

Unsteady two-dimensional Navier-Stokes equations and Navier-Stokes type model equations for porous flow were solved numerically to simulate the propagation of water waves over a permeable rippled bed. A boundary-fitted coordinate system was adopted to make the computational meshes consistent with the rippled bed. The accuracy of the numerical scheme was confirmed by comparing the numerical results concerning the spatial distribution of wave amplitudes over impermeable and permeable rippled beds with the analytical solutions. For periodic incident waves, the flow field over the wavy wall is discussed in terms of the steady Eulerian streaming velocity. The trajectories of the fluid particles that are initially located close to the ripples were also determined. One of the main results herein is that under the action of periodic water waves, fluid particles on an impermeable rippled bed initially moved back and forth around the ripple crest, with increasing vertical distance from the rippled wall. After one or two wave periods, they are then lifted towards the next ripple crest. All of the marked particles on a permeable rippled bed were shifted onshore with a much larger displacement than those on an impermeable bed. Finally, the flow fields and the particle motions close to impermeable and permeable beds induced by a solitary wave are elucidated.     

Inleakage of a vortex-ring bunch onto a plane screen

A method is suggested for simulating axisymmetric laminar or turbulent flows formed during the motion of a vortex-ring bunch of given geometry and circulation toward a plane screen. Earlier, similar problems were simulated with the numerical solution of the Navier-Stokes equations for laminar flows. Turbulent flows have remained unconsidered until now. When a vortex ring approaches the screen, the secondary nonstationary flow is induced near the screen’s surface and this secondary flow causes the formation of the radial boundary layer (provided that air viscosity is taken into account). First, the medium spreads out from the critical point at the screen’s center with the negative pressure gradient along the radial coordinate and then detaches in the region of the positive pressure gradient. This radial wall flow and the corresponding boundary layer are considered in the quasi-stationary approximation. When the boundary layer detaches at successive instances, the flow is replenished with the radially moving secondary vortex rings whose circulations have the sign opposite to that of the circulation of the primary vortex ring. It is the interaction of the primary and secondary vortices that governs process dynamics, which differs substantially from that in the case when the formation of secondary vortices is disregarded. The suggested method is based on the method of discrete vortices (a perfect liquid) and the boundary-layer (laminar or turbulent) theory. During the development of the flow under investigation, the nonstationary ascending flow in the direction perpendicular to the screen’s plane is formed and then this flow decays and dissipates. Simulations for large Reynolds numbers corresponding to the formation of the turbulent boundary layer show that the velocity of ascending vortices in the plane of the initial vortex bunch is less than one-tenth of the initial velocity of the descending vortex ring. The boundary layer is introduced into calculations with the sole goal of determining the parameters of the secondary vortex rings formed during boundary-layer detachments. The interaction of the primary and secondary vortices is then considered within the framework of a perfect medium. Simulations for large Reynolds numbers corresponding to the formation of the turbulent boundary layer on the screen were correlated with the available data obtained in laboratory experiments for small Reynolds numbers. Qualitative agreement between the simulations and experiments is fairly satisfactory. The simulation for one combination of the circulation and vortex-ring geometry takes at most 10–15 min with the use of an average PC.     

Dynamic parameters in models of atmospheric vortex structures

Vortex simulation and the computation of fields of dynamic parameters of vortex structures (velocity, rotor velocity, and helicity) are carried out with the use of exact hydrodynamic equations in a cylindrical coordinate system. Components of centripetal and Coriolis accelerations are taken into account in the initial equations. Internal and external solutions are defined. Internal solutions ignore the disturbances of the pressure field, but they are considered in external solutions. The simulation is carried out so that the effect of accounting for spatial coordinates on the structure of the above fields is pronounced. It is shown that the initial kinetic energy of rotating motion transforms into the kinetic energy of radial and vertical velocity components in models with centripetal acceleration. In models with Coriolis acceleration, the Rossby effect is clearly pronounced. The method of an “inverse problem” is used for finding external solutions, i.e., reconstruction of the pressure field at specified velocity components. Computations have shown that tangential components mainly contribute to the velocity and helicity vortex moduli at the initial stage.     

Transformation of a strongly nonlinear wave in a shallow-water basin

The transformation of a nonlinear wave in shallow water is investigated analytically and numerically within the framework of long-wave theory. It is shown that the nonlinearity parameter (the Mach number), which is defined as the ratio of the particle velocity in the wave to the propagation velocity, can be well above unity in a deep trough and that a jump appears initially in the trough. It is demonstrated that shockwave amplitudes at large times change in accordance with the prediction of weakly nonlinear theory. The shock front generates a reflected wave, which, in turn, transforms into a shock wave if the initial amplitude is large enough. The amplitude of the reflected wave is proportional to the cube of the initial amplitude (as predicted by weakly nonlinear theory) over a wide range of amplitudes except for the case of anomalously strong nonlinearity. When there is a sign-variable sufficiently intense initial perturbation, the basic wave transforms into a positive shock pulse (crest) and the reflected wave turns into a negative pulse (trough).     

Polar lows and tropical hurricanes: Their energy and sizes and a quantitative criterion for their generation

Similarity and dimension considerations applied to convection in a rotating fluid allows one to estimate the sizes and horizontal velocities of generated vortices. To do this, it is necessary to know the buoyancy flux in the fluid and the angular velocity of fluid rotation [1, 2]. The author’s preliminary efforts [3] have shown that the sizes, wind speeds, and total kinetic energy can thus be estimated correctly for tropical cyclones (TCs), as well as for polar lows (PLs) (which are often called explosive mesocyclones because they take just a few hours to develop). In this study, the sensible and latent heat fluxes for U = 33 m/s and the related buoyancy fluxes are estimated on the basis of climatology, bulk formulas, and the velocity scale of convection in a rotating fluid. In the tropics, at hurricane wind speeds U ≥ 33 m/s and climatological air humidity r = 80%, the total heat flux at the water surface temperature T _s ≥ 26°C becomes equal to or greater than 700 W/m². Due to the Clausius-Clapeyron equation, the latent heat flux to the atmosphere (the main part of the flux in the tropics) decreases substantially at lower values of T _s. Thus, an energy flux from the ocean to the atmosphere of 700 W/m² or greater should be regarded as the first necessary condition for TC genesis instead of the temperature T _s. Low static stability, which must be at least half its climatological value as estimated here, is another necessary condition [4]. In polar regions, total fluxes roughly twice those in the tropics are needed for the formation of explosive mesocyclones, PLs, which is explained by the much smaller role of latent heat, greater geostrophicity, and stronger static stability of the atmosphere there. Enthalpy fluxes and wind speeds are interrelated: the larger the flux is, the stronger the convection, the higher the concentration of angular momentum in an ascending convective air column, and the greater the azimuthal velocity in the vortex are, which in turn enhances the transfer of energy from the ocean. Considering the problem with the use of simple analytic relations makes it possible, for the first time, to find a numerical criterion for their generation. It is hoped that this material may be useful for educational purposes as well.     

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。     

实验室造波条件对内孤立波发展影响的直接数值模拟

内孤立波具有振幅尺度大、能量集中的特点,其引起流场和密度场的迅速变化可能对海洋工程结构物以及水下潜体造成严重威胁.因此研究不同造波条件下生成的内孤立波运动的流场特征具有重要的学术意义和实际应用价值.采用直接数值模拟方法和给定的初始密度场密度跃迁函数,对重力塌陷激发内孤立波的运动过程进行研究,探讨了不同造波条件下,激发产...