Analysis of wake behind a rotating propeller using PIV technique in a cavitation tunnel

A two-frame particle image velocimetry (PIV) technique is used to investigate the wake characteristics behind a marine propeller with 4 blades at high Reynolds number. For each of 9 different blade phases from 0° to 80°, 150 instantaneous velocity fields are measured. They are ensemble averaged to study the spatial evolution of the propeller wake in the region ranging from the trailing edge to one propeller diameter (D) downstream location. The phase-averaged mean velocity shows that the trailing vorticity is related to radial velocity jump, and the viscous wake is affected by boundary layers developed on the blade surfaces and centrifugal force. Both Galilean decomposition method and vortex identification method using swirling strength calculation are very useful for the study of vortex behaviors in the propeller wake region. The slipstream contraction occurs in the near-wake region up to about X/D=0.53 downstream. Thereafter, unstable oscillation occurs because of the reduction of interaction between the tip vortex and the wake sheet behind the maximum contraction point.     

深海油水主动旋流分离器强制涡流前推段结构对分离性能影响数值模拟

针对深水油气田主动旋流分离器强制涡流前推段锥度对分离性能的影响进行研究,应用RSM(reynolds stress model)湍流模型对主动旋流器内部强旋流场进行数值模拟计算,在强制涡流前推段锥角变化时,合理预测并对比其内部轴向速度、切向速度、离心力以及分离效率的变化。研究表明在一定范围内,前推段锥度的增加可以提高混合液在前推段内的轴向速度和切向速度,进而可以获得更高的分离效率。当锥角达到15°时,可以获得最为理想的分离效果。此外,在不同深水环境下对该主动旋流分离器进行仿真计算表明,不同的环境压力对旋流器分离效率影响很小。     

Numerical investigation of oscillations induced by submerged sliding masses within a harbor of constant slope

Oscillations within a rectangular harbor of constant slope induced by submerged sliding masses are investigated numerically based on Boussinesq-type equations and results are used to reveal the characteristics of the generated oscillations. The numerical result of each transverse eigenfrequency is very close to the theoretical prediction and the spatial structure of each mode of the oscillations may also be well captured by the existing analytical solutions based on shallow water equations. The investigation shows that relatively small-scale sliding masses whose width is small compared with the harbor width may induce obvious transverse oscillations. The predominant transverse components are those with small mode numbers when the solid slides start moving from the backwall. In comparing the oscillations induced by the slides of constant velocity and those accelerated by gravity force with bottom friction, it is observed that the movements accelerated by gravity force may facilitate the development of very low transverse oscillation modes while those with constant velocity may also be in favor of the higher ones. The augmentation of the sliding velocity along the constant slope may shift the amplitudes of the oscillation components to smaller values, which corresponds to the physical understandings of the waves generated by underwater sliding masses or landslides. While the sliding masses may not act on an isolated point of the bottom but follow a certain trajectory along the harbor, the transverse oscillations induced by them are sensitive to their position of departure in both the cross-harbor direction and the offshore direction. Longitudinal oscillations may be induced by relatively large sliding masses of harbor width on a constant slope within the harbor. Although the longitudinal oscillations may not reach a steady state without forcing terms at the entrance of the harbor, some patterns of several low-mode ones occur and wavelet spectra are used to analyze their evolutions and comparisons are made with theoretical predictions. It is revealed that the longitudinal oscillations are also sensitive to the moving velocity and initial location of the sliding masses.     

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.     

海翼水下滑翔机测流应用

水下滑翔机其通过集成生物、化学、物理传感器可以测量如温度、盐度、溶解氧等多种海洋基础水文要素,其利用卫星定位系统获得实际出水速度和理论出水模型获得理论出水速度之差可以计算深度平均流,。本文利用海翼水下滑翔机获得温盐场及卫星定位数据评估深度平均流,结果显示利用温盐场获得深度平均地转流与水下滑翔机获得深度平均流相关系数0.95,表明其流场的一致性,同时根据船载观测ADCP误差分析法估算深度平均流误差约为0.036 m/s。借助深度平均流可以估算绝对地转流,包括正压地转流和斜压地转流。在零动力面的假设下,我们选取了海翼号水下滑翔机在南海的一组实验对流量误差进行了评估。该实验为2019年1月3日-2月16日海翼号水下滑翔机自南向北穿越西沙群岛附近一个中尺度涡观测。观测结果表明,该中尺度涡为冷涡流核,在涡心以南,绝对地转流为东向流,最大流速约为0.48 m/s;涡心以北,绝对地转流为西向流,最大流速约为0.47 m/s,稍弱于南侧。受不均匀时空观测计划影响,本文未对流量做出估计。     

On a translating and transversely oscillating cylinder. Part 1—The effect of the strouhal number on the hydrodynamic forces and the near-wake structure

The problem of unsteady, laminar flow past a circular cylinder which starts translating and oscillating impulsively from rest in a viscous fluid is numerically investigated at a Reynolds number of R = 10³. The flow is incompressible and two-dimensional, and the cylinder oscillations are harmonic. The transverse oscillations are only allowed when the maximum oscillatory-to-translational velocity ratio is 0.5. The investigation is based on an implicit finite difference scheme for integrating the unsteady Navier-Stokes equations together with the mass-conservation equation in their vorticity stream function formulation. A non-inertial coordinate transformation is used so that the grid mesh remains fixed relative to the accelerating cylinder. Present calculations are performed within the range of sufficiently large oscillation amplitude to induce separation. The time variation of the in-line and transverse force coefficients are presented. The study also focuses on the laminar asymmetric flow structure in the near-wake region. In this flow regime, it is found that there is alternate shedding of vortices from either side of the cylinder over an oscillation cycle (as predicted experimentally); this is the classical mode of vortex shedding leading to formation of the Kármán street.     

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.     

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.     

Nonlinear inertial oscillations of a multilayer eddy: An analytical solution

Nonlinear axisymmetric oscillations of a warm baroclinic eddy are considered within the framework of an reduced-gravity model of the dynamics of a multilayer ocean. A class of exact analytical solutions describing pure inertial oscillations of an eddy formation is found. The thicknesses of layers in the eddy vary according to a quadratic law, and the horizontal projections of the velocity in the layers depend linearly on the radial coordinate. Owing to a complicated structure of the eddy, weak limitations on the vertical distribution of density, and an explicit form of the solution, the latter can be treated as a generalization of the exact analytical solutions of this form that were previously obtained for homogeneous and baroclinic eddies in the ocean.     

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。     

Movement of heavy particles in tornadoes

The horizontal movement of inertial particles in the intensive vortices, where the centrifugal force can be substantially higher than the gravity, is studied analytically. A similar problem was studied earlier for small (Stokes) particles at low Reynolds number, which allow one to be limited to the linear resistance law. It is shown that the previous results to a great extent can be extrapolated to the case of considerably heavier particles (e.g., water droplets with a diameter up to 1 mm at Reynolds numbers up to 10³). The nonlinear nature of the resistance, i.e., its dependence on the particle velocity relative to the medium, should be taken into account for such particles. Some general laws are established for particle dynamics. In particular, their tangential velocity is close to the velocity of the medium, while the radial velocity is substantially lower (it is close on the order of magnitude to the geometric mean of the particle tangential velocity and the difference between the latter and the tangential velocity of the medium). The limits of applicability of the results are found, i.e., the restrictions to the size and mass/density of particles.     

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.     

Finite element analysis of two-dimensional nonlinear sloshing problems in random excitations

A two-dimensional nonlinear random sloshing problem is analyzed by the fully nonlinear wave velocity potential theory based on the finite element method. A rectangular container filled with liquid subjected to specified horizontal random oscillations is studied. Both wave elevation and hydrodynamic force are obtained. The spectra of random waves and forces have also been investigated, and the effects of the peak frequencies and spectral width of the specified spectrum used for the generation of the random oscillations are discussed. It is found that the energy mainly concentrates at the natural frequencies of the container and is dominant at the ith order natural frequency when the peak frequency is close to the ith order natural frequency. Some results are compared between the fully nonlinear solutions, the linear solutions and the linear plus second-order solutions.     

Surface manifestations of internal waves investigated by a subsurface buoyant Jet: 1. The mechanism of internal-wave generation

In a large test reservoir with artificial temperature stratification at the Institute of Applied Physics, Russian Academy of Sciences, we have performed a major laboratory simulation of the nonstationary dynamics of buoyant turbulent jets generated by wastewater flows from underwater collector diffusers. The interaction of buoyant jets with the pycnocline leads to an active generation of internal waves. An analysis of the dependence of wave amplitude on the control parameter proportional to the rate of liquid flow from the collector diffuser has indicated that this dependence is adequately described by a function that is characteristic for the presence in the Hopf bifurcation system, which occurs for a soft actuation mode of self-oscillations of the globally instable mode. To check the conditions for the actuation of the globally instable mode, we have performed an auxiliary experiment in a small reservoir with a salt stratification formulated similar to the experiment in the big reservoir. Using the particle image velocimetry (PIV) method, we have measured the velocity field in the buoyant jet and constructed the profiles of transverse velocity in several sections. When the jet approaches the pycnocline, a counterflow is generated at the edges. A stability analysis for the resulting profiles of flow velocities performed by the method of normal modes has revealed that, for the jet portions with counterflow, the condition of absolute instability by the Briggs criterion for axisymmetric jet oscillations is satisfied, which testifies to the fact that the globally instable mode is actuated. The estimates for oscillation frequencies of the globally instable mode are well consistent quantitatively with the measured spectrum of jet oscillations.     

Viscous Effects on Wave Forces on A Submerged Horizontal Circular Cylinder

Numerical simulations are carried out for wave action on a submerged horizontal circular cylinder by means of a viscous fluid model, and it is focused on the examination of the discrepancies between the viscous fluid results and the potential flow solutions. It is found that the lift force resulted from rotational flow on the circular cylinder is always in anti-phase with the inertia force and induces the discrepancies between the results. The influence factors on the magnitude of the lift force, especially the correlation between the stagnation-point position and the wave amplitude, and the effect of the vortex shedding are investigated by further examination on the flow fields around the cylinder. The viscous numerical calculations at different wave frequencies showed that the wave frequency has also significant influence on the wave forces. Under higher frequency and larger amplitude wave action, vortex shedding from the circular cylinder will appear and influence the wave forces on the cylinder substantially.     

杭州湾南部主水道内温度、盐度、潮流的变化特征

本文基于船载及锚定ADCP、CTD观测,获得了大、小潮时的温度、盐度、浊度、潮位、流速等观测数据,研究杭州湾南部的一个主要弯曲航道——螺头水道内的潮流动力学特性。螺头水道水深超过100 m、最大潮差大于2.5 m。涨潮时,强潮流速出现在水道北岸,落潮时,强潮流速出现在水道南岸,最大流速值分别为约2 m/s和1.8 m/s。受压强梯度、密度梯度、科氏力和离心力影响,涨落潮过渡时在水道的横断面产生较为明显的环流。夏季存在较弱的层化现象,深水处受环流的影响,盐度、温度的混合较强。锚定观测数据表明,温度、盐度的变化频率与潮流的变化频率相似,但存在高于M2分潮频率的谱峰值。因此,笔者认为潮流与横向环流的相互作用,可能导致更高频率的盐度和温度变化。     

The asymptotic theory of the generation of long-wave structures in critical layers of weakly dissipative jet flows

The mechanisms of the large-scale vortex structures formation in zonal jet flows (atmospheric blockings, cyclonic, and anticyclonic vortices) is investigated. Nonlinear perturbations formed during the onset of barotropic instability of a long-wave mode in weakly-dissipative and weakly supercritical jet flows with a symmetric velocity profile are considered in the β-plane approximation. This analysis is performed within the framework of the asymptotic theory based on the concept of a nonlinear critical layer. The equations describing the interaction of a wave with vorticity perturbations in a critical layer are derived. The regimes of a quasi-stationary and nonstationary nonlinear critical layer are considered separately. Combined equations of evolution covering the principle regimes of instability development are proposed. The existence of autowave-type structures characterized by a balance between the energy receipt to the wave and its dissipation are obtained within the framework of a numerical simulation. The dependence of the parameters of generated autowave structures on the shape of the zonal jet profile and the flow supercriticality level is studied.