Self-consistent turbulence in the two-dimensional nonlinear Schrödinger equation with a repulsive potential

The dynamics of dark solitons (vortices) with the same topological charge (vorticity) in the two-dimensional nonlinear Schr?dinger (NLS) equation in a defocusing medium is studied. The dynamics differ from those in incompressible media due to the possibility of energy and angular momentum radiation. The problem of the breakup of a multicharged dark soliton, which is a local decrease of the wave function intensity, into a number of chaotically moving vortices with single charge, is studied both analytically and numerically. After an initial period of intensive wave radiation, there emerges a nonuniform, steady turbulent self-organized motion of these vortices which is restricted in space by the size of the potential well of the initial multicharged dark soliton. Separate orbits of finite widths arise in this turbulent motion. That is, the statistical probability to observe a vortex in a given point has maxima near certain points (orbit positions). In spite of the fact that numerical calculations were performed in a finite region, the turbulent distributions of the vortices do not depend on the size of the container when its radius is larger than the size of the potential well of the primary multicharged dark soliton. The steady turbulent distribution of vortices on these orbits can be obtained as the extremal of the Lyapunov functional of the NLS equation, and obeys some simple rules. The first is the absence of Cherenkov resonance with linear (sound) waves. The second is the condition of a potential energy maximum in the region of vortex motion. These conditions give an approximately equidistant disposition of orbits of the same number of vortices on each orbit, which corresponds to a constant rotating velocity. The magnitude of this velocity is mainly determined by the sound velocity. An integral estimation of the self-consistent rotation of the vortex zone is given.     

Dissipative flow and vortex shedding in the Painlevé boundary layer of a Bose-Einstein condensate

This paper addresses the drag force and formation of vortices in the boundary layer of a Bose-Einstein condensate stirred by a laser beam following the experiments of Phys. Rev. Lett. 83, 2502 (1999)]. We make our analysis in the frame moving at constant speed where the beam is fixed. We find that there is always a drag around the laser beam. We also analyze the mechanism of vortex nucleation. At low velocity, there are no vortices and the drag has its origin in a wakelike phenomenon: This is a particularity of trapped systems since the density gets small in an extended region. The shedding of vortices starts only at a threshold velocity and is responsible for a large increase in drag. This critical velocity for vortex nucleation is lower than the critical velocity computed for the corresponding 2D problem at the center of the cloud.     

Characteristic parameters of drift vortices coupled to Alfvén waves in an inhomogeneous space plasma

We present detailed measurements of ion scale vortices of drift type coupled to Alfvén waves in an inhomogeneous and collisionless space magnetoplasma. The two free parameters of a dipolar vortex, intensity and spatial radius, are measured. The vortices are driven by a strong density gradient on a boundary layer with scale size of the same order as the vortex diameter. Observations of vortices off the gradient show that symmetry-breaking conditions in a real inhomogeneous plasma can lead not only to cross-field but also to cross-boundary anomalous transport of particles and energy.     

致密油藏微纳米喉道中的边界层特征

通过引入吸引力修正耗散粒子动力学（DPD）方法,实现流体和固体的相互吸引作用,模拟纳米喉道中的微尺度流动,探讨边界层的产生机理,结合微圆管实验,定量表征微纳米喉道中边界层的特征,明确微纳米喉道中边界层的影响因素.研究发现：分子尺度,热运动对速度影响很大;超过分子尺度,压差占主导作用.热运动使粒子在原位置振动,不改变粒子的整体移动方向.随着喉道半径的增大,泊肃叶流动的抛物线特征越来越明显.边界层厚度受压力梯度、喉道半径和流体粘度的影响.当压力梯度增大或流体粘度减小时,边界层厚度增大;当喉道半径减小时,边界层厚度先增大后减小.边界层厚度是导致非线性渗流特征的根本原因.随着边界层厚度增大,非线性渗流特征越来越明显.     

基于涡流发生器的风洞试验段附面层控制数值模拟

沿试验段侧壁发展的附面层是影响飞行器半模型实验数据精准度的主要因素之一.利用数值模拟方法验证了涡流发生器减小附面层影响的可行性,重点分析了安装角度、结构尺寸、安装位置及个数等设计参数对附面层内速度分布的影响规律,对涡流发生器尾涡强度以及沿流向的发展规律进行了初步探讨.结果表明,涡流发生器产生的尾涡能够有效改善附面层内的速度分布,进而减小附面层厚度,降低附面层影响;涡流发生器的后缘应略高于当地附面层厚度,安装角度、位置、个数等参数必须合理设计以减小涡流发生器对试验段主气流的影响.基于计算结果初步设计了可用于2.4 m跨声速风洞半模试验段的涡流发生器,在亚声速范围内能够减小模型区侧壁附面层厚度66%左右,对核心流Mach数影响小于0.003,为涡流发生器的实际应用提供了依据.      

Finite number of vortices and bending of finite vortex lines in a confined rotating Bose-Einstein condensate

The minimal energy configurations of finite N_v-body vortices in a rotating trapped Bose-Einstein condensate is studied analytically by extending the previous work [Y. Castin, R. Dum, Eur. Phys. J. D 7, 399 (1999)], and taking into account the finite size effects on z-direction and the bending of finite vortex lines. The calculation of the energy of the vortices as a function of the rotation frequency of the trap gives number, curvature, configuration of vortices and width of vortex cores self-consistently. The numerical results show that (1) the simplest regular polynomial of the several vortex configurations is energetically favored; while the hexagonal vortex lattice is more stable than square lattice; (2) bending is more stable then straight vortex line along the z-axis for λ<1; (3) the boundary effect is obvious: compared with the estimation made under infinite boundary, the finite size effect leads to a lower vortex density, while the adding vortex bending results in a less higher density because of the expansion. The results are in well agreement with the other authors' ones.     

Observation of vortex packets in direct numerical simulation of fully turbulent channel flow

A number of experimental studies have inferred the existence of packets of inclined, hairpinlike vortices in wall turbulence on the basis of observations made in two-dimensional x−y planes using visualization and particle image velocimetry (PIV). However, there are very few observations of hairpins in existing three-dimensional studies made using direct numerical simulation (DNS), and no such study claims to have revealed packets. We demonstrate, for the first time, the existence of hairpin vortex packets in DNS of turbulent flow. The vortex packet structure found in the present study at low Reynolds number,Re _t=300, is consistent with and substantiates the observations and the results from twodimensional PIV measurements at higher Reynolds numbers in channel, pipe and boundary layer flows. Thus, the evidence supports the view that vortex packets are a universal feature of wall turbulence, independent of effects due to boundary layer trips or critical conditions in the aforementioned numerical studies. Visualization of the DNS velocity field and vortices also shows the close association of hairpin packets with long low-momentum streaks and the regions of high Reynolds shear stress.     

Fluid particle advection in the vicinity of the Föppl vortex system

Fluid particle advection in the vicinity of the Föppl vortex system is considered. Due to periodic motion of vortices about the Föppl equilibrium, fluid particles within the vortex atmosphere, the fluid region with a velocity field being induced by the vortices, can move chaotic in the sense of exponential divergence of near trajectories. This chaotic motion leads to the vortex atmosphere particles to be carried away from the atmosphere to the exterior flow. In this Letter, the part of the carried away fluid particles is numerically assessed and the dynamics of the fluid release from the vortex atmosphere is demonstrated.     

Simulation of Dynamics in Two-Dimensional Vortex Systems in Random Media

Dynamics in two-dimensional vortex systems with random pinning centres is investigated using molecular dynamical simulations. The driving force and temperature dependences of vortex velocity are investigated. Below the critical depinning force Fc, a creep motion of vortex is found at low temperature. At forces slightly above Fc, a part of vortices flow in winding channels at zero temperature. In the vortex channel flow region, we observe the abnormal behaviour of vortex dynamics： the velocity is roughly independent of temperature or even decreases with temperature at low temperatures. A phase diagram that describes different dynamics of vortices is presented.     

Quantized vortex pair production in 4He films as a boundary-layer problem

We show that the idea of a boundary layer for discrete vortices arises naturally from the equation of motion for the probability distribution of an interacting vortex pair. In contrast with classical hydrodynamics, this boundary layer is of statistical origin, and the method leads to a scaling law for the exact dissociation rate of a bound vortex pair.     

Anisotropic origin of the bending instability of the flux-antiflux interface in type-II superconductors

The physical nature of the macroturbulence in vortex matter in YBCO superconductors is investigated by means of a magneto-optic study of the instability in a single crystal prepared especially for this purpose. The instability develops near those sample edges where the oppositely directed flow of vortices and antivortices, guided by twin boundaries, is characterized by the discontinuity of the tangential component of the hydrodynamic velocity. This fact indicates that the macroturbulence is analogous to the instability of fluid flow at a surface of a tangential velocity discontinuity in classical hydrodynamics and is related to the anisotropic flux motion in the superconductor.     

Superfluid vortex front at T→0: decoupling from the reference frame

Steady-state turbulent motion is created in superfluid (3)He-B at low temperatures in the form of a turbulent vortex front, which moves axially along a rotating cylindrical container of (3)He-B and replaces vortex-free flow with vortex lines at constant density. We present the first measurements on the thermal signal from dissipation as a function of time, recorded at 0.2T(c) during the front motion, which is monitored using NMR techniques. Both the measurements and the numerical calculations of the vortex dynamics show that at low temperatures the density of the propagating vortices falls well below the equilibrium value, i.e., the superfluid rotates at a smaller angular velocity than the container. This is the first evidence for the decoupling of the superfluid from the container reference frame in the zero-temperature limit.     

Visualizing shear stress in Görtler vortex flow

Shear stress distributions were obtained from velocity measurements in a concave surface boundary layer flow in the presence of Görtler vortices by means of a single hot-wire probe for several streamwise (x) locations. A set of vertical wires of 0.20 mm diameter were positioned at a distance of 10 mm upstream from the leading edge of a concave surface of radius of curvature R=1.0 m to pre-set the wavelength of the vortices so to obtain the most amplified wavelength Görtler vortices. Consequently, the wavelength of the vortices was set equal to the wire spacing and preserved downstream. In addition to the high shear regions near the wall, one positive peak at the head of the mushroom-like structures and two relatively weak negative peaks at the vicinity of the low-speed streaks are found in the iso-?u/?y contours. They are believed to be related to the formation of the inflectional point in the velocity profile across boundary layer. The occurrence of the inflection points in the spanwise distributions of streamwise velocity component u is associated with the appearance of the second peak of the ?u/?z shear near the boundary layer edge. The nonlinear effect of Görtler instability is to increase the wall shear stress, and further enhancement beyond the turbulent values is due to the presence of secondary instability.     

Large-Scale Coherent Vortex Formation in Two-Dimensional Turbulence

The evolution of a vortex flow excited by an electromagnetic technique in a thin layer of a conducting liquid was studied experimentally. Small-scale vortices, excited at the pumping scale, merge with time due to the nonlinear interaction and produce large-scale structures—the inverse energy cascade is formed. The dependence of the energy spectrum in the developed inverse cascade is well described by the Kraichnan law k^–5/3. At large scales, the inverse cascade is limited by cell sizes, and a large-scale coherent vortex flow is formed, which occupies almost the entire area of the experimental cell. The radial profile of the azimuthal velocity of the coherent vortex immediately after the pumping was switched off has been established for the first time. Inside the vortex core, the azimuthal velocity grows linearly along a radius and reaches a constant value outside the core, which agrees well with the theoretical prediction.     

Free-surface flows under impacting droplets

A numerical method which fulfils the free-surface boundary conditions and extrapolates the fluid velocity into empty grid cells outside the fluid region on a fixed Cartesian grid system is presented. The complex, three-dimensional, vortex structures formed via surface/vortex interaction and induction between vortices have been computed using the proposed technique implemented within a level-set method for both vertical and oblique droplet impacts in incompressible fluids. The present results have been validated through numerical tests which confirm zero tangential shear at the free-surface and comparisons with experimental observations of cavity and vortex ring formation underneath the impact location. In some cases, transitions from a concentric vortex ring to a fully three-dimensional vortex structure has been confirmed. Whilst the primary vortex ring is initiated at the highly curved contact surface between the droplet and receiving surface, azimuthal instabilities are manifested in the shear layer around the cavity crater developing after the vertical impact, resulting in axial counter-rotating vorticity between the cavity and descending vortex ring. Underlying mechanisms which induce local deformation of the free-surface, creating a so-called scar, due to the sub-surface vortices at the oblique impacts are also discussed.     

高聚物减阻溶液对壁湍流输运过程的影响

基于相同雷诺数下清水和高分子聚合物溶液壁湍流的高时间分辨率粒子图像测速技术(time-resolved particle image velocimetry, TRPIV)的对比实验, 从高聚物溶液对湍流边界层动量能量输运影响的角度分析其减阻的机理. 对比两者的雷诺应力发现高聚物的存在抑制了湍流输运过程. 这一影响与高聚物对壁湍流中占主导地位的涡旋运动和低速条带等相干结构的作用密切相关. 运用条件相位平均、相关函数和线性随机估计(linear stochastic estimation, LSE)等方法, 分析提取了高聚物溶液流场中的发卡涡和发卡涡包等典型相干结构的空间拓扑形态. 相比于清水, 高聚物溶液中相干结构的流向尺度增大, 涡旋运动的发展及低速流体喷射的强度受到削弱, 表明了添加的高聚物阻碍了湍流原有的能量传递和自维持的机理. 正是通过影响相干结构, 高聚物抑制了湍流边界层中近壁区与外区之间的动量和能量输运, 使得湍流的无序性降低, 从而减小了湍流流动的阻力.     

Cherenkov interaction of vortices with a free surface

The interaction of vortex filaments in an ideal incompressible fluid with the free surface of the latter is investigated in the canonical formalism. A Hamiltonian formulation of the equations of motion is given in terms of both canonical and noncanonical Poisson brackets. The relationship between these two approaches is analyzed. The Lagrangian of the system and the Poisson brackets are obtained in terms of vortex lines, making it possible to study the dynamics of thin vortex filaments with allowance for finite thickness of the filaments. For two-dimensional flows exact equations of motion describing the interaction of point vortices and surface waves are derived by transformation to conformal variables. Asymptotic steady-state solutions are found for a vortex moving at a velocity lower than the minimum phase velocity of surface waves. It is found that discrete coupled states of surface waves above a vortex are possible by virtue of the inhomogeneous Doppler effect. At velocities higher than the minimum phase velocity the buoyant rise of a vortex as a result of Cherenkov radiation is described in the semiclassical limit. The instability of a vortex filament against three-dimensional kink perturbations due to interaction with the “image” vortex is demonstrated. Zh. éksp. Teor. Fiz. 115, 894–919 (March 1999)     

Unsteady wake vortices in jets in cross-flow

Abstract  

The current flow visualization study investigates unsteady wake vortices of jets in cross-flow in order to (1) advance the understanding of their origin and characteristics and (2) explore various excitation techniques for organizing and accentuating them. An isolated circular jet passed through a nozzle and entered the cross-flow normal to the wall. Free stream velocities up to 5 m/s and jet-to-cross-flow velocity ratio range between 1 and 10 were covered. While mechanical perturbation did not result in any significant periodic organization of the wake vortices, the database obtained for the unperturbed flow provided further insight into their behavior. The key finding was that the wake vortices always originated from the lee-side of the jet where the jet efflux boundary layer and the wall boundary layer intersected. In no case these vortices were seen to form either from the wall boundary layer or the jet shear layer at downstream locations. After formation the wake vortex twists and stretches as it convects downstream with the base still attached to the near-wall region on the jet’s lee side. The top remains connected to the underside of the jet where the tracer particles dissipate due to high turbulence in the shear layer.     

A study on drag reduction of a rotationally oscillating circular cylinder at low Reynolds number

The flow field around a rotationally oscillating circular cylinder in a uniform flow is studied by using a particle image velocimetry to understand the mechanism of drag reduction and the corresponding suppression of vortex shedding in the cylinder wake at low Reynolds number. Experiments are conducted on the flow around the circular cylinder under rotational oscillation at forcing Strouhal number 1, rotational amplitude 2 and Reynolds number 2,000. It is found from the flow measurement by PIV that the width of the wake is narrowed and the velocity fluctuations are reduced by the rotational oscillation of the cylinder, which results in the drag reduction rate of 30%. The mechanism of drag reduction is studied by phase-averaged PIV measurement, which indicates the formation of periodic small-scale vortices from both sides of the cylinder. It is found from the cross-correlation measurement between the velocity fluctuations that the large-scale structure of vortex shedding is almost removed in the cylinder wake, when the small-scale vortices are generated at the unstable frequency of shear layer by the influence of rotational oscillation.