scholarly journals The nature of bubble entrapment in a Lamb–Oseen vortex

2021 ◽  
Vol 33 (6) ◽  
pp. 061702
Author(s):  
Ryan Kelly ◽  
David B. Goldstein ◽  
Saikishan Suryanarayanan ◽  
Marcos Botto Tornielli ◽  
Robert A. Handler
Keyword(s):  
Oseen Vortex

Oseen vortex as a maximum entropy state of a two dimensional fluid

2011 ◽  
Vol 23 (7) ◽  
pp. 075104 ◽  
Author(s):  
D. C. Montgomery ◽  
W. H. Matthaeus
Keyword(s):  
Maximum Entropy ◽  
Two Dimensional ◽  
Oseen Vortex

The Okubo-Weiss criterion in hydrodynamic flows:Geometric aspects and further extension

2022 ◽  
Author(s):  
Bhimsen Shivamoggi ◽  
G Heijst ◽  
Leon Kamp
Keyword(s):  
Flow Field ◽  
Polar Coordinates ◽  
Coriolis Parameter ◽  
Laminar Jet ◽  
Type Criterion ◽  
Burgers Vortex ◽  
2D Flow ◽  
Flow Configurations ◽  
Elliptic Regions ◽  
Oseen Vortex

Abstract The Okubo [5]-Weiss [6] criterion has been extensively used as a diagnostic tool to divide a two-dimensional (2D) hydrodynamical flow field into hyperbolic and elliptic regions and to serve as a useful qualitative guide to the complex quantitative criteria. The Okubo-Weiss criterion is frequently validated on empirical grounds by the results ensuing its application. So, we will explore topological implications into the Okubo-Weiss criterion and show the Okubo-Weiss parameter is, to within a positive multiplicative factor, the negative of the Gaussian curvature of the underlying vorticity manifold. The Okubo-Weiss criterion is reformulated in polar coordinates, and is validated via several examples including the Lamb- Oseen vortex, and the Burgers vortex. These developments are then extended to 2D quasi- geostrophic (QG) flows. The Okubo-Weiss parameter is shown to remain robust under the -plane approximation to the Coriolis parameter. The Okubo-Weiss criterion is shown to be able to separate the 2D flow-field into coherent elliptic structures and hyperbolic flow configurations very well via numerical simulations of quasi-stationary vortices in QG flows. An Okubo-Weiss type criterion is formulated for 3D axisymmetric flows, and is validated via application to the round Landau-Squire Laminar jet flow.

The Effect of Non-Normality of Navier-Stokes Operator Mechanism on Dynamics of an Axisymmetric Swirling Flow

2013 ◽  
Vol 681 ◽  
pp. 72-78
Author(s):  
Cheng Chen ◽  
Ya Yong Shi
Keyword(s):  
Swirling Flow ◽  
Initial Perturbation ◽  
Fluid Motion ◽  
Nonlinear Behavior ◽  
Stokes Operator ◽  
Navier Stokes ◽  
Transient Growth ◽  
Optimal Perturbation ◽  
Energy Growth ◽  
Oseen Vortex

The effect of non-normality of the Navier-Stokes operator on the dynamics of an axisymmetric swirling flow, namely, the Oseen vortex, has been investigated. The eigenvalue analysis and transient growth analysis have been employed in order to obtain the least stable eigenmode and the global optimal perturbation, which are both considered as the initial perturbation. Three stages of dynamic process have been put into evidence for the evolution of the optimal perturbation. The early (linear) stage is characterized by the amplification of radial perturbation, consistent with the prediction of transient growth theory. Having come into the nonlinear stage, the perturbation energy growth is suppressed by the interaction between the vortex ring and the Oseen vortex core. Finally, the phenomena of secondary energy growth are also observed. Compared with the results obtained by applying the least stable eigenmode as the initial disturbance, the nonlinear behavior of the optimal perturbation features radial fluid motion and the rapid production of small eddies, which are both thought to be beneficial to fluid entrainment or mixing. The effect of perturbation amplitude on the nonlinear evolution of flows is also studied.

A stochastic Lamb–Oseen vortex solution of the 2D Navier–Stokes equations

2009 ◽  
Vol 26 (12) ◽  
pp. 1756-1763 ◽  
Author(s):  
J. L. Sereno ◽  
J. M. C. Pereira ◽  
J. C. F. Pereira
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vortex Solution ◽  
Oseen Vortex

The vortex line in steady, incompressible Oseen flow

2005 ◽  
Vol 462 (2066) ◽  
pp. 391-401 ◽  
Author(s):  
Edmund Chadwick
Keyword(s):  
Velocity Field ◽  
Vortex Line ◽  
Horseshoe Vortex ◽  
Transverse Plane ◽  
Far Field ◽  
Two Dimensional ◽  
Streamwise Direction ◽  
Oseen Flow ◽  
Laminar Wake ◽  
Oseen Vortex

The horseshoe vortex is given in Oseen flow as a constant spanwise distribution of lift Oseenlets. From this, the vortex line is represented in steady, incompressible Oseen flow. The velocity near to the vortex line is determined, as well as near to and far from the far field wake. The velocity field in the transverse plane near to the vortex line is shown to approximate to the two-dimensional Lamb–Oseen vortex, and the velocity field in the streamwise direction is generated by the bound vortex line of the horseshoe vortex giving a streamwise decay much faster than that of the Batchelor vortex. The far field wake description is shown to be consistent with laminar wake theory.

Viscous stability properties of a Lamb–Oseen vortex in a stratified fluid

2010 ◽  
Vol 645 ◽  
pp. 255-278 ◽  
Author(s):  
XAVIER RIEDINGER ◽  
STÉPHANE LE DIZÈS ◽  
PATRICE MEUNIER
Keyword(s):  
Unstable Mode ◽  
Temporal Stability ◽  
Three Dimensional ◽  
Normal Modes ◽  
Reynolds Numbers ◽  
Boussinesq Approximation ◽  
Stability Properties ◽  
Displacement Mode ◽  
Ring Mode ◽  
Oseen Vortex

In this work, we analyse the linear stability of a frozen Lamb–Oseen vortex in a fluid linearly stratified along the vortex axis. The temporal stability properties of three-dimensional normal modes are obtained under the Boussinesq approximation with a Chebychev collocation spectral code for large ranges of Froude numbers and Reynolds numbers (the Schmidt number being fixed to 700). A specific integration technique in the complex plane is used in order to apply the condition of radiation at infinity. For large Reynolds numbers and small Froude numbers, we show that the vortex is unstable with respect to all non-axisymmetrical waves. The most unstable mode is however always a helical radiative mode (m = 1) which resembles either a displacement mode or a ring mode. The displacement mode is found to be unstable for all Reynolds numbers and for moderate Froude numbers (F ~ 1). The radiative ring mode is by contrast unstable only for large Reynolds numbers above 104 and is the most unstable mode for large Froude numbers (F > 2). The destabilization of this mode for large Froude numbers is shown to be associated with a resonance mechanism which is analysed in detail. Analyses of the scaling and of the spatial structure of the different unstable modes are also provided.

Inviscid waves on a Lamb–Oseen vortex in a rotating stratified fluid: consequences for the elliptic instability

2008 ◽  
Vol 597 ◽  
pp. 283-303 ◽  
Author(s):  
STÉPHANE LE DIZÈS
Keyword(s):  
Plane Waves ◽  
Stratified Fluid ◽  
Lagrangian Description ◽  
Small Range ◽  
Local Approach ◽  
Coriolis Parameter ◽  
Centrifugal Instability ◽  
Local Plane ◽  
Core Modes ◽  
Oseen Vortex

The inviscid waves propagating on a Lamb–Oseen vortex in a rotating medium for an unstratified fluid and for a strongly stratified fluid are analysed using numerical and asymptotic approaches. By a local Lagrangian description, we first provide the characteristics of the local plane waves (inertia–gravity waves) as well as the local growth rate associated with the centrifugal instability when the vortex is unstable. A global WKBJ approach is then used to determine the frequencies of neutral core modes and neutral ring modes. We show that these global Kelvin modes only exist in restricted domains of the parameters. The consequences of these domain limitations for the occurrence of the elliptic instability are discussed. We argue that in an unstratified fluid the elliptic instability should be active in a small range of the Coriolis parameter which could not have been predicted from a local approach. The wavenumbers of the sinuous modes of the elliptic instability are provided as a function of the Coriolis parameter for both an unstratified fluid and a strongly stratified fluid.

An experimental study of the effect of external turbulence on the decay of a single vortex and a vortex pair

2011 ◽  
Vol 670 ◽  
pp. 214-239 ◽  
Author(s):  
J. P. J. van JAARSVELD ◽  
A. P. C. HOLTEN ◽  
A. ELSENAAR ◽  
R. R. TRIELING ◽  
G. J. F. van HEIJST
Keyword(s):  
Vortex Breakdown ◽  
Symmetry Plane ◽  
Vortex Pair ◽  
Azimuthal Velocity ◽  
Single Vortex ◽  
Image Velocimetry ◽  
Vortex Centre ◽  
Observed Behaviour ◽  
External Turbulence ◽  
Oseen Vortex

This study is concerned with the effect of external turbulence on the decay of vortices. Single vortices and vortex pairs were generated with wing(s) mounted in the sidewalls of a wind tunnel. The distance between the two vortices could be adjusted such that they just touched each other or overlapped. The intensity of the turbulence could be controlled with a turbulence grid. The development of the vortex was measured at a number of downstream stations with particle image velocimetry for a range of wing settings. The results indicate that the single vortex can be described by the ‘two length scales’ model of Jacquin, Fabre & Geffroy (AIAA, vol. 1038, 2001, p. 1). A vortex core, which decays like a Lamb–Oseen vortex, is embedded in a region with an almost constant radius and a much lower azimuthal velocity that obeys a ~r−β power law, with r being the radius measured from the vortex centre. For the turbulence levels and the test section length used in this study, the single-vortex behaviour is independent of the external turbulence and in contrast with the decay of the vortex pair that strongly depends on the external turbulence. In the initial stages of the vortex pair evolution, the vortices decay due to cancellation of vorticity at the symmetry plane. At a later stage, Crow oscillations are observed, followed by a breakdown of the vortices. This vortex breakdown might be due to direct turbulent action. The observed behaviour is in agreement with the theoretical model of Crow & Bate (J. Aircraft, vol. 13, 1976, p. 476).

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