The formation of vortex streets

1962 ◽  
Vol 13 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Frederick H. Abernathy ◽  
Richard E. Kronauer
Keyword(s):  
Incompressible Fluid ◽  
Vortex Street ◽  
Bluff Bodies ◽  
Two Dimensional ◽  
Vortex Sheets ◽  
Linear Interaction ◽  
Inviscid Incompressible Fluid ◽  
Fixed Distance ◽  
Vortex Streets ◽  
Non Linear

The formation of vortex streets in the wake of two-dimensional bluff bodies can be explained by considering the non-linear interaction of two infinite vortex sheets, initially a fixed distance, h, apart, in an inviscid incompressible fluid. The interaction of such sheets (represented in the calculation by rows of point-vortices) is examined in detail for various ratios of h to the wavelength, a, of the initial disturbance. The number and strength of the concentrated regions of vorticity formed in the interaction depend very strongly on h/a. The non-linear interaction of the two vortex sheets explains both the cancellation of vorticity and vortex-street broadening observed in the wakes of bluff bodies.

scholarly journals Some Nonlinear Vortex Solutions

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Michael C. Haslam ◽  
Christopher J. Smith ◽  
Ghada Alobaidi ◽  
Roland Mallier
Keyword(s):  
Steady State ◽  
Incompressible Fluid ◽  
Poisson Equation ◽  
Specific Form ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Vortex Solutions

We consider the steady-state two-dimensional motion of an inviscid incompressible fluid which obeys a nonlinear Poisson equation. By seeking solutions of a specific form, we arrive at some interesting new nonlinear vortex solutions.

Large-amplitude motions of a liquid—vapour interface in an accelerating container

1969 ◽  
Vol 35 (1) ◽  
pp. 77-96 ◽  
Author(s):  
L. M. Perko
Keyword(s):  
Surface Tension ◽  
Incompressible Fluid ◽  
Numerical Method ◽  
Large Amplitude ◽  
Linear Method ◽  
Initial Development ◽  
Inviscid Incompressible Fluid ◽  
Non Linear ◽  
Large Amplitude Motions

This paper considers the large-amplitude symmetric and asymmetric irrota-tional motion of an inviscid incompressible fluid with a liquid—vapour interface in an accelerating container of revolution. A combined analytical—numerical method which involves no linearizations in the hydrodynamical equations and applies to all but surface-tension dominated motions is used to compute a variety of such motions. One important aspect of this non-linear method is that it accurately determines the initial development of surface instabilities such as breakers near the wall of the container.

The aerodynamic forces on an oscillating aerofoil in a free jet

1955 ◽  
Vol 229 (1177) ◽  
pp. 235-250 ◽  
Keyword(s):  
Wind Tunnel ◽  
Incompressible Fluid ◽  
Classical Theory ◽  
Direct Application ◽  
Two Dimensional ◽  
Aerodynamic Forces ◽  
Small Oscillations ◽  
Free Jet ◽  
Inviscid Incompressible Fluid ◽  
Wind Tunnel Measurements

The forces acting on an aerofoil placed centrally in a two-dimensional jet of inviscid incompressible fluid are calculated exactly for the case when the aerofoil is performing small oscillations about its mean position. The theory is a generalization of the classical theory due to Theodorsen and others for an oscillating aerofoil in an infinite stream. The results, which are expressed in terms of a ‘generalized Theodorsen function’, have a direct application to the correction of open-jet wind-tunnel measurements on oscillating aerofoils.

scholarly journals Non-stationary vortex streets in shear flows

2019 ◽  
Vol 55 (6) ◽  
pp. 127-138
Author(s):  
М. V. Кalashnik ◽  
О. G. Chkhetiani
Keyword(s):  
Shear Flows ◽  
Vortex Street ◽  
Two Dimensional ◽  
Free Shear Layer ◽  
Horizontal Shear ◽  
Vortex Streets ◽  
Stationary Vortex ◽  
Spatially Periodic ◽  
Current Lines ◽  
Vorticity Transport

Spatially periodic vortex systems that form due to unstable shear flows are called vortex streets. A number of exact and asymptotic solutions of two-dimensional hydrodynamic equations describing nonstationary vortex streets have been constructed. It is shown that the superposition of the flow with a constant horizontal shear and its perturbations in the form of a nonmodal wave provides an exact solution that describes a nonstationary vortex street with rotating elliptic current lines. The width of the zone occupied by such a vortex street has been determined. The equation of separatrix separating vortex cells with closed current lines from an external meandering flow has been obtained. The influence of the quasi-two-dimensional compressibility and beta effect on the dynamics of vortex streets has been studied based on the potential vorticity transport equation. The solutions describing the formation of vortex streets during the development of an unstable zonal periodic flow and a free shear layer have been constructed using a longwave approximation.

Evolution and breakdown of a vortex street in two dimensions

1981 ◽  
Vol 109 ◽  
pp. 435-463 ◽  
Author(s):  
Hassan Aref ◽  
Eric D. Siggia
Keyword(s):  
Opposite Sign ◽  
Initial Perturbation ◽  
Subsequent Development ◽  
Two Dimensions ◽  
Point Vortices ◽  
Vortex Street ◽  
Turbulent Shear ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Vortex Sheets

The initial-value problem defined by two parallel vortex sheets of opposite sign is studied. Strictly two-dimensional, incompressible, nearly inviscid dynamics is assumed throughout. The roll-up of the sheets into a vortex street is simulated numerically using 4096 point vortices. Much longer runs than in previous work are performed, and it is found that only for a finite range of values of the ratio, h/λ, of sheet separation to perturbation wavelength, does a long-lived vortex street emerge. For h/λ [gsim ] 0·6 a pairing transition within each row intervenes. For h/λ [lsim ] 0·3 we find oscillatory modes.Using up to 16384 point vortices, we also study the breakdown of the metastable street to a two-dimensional, turbulent shear flow. The vortex blobs that made up the street may merge with others of the same sign after the breakdown, but otherwise persist throughout the turbulent regime. Neither their disintegration nor amalgamation with vortices of opposite sign was observed. Using dimensional arguments we derive the relevant scaling theory, and show that it applies to a flow started from two random vortex sheets. The resulting turbulence is not self-similar. For the turbulent flow that follows from the breakdown of a regular vortex street two length scales with different power-law growth in time appear to be necessary. The important differences in the asymptotic structure of flows initialized from random and regular sheets leads us to question the idea of universality. The influence of the symmetry of the initial perturbation on the subsequent development is also considered.

scholarly journals Transition to the secondary vortex street in the wake of a circular cylinder

2019 ◽  
Vol 867 ◽  
pp. 691-722 ◽  
Author(s):  
Hongyi Jiang ◽  
Liang Cheng
Keyword(s):  
Circular Cylinder ◽  
Transverse Velocity ◽  
Broad Band ◽  
Flow Characteristics ◽  
Vortex Street ◽  
Bluff Bodies ◽  
Secondary Vortex ◽  
Frequency Spectra ◽  
Vortex Streets ◽  
Merging Process

Instabilities and flow characteristics in the far wake of a circular cylinder are examined through direct numerical simulations. The transitions to the two-layered and secondary vortex streets are quantified by a new method based on the time-averaged transverse velocity field. Two processes for the transition to the secondary vortex street are observed: (i) the merging of two same-sign vortices over a range of low Reynolds numbers ($Re$) between 200 and 300, and (ii) the pairing of two opposite-sign vortices, followed by the merging of the paired vortices into subsequent vortices, over a range of $Re$ between 400 and 1000. Single vortices may be generated between the merging cycles due to mismatch of the vortices. The irregular merging process results in flow irregularity and an additional frequency signal $f_{2}$ (in addition to the primary vortex shedding frequency $f_{1}$) in the two-layered and secondary vortex streets. In particular, a gradual energy transfer from $f_{1}$ to $f_{2}$ with distance downstream is observed in the two-layered vortex street prior to the merging. The frequency spectra of $f_{2}$ are broad-band for $Re=200$–300 but become increasingly sharp-peaked with increasing $Re$ because the vortex merging process becomes increasingly regular. The ratio of the sharp-peaked frequencies $f_{2}$ and $f_{1}$ is equal to the ratio of the numbers of vortices observed after and before the merging. The general conclusions drawn from a circular cylinder are expected to be applicable to other bluff bodies.

scholarly journals Two-dimensional simulations of internal gravity waves in the radiation zones of intermediate-mass stars

2020 ◽  
Vol 497 (4) ◽  
pp. 4231-4245 ◽  
Author(s):  
R P Ratnasingam ◽  
P V F Edelmann ◽  
T M Rogers
Keyword(s):  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Two Dimensional ◽  
Intermediate Mass ◽  
Single Wave ◽  
Linear Interaction ◽  
Generation Spectrum ◽  
Non Linear ◽  
Hydrodynamical Simulations ◽  
Spectrum Slope

ABSTRACT Intermediate-mass main-sequence stars have large radiative envelopes overlying convective cores. This configuration allows internal gravity waves (IGWs) generated at the convective–radiative interface to propagate towards the stellar surface. The signatures of these waves can be observed in the photometric and spectroscopic data from stars. We have studied the propagation of these IGWs using two-dimensional (2D) fully non-linear hydrodynamical simulations with realistic stellar reference states from the 1D stellar evolution code, Modules for Stellar Astrophysics (mesa). When a single wave is forced, we observe wave self-interaction. When two waves are forced, we observe non-linear interaction (i.e. triadic interaction) between these waves forming waves at different wavelengths and frequencies. When a spectrum of waves similar to that found in numerical simulations is forced, we find that the surface IGW frequency slope is consistent with recent observations. This power law is similar to that predicted by linear theory for the wave propagation, with small deviations that can be an effect of non-linearities. When the same generation spectrum is applied to 3 M⊙ models at different stellar rotation and ages, the surface IGW spectrum slope is very similar to the generation spectrum slope.

The distortion of a bubble in a corner flow

2000 ◽  
Vol 11 (2) ◽  
pp. 171-179 ◽  
Author(s):  
E. OZUGURLU ◽  
J.-M. VANDEN-BROECK
Keyword(s):  
Incompressible Fluid ◽  
Numerical Solutions ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Corner Flow

The distortion of a two-dimensional bubble (or drop) in a corner flow of an inviscid incompressible fluid is considered. Numerical solutions are obtained by series truncation. The results confirm and extend previous calculations.

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