Interaction and “apparent” reconnection of 3D vortex tubes via direct numerical simulations

We present evidence of: “binding” of anti-parallel vortex tube segments; strong noncircular core development; evolution of new secondary finger-like vortex structures: and finally “apparent” vortex reconnections due to entanglement. The latter three processes are not present in Biot-Savart filament simulations.     

Vortex dynamics simulation of interacting vortex rings and filaments

Interaction between a vortex ring and a vortex filament of the same strength has been simulated by a three-dimensional vortex method which employs vortex arrows with the Rosenhead-Moore core structure. The power spectrum of the velocity field and the enstrophy spectrum are obtained in a closed form whose limit of the core radius tending to zero is equivalent to that given be Aksman et al. (1985) Phys. Rev. Lett. 54. 2410. Four basic modes of the interaction are shown to exist. Temporal evolution of the spectrum during the interaction is also obtained for the basic modes: the energy of the velocity field is generally transferred to the high-wavenumber range as the interaction proceeds.     

Spiral Waves in Three-Dimensional Helical Viscous Flows

A study is made of an unbounded viscous incompressible flow in the case in which the vortex lines of the absolute motion coincide with the streamlines of the relative motion; after Joukowsky, this flow is called helical flow. The vector potential of the flow is constructed and the notion of the stream function is generalized to include three-dimensional uniform helical flows in an arbitrary orthogonal coordinate system. It is shown that both axisymmetric and asymmetric waves may propagate in a rotating fluid; the amplitude of these waves decays exponentially with time, the decrement being proportional to the square of the rotational velocity of the fluid and the kinematic viscosity and inversely proportional to the square of the phase velocity.     

IMPLEMENTATION OF VORTEX FILAMENT METHODS ON PARALLEL MACHINES WITH DISTRIBUTED ADAPTIVE DATA STRUCTURE

This paper addressed the implementation of vortex filament methods on parallel machines with distributed memory to simulate a three-dimensionally evolving jet. Vortical structure developments due to Kelvin–Helmholtz instability of the axially perturbed jet are also examined. The implementation is conducted in a single-programme multiple-data (SPMD) environment and the parallelism is focused on issues of data distribution, efficient support of parallel I/O and overlapping of communications with computations. In addition, since the number of segment markers in a filament is dynamically growing according to the requirement of numerical accuracy, a novel packet-oriented data structure is proposed not only to partition filament segment markers among distributed processors but also to support dynamical load balancing at run time. This work is the first to apply packet-oriented structures to implement a parallel vortex filament method. Experimental results indicate performance improvement from 1·5 to 2·6 times over static schemes on nCUBE2, DEC Alpha and IBM SP2 by incorporating the proposed scheme with packet-oriented structures. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 939–951, 1997.     

Effusing core at the center of A potential vortex

Experiments were carried out to measure the base pressure distribution of a flow field induced by a potential vortex with its axis normal to a stationary disk. The center base pressure coefficient of the vortex, C₀(0), was found to be proportional to Reynolds number from Re = 2.0 × 10³ to Re > 2.5 × 10⁴, where Re is based on the disk radius and azimuthal velocity at the disk edge. This behavior of C₀(0) is at variance with the experimental results of Phillips (Phys. Fluids, 27, 2215, 1984) and Khoo (M. Eng. Thesis, Natl. Univ. Singapore, 1984), which showed vastly different trends depending on Re. Plausible reasons are suggested for the apparent discrepancies observed. Finally, the extent of the effusing core at the center, r₁ (taken to be the radial position where departure from the outer potential flow took place), was found to be proportional to Re^−1/2 for all Re values considered.     

Formation of vortex street and vortex pair from a circular cylinder oscillating in water

The flow around a circular cylinder undergoing sinusoidal oscillating movement in still water is investigated by phase-locked PIV measurements. The pattern and development of large-scale vortex structures in the flow are studied from the velocity vectors and vorticity contours obtained at eight successive phases of an oscillating cycle. Experiments are performed at three Keulegan–Carpenter numbers; KC=12, 6.28 and 4.25. Results at KC=12 reveal the mechanism of vortex formation and the development of the shed vortices into a vortex street at a lateral direction to the line of cylinder movement. The role of a biased flow stream and the length of the cylinder stroke in the formation of the vortex street are discussed. At the lower KC numbers, a symmetric pair of vortices is found attached to the leeward face of the cylinder. The vortex pair exhibits an increasing degree of asymmetry when KC increases from 4.25 to 6.28. An explanation in terms of the length of the cylinder strokes and the degree of flow asymmetry is offered for the transition of flow regimes from a vortex pair to a vortex street. The present results are compared with the observations made in previous experimental and numerical studies in the literature.     

Pseudo-canonical formulation of 3-dimensional vortex motion and vorton model analysis

From the author's pseudo-canonical formulation of 3-dimensional vortex motion, the basic equations for the vorton model are derived. The division of vorton and reduction of meshes of time integration are assumed, in numerical calculations. This method is applied to numerical studies on evolutions of a connected 3-ring vortex and a vortex ring inside or outside a sphere. These seem to show cutting of the vortex filament and the following reconnection or attachment to the wall. The dissipation effect due to the approximation scheme and the singularity of vorton are discussed.     

Vortex on the surface of a viscous fluid

The system of Navier-Stokes equations is solved for boundary conditions corresponding to the case when an axisymmetric tangential transversal load acts at the surface of a gravity viscous incompressible fluid of infinite depth. An integral representation is obtained for the shape of the free surface under the prolonged effect of a stationary vortex load. The example of a tangential load, similar to a concentrated vortex, is examined. In this case a column is squeezed out of the fluid, the height of the column being directly proportional to the square of the moment of the transverse tangential forces and inversely proportional to the square of the product of the dynamic fluid viscosity and the area of the tangential stress distribution. The depth of the annular funnel being formed in front of the column is determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 127–132, July–August, 1978.     

Vortex shedding behind rings and discs

The wake structure of discs and bluff rings has been investigated experimentally in a wind tunnel. The rings have an inner diameter d_i, and an outer diameter d_o and are classified according to the parameter (d_o + d_i)/(d_o − d_i) = d/w. the ratio of mean diameter to ring width. As d/w → ∞ the flow approaches that around a two dimensional bluff body whereas as d/w tends to unity the body approaches a solid disc. A distinct change in the vortex shedding pattern is found around d/w = 5. Below this critical value velocity fluctuations in the wake have a weak periodic component which is 180° out of phase across a diameter of the body. Above d/w = 5. regular and coherent axisymmetric vortex ring shedding is observed with shedding occurring alternately from the inner and outer circumferences of the bluff body. Flow visualization and conditional averaging of hot-wire data are used to investigate the vortex structure.     

Drag reduction of square cylinders with cut-corners at the front edges

Flow around square cylinders with cut-corners at the front edges is investigated using particle image velocimetry. It is found that drag reduction can be achieved for the tested cut-corner dimensions. The mechanism for the drag reduction is explored on the statistical and structural aspects of the flow. After cutting the corners, the fluctuation intensity of the wake is weakened, the length of the recirculation region behind the square cylinder is increased, while the width of the wake decreases. It is found that the drag coefficient is proportional to the minimum wake width, and the Strouhal number St is inversely proportional to the minimum wake width. It is revealed that the reduced wake width is due to the suppressed separation over the side surfaces for the cylinders with cut-corners at the front edges. On the structural aspect, the phase-averaged flow field and the modes from proper orthogonal decomposition both indicate a decrease in the wake vortex size. A statistical analysis of instantaneous vortices based on Oseen vortex fit reveals that not only the size of the vortex is reduced, but also the strength is weakened.     

Investigation on vortex shedding of a swept-back wing

Effects of Reynolds number and angle of attack on the vortex shedding of a finite swept-back wing are experimentally studied. The cross-sectional profile of the wing is NACA 0012, and the sweep-back angle is 15° The time series signals detected by hot-wire in the wake region shows four distinct behaviors: laminar, subcritical, transitional, and supercritical. The derived Strouhal number curves are significantly different in these four behaviors. In addition, the statistical properties of turbulence, that is, the power spectrum density function, probability density function, correlation coefficient, Lagrangian integral time scales, and length scales are also presented in this paper.     

Evolution of a vortex street in the far wake of a cylinder

The evolution of a primary vortex street shed from a circular cylinder in the far wake is experimentally examined for 70 R 154 (R is the Reynolds number). According to the vorticity fields obtained using digital image processing for visualized flow fields, the primary vortex street breaks down into a nearly parallel shear flow of Gaussian profile at a certain downstream distance, before a secondary vortex street of larger scale appears further downstream. The process leading to the nearly parallel flow can be explained as the evolution of the vortex regions of an inviscid fluid if we invoke the observation that the distance between the two rows in the primary vortex street increases with the downstream distance, although the viscous effect probably contributes to this increase. Numerical computations with the discrete vortex method also support this explanation. The wavelengths and speeds of the primary and secondary vortex street are also measured.     

Asymptotic model of the axisymmetric breakdown of a vortex filament in an incompressible fluid

The axisymmetric flow of an incompressible fluid is considered. An exact solution of the Euler equations corresponding to the breakdown of a straight vortex filament of intensity ₀ into a vortex filament of lesser intensity and a conical vortex surface is obtained. It is shown that beyond the breakdown point in the region bounded by the conical vortex surface reverse flows occur. An investigation of the problem with allowance for viscous effects at large Reynolds numbers makes it possible to establish a relation between the free parameters entering into the solution of the Euler equations. The results obtained are useful for investigating the problem of the breakdown of a swirled jet, whose solution has recently been receiving much attention [1, 2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 47–52, November–December, 1989.     

Viscous dissipation of Rankine vortex profile in zero meridional flow

An analytical solution is given for a time-decay Rankine vortex profile due to viscous effects. The vortex filament is assumed to be isolated, strong, concentrated and having zero-meridional flow (i.e. radial and axial velocities are equal to zero). Zero-meridional renders the governing equations for an unsteady, incompressible and axisymmetric vortex in a simple form. Based on the tangential momentum equation, the spatial-temporal distributions of the swirl velocity are given in terms of Fourier-Bessel series by using separation of variables technique. A general formula is derived by total differentiation of the swirl velocity with respect to time, depicting the viscous dissipation for Oseen and Taylor-like vortex profiles. This analysis is validated by comparison with previous experimental data.     

圆盘近尾迹流场相关谱分析

对Re=22 000 时径厚比D/h=5 圆盘近尾迹开展大涡模拟数值研究. 通过对x/D=1, 2 和8 处脉动速度进行快速傅里叶变换（fast Fourier transformation, FFT）,发现3 个特征频率：斯特劳哈尔数St₂=0.123 为自然脱落频率,与文献结果相符;较小频率St₁=0.035,与回流区伸缩和剪切层附近涡旋脱落点的旋转相关;高频率St₃=1.3～1.7 则与剪切层湍流结构相关. 通过分析截面r/D=2.8 圆周上两点间流向速度相关系数、相干谱和相位谱,发现相关系数受涡旋脱落影响出现以30°或45°为周期的正负波动,表明轴面上涡旋脱落点具有随机性.     

Singularity formation in three-dimensional inviscid flow

A phenomenological model to explain finite time singularity formation in a three-dimensional inviscid vorticity field is given. The thin filament approximation for a vorticity field is used, and the model is based on the three-dimensional interaction of two approximately straight vortex filaments. It is shown that the model has a solution which exhibits finite time singularity formation in a vorticity field.     

Viscous dissipation of Rankine vortex profile in zero meridional flow

An analytical solution is given for a time-decay Rankine vortex profile due to viscous effects. The vortex filament is assumed to be isolated, strong, concentrated and having zero-meridional flow (i.e. radial and axial velocities are equal to zero). Zero-meridional renders the governing equations for an unsteady, incompressible and axisymmetric vortex in a simple form. Based on the tangential momentum equation, the spatial-temporal distributions of the swirl velocity are given in terms of Fourier-Bessel series by using separation of variables technique. A general formula is derived by total differentiation of the swirl velocity with respect to time, depicting the viscous dissipation for Oseen and Taylor-like vortex profiles. This analysis is validated by comparison with previous experimental data. The English text was polished by Yunming Chen.     

Generalised vortex rings with and without swirl

Steady solutions of the Euler equations for flow of an inviscid incompressible fluid may be obtained by considering the process of magnetic relaxation to analogous magnetostatic equilibria in a viscous perfectly conducting fluid. In particular, solutions which represent rotational disturbances propagating without change of structure in an unbounded fluid may be obtained by this method. When conditions are axisymmetric, these disturbances are vortex rings of general structure, which may include a swirl component of velocity. This situation is analysed in some detail, and it is shown that the vortex is characterised by two functions: V(ψ), the volume within toroidal surfaces ψ = cst. and W(ψ), the toroidal volume flux inside the torus ψ = cst. For each choice of {V(ψ), W(ψ)}, satisfying appropriate limit conditions, there exists at least one vortex ring of steady structure.     

薄矩形柱绕流旋涡脱落的抑制

用窄条形控制件对截面宽度为B、厚度为H的矩形柱体绕流的旋涡脱落进行抑制.实验在风洞中进行, 实验范围为B/H=2.0~5.0,Re=V_∞H/\nu=3.75× 103~1.05×104. 矩形柱的宽边B与来流平行, 窄条与柱体等长, 且两者轴线相互平行放置. 窄条宽度为b/H=0.5, 窄条厚度远小于其宽度; 窄条位置可变, 但窄条表面保持与来流垂直. 尾流脉动速度测量和流动显示结果表明: 当窄条位于一个有效区内时, 矩形柱体两侧的旋涡脱落被抑制; 而当窄条位于一个单侧有效区内时, 矩形体一侧的旋涡脱落被抑制, 在另一侧旋涡脱落却仍存在. 有效区范围从矩形体的上游某点一直延续到矩形体的下游某点. 单侧有效区将整个有效区围在其中. 有效区和单侧有效区范围随着B/H的增大而增大, 但随着Re的增大而减小.      

Self-similar collapse of 2D and 3D vortex filament models

In this article, a very simple toy model for a candidate blow-up solution of the Euler equation by Boratav and Pelz (vortex dodecapole) is investigated. In this model, vortex tubes are replaced with straight vortex filaments of infinitesimal thickness, and the entire motion is monitored by tracing the motion of a representative point on one vortex filament. It is demonstrated that this model permits a self-similar collapse solution which provides the time dependence of the length scale as (t _c ? t)^1/2, (t < t _c), where the collapse time t _c depends on the initial configuration. From the conservation of circulation, this time dependence implies that vorticity ω scales as (t _c ? t) ^?1, which agrees with the one observed in the direct numerical (pseudo spectral) simulations of the vortex dodecapole. Finally, possible modification of the model is considered.