Nonlinear Singular Kelvin Modes in a Columnar Vortex

2009 ◽  
pp. 95-105
Author(s):  
Philippe Caillol ◽  
Sherwin A. Maslowe
Keyword(s):  
Columnar Vortex

scholarly journals Response of a columnar vortex to a wrapped vortex loop

1999 ◽  
Vol 7 ◽  
pp. 280-291
Author(s):  
J. S. Marshall
Keyword(s):  
Vortex Loop ◽  
Columnar Vortex

A sufficient condition for the instability of columnar vortices

1983 ◽  
Vol 126 ◽  
pp. 335-356 ◽  
Author(s):  
S. Leibovich ◽  
K. Stewartson
Keyword(s):  
Numerical Solutions ◽  
Three Dimensional ◽  
Azimuthal Velocity ◽  
Unstable Wave ◽  
Sufficient Condition ◽  
Asymptotic Results ◽  
Specific Flow ◽  
Columnar Vortex ◽  
Swirl Velocity ◽  
Inviscid Instability

The inviscid instability of columnar vortex flows in unbounded domains to three-dimensional perturbations is considered. The undisturbed flows may have axial and swirl velocity components with a general dependence on distance from the swirl axis. The equation governing the disturbance is found to simplify when the azimuthal wavenumber n is large. This permits us to develop the solution in an asymptotic expansion and reveals a class of unstable modes. The asymptotic results are confirmed by comparisons with numerical solutions of the full problem for a specific flow modelling the trailing vortex. It is found that the asymptotic theory predicts the most-unstable wave with reasonable accuracy for values of n as low as 3, and improves rapidly in accuracy as n increases. This study enables us to formulate a sufficient condition for the instability of columnar vortices as follows. Let the vortex have axial velocity W(r), azimuthal velocity V(r), where r is distance from the axis, let Ω be the angular velocity V/r, and let Γ be the circulation rV. Then the flow is unstable if $ V\frac{d\Omega}{dr}\left[ \frac{d\Omega}{dr}\frac{d\Gamma}{dr} + \left(\frac{dW}{dr}\right)^2\right] < 0.$

scholarly journals Waves on a columnar vortex in a strongly stratified fluid

2009 ◽  
Vol 21 (10) ◽  
pp. 106602 ◽  
Author(s):  
Paul Billant ◽  
Stéphane Le Dizès
Keyword(s):  
Stratified Fluid ◽  
Columnar Vortex

Optimization of a columnar vortex generator installed over an aircraft carrier ski-jump ramp

2019 ◽  
Vol 234 (1) ◽  
pp. 223-230
Author(s):  
Rafael Bardera
Keyword(s):  
Vortex Generator ◽  
Wind Tunnel Testing ◽  
Low Velocity ◽  
Aircraft Carrier ◽  
Recirculation Bubble ◽  
Columnar Vortex ◽  
Flow Disturbances ◽  
Image Velocimetry ◽  
Field Velocity ◽  
Flight Deck

Aircraft performances over aircraft carriers are essential in modern navies. Take-off operation is critical due to the short runway available. The ski-jump ramp is a useful system that allows to operate under safe conditions. However, the sharp edge at the end of the runway provokes a region with recirculation bubble and low velocity producing strong flow disturbances. Hence, the aircraft performances are affected and the pilot’s workload is augmented. Previous researches showed that columnar vortex generator reduces the recirculation bubble generated over the end of flight deck. This article presents an in-depth experimental study performed by wind tunnel testing in order to determine the relation between the columnar vortex generator size and the recirculation bubble reduction. Particle image velocimetry is used to investigate the flow field velocity and flow structure around the ski-jump ramp as a non-intrusive experimental technique. Encouraging results were found for the biggest columnar vortex generator studied.

Swirling Flow in a Fixed Container: Generation and Attenuation of a Vortex Column

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
A. Nahas ◽  
A. Calvo ◽  
M. Piva
Keyword(s):  
Boundary Layer ◽  
Swirling Flow ◽  
Vortex Formation ◽  
Fluid Motion ◽  
Bottom Boundary ◽  
Global Circulation ◽  
Columnar Vortex ◽  
Central Nozzle ◽  
Suction Flow ◽  
Vessel Bottom

The development of a columnar vortex and its attenuation using radial rods at the bottom boundary of a stationary container are experimentally studied. The fluid motion is achieved combining two independent flows: a global circulation around the cylinder axis and a meridian flow generated by recirculating fluid through a central nozzle located at the vessel bottom. The resulting velocity field is analyzed under two conditions: with and without the meridian or suction flow. It is shown that in the second condition a columnar vortex merges and that its intensity increases when the suction flow rate is increased. The key role played by the bottom boundary layer in the vortex formation is demonstrated. In the last part of the work, the attenuation of the vortex intensity produced by a set of rods located at the vessel bottom is investigated. It is found that obstacles with heights of the order of the boundary layer thickness are enough to produce the total annihilation of the vortex column.

scholarly journals Turbulence and columnar vortex formation through inertial-wave focusing

2013 ◽  
Vol 87 (4) ◽  
Author(s):  
Matias Duran-Matute ◽  
Jan-Bert Flór ◽  
Fabien S. Godeferd ◽  
Clément Jause-Labert
Keyword(s):  
Vortex Formation ◽  
Wave Focusing ◽  
Columnar Vortex ◽  
Inertial Wave

scholarly journals Instabilities and waves on a columnar vortex in a strongly stratified and rotating fluid

2013 ◽  
Vol 25 (8) ◽  
pp. 086601 ◽  
Author(s):  
Junho Park ◽  
Paul Billant
Keyword(s):  
Rotating Fluid ◽  
Columnar Vortex

scholarly journals Theoretical analysis of the zigzag instability of a vertical columnar vortex pair in a strongly stratified fluid

2000 ◽  
Vol 419 ◽  
pp. 29-63 ◽  
Author(s):  
PAUL BILLANT ◽  
JEAN-MARC CHOMAZ
Keyword(s):  
Froude Number ◽  
Evolution Equations ◽  
Vortex Pair ◽  
Horizontal Velocity ◽  
Phase Variable ◽  
Two Dimensional ◽  
Stratified Turbulence ◽  
Periodic Patterns ◽  
Phase Dynamics ◽  
Columnar Vortex

A general theoretical account is proposed for the zigzag instability of a vertical columnar vortex pair recently discovered in a strongly stratified experiment.The linear inviscid stability of the Lamb–Chaplygin vortex pair is analysed by a multiple-scale expansion analysis for small horizontal Froude number (Fh = U/LhN, where U is the magnitude of the horizontal velocity, Lh the horizontal lengthscale and N the Brunt–Väisälä frequency) and small vertical Froude number (Fv = U/LvN, where Lv is the vertical lengthscale) using the scaling of the equations of motion introduced by Riley, Metcalfe & Weissman (1981). In the limit Fv = 0, these equations reduce to two-dimensional Euler equations for the horizontal velocity with undetermined vertical dependence. Thus, at leading order, neutral modes of the flow are associated, among others, to translational and rotational invariances in each horizontal plane. To each broken invariance is related a phase variable that may vary freely along the vertical. Conservation of mass and potential vorticity impose at higher order the evolution equations governing the phase variables that we derive for Fh [Lt ] 1 and Fv [Lt ] 1 in the spirit of phase dynamics techniques established for periodic patterns. In agreement with the experimental observations, this asymptotic analysis shows the existence of an instability consisting of a vertically modulated rotation and a translation of the columnar vortex pair perpendicular to the travelling direction. The dispersion relation as well as the spatial eigenmode of the zigzag instability are determined. The analysis predicts that the most amplified vertical wavelength should scale as U/N and the maximum growth rate as U/Lh.Our main finding is thus that the typical thickness of the ensuing layers will be such that Fv = O(1) and not Fv [Lt ] 1 as assumed by Riley et al. (1981) and Lilly (1983). This implies that such strongly stratified flows are not described by two- dimensional horizontal equations. These results may help to understand the layering commonly observed in stratified turbulence and the fundamental differences with strictly two-dimensional turbulence.

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