scholarly journals An experimental investigation on elliptical instability of a strongly asymmetric vortex pair in a stable density stratification

2006 ◽  
Vol 13 (6) ◽  
pp. 641-649 ◽  
Author(s):  
B. Cariteau ◽  
J.-B. Flór
Keyword(s):  
Froude Number ◽  
Vortex Pair ◽  
Azimuthal Velocity ◽  
Buoyancy Frequency ◽  
Nonlinear Interactions ◽  
Secondary Vortex ◽  
Asymmetric Vortex ◽  
Elliptical Instability ◽  
Acceleration And Deceleration ◽  
Instability Growth

Abstract. We investigate the elliptical instability of a strongly asymmetric vortex pair in a stratified fluid, generated by the acceleration and deceleration of the rotation of a single flap. The dominant parameter is the Froude number, Fr=U/(NR), based on the maximum azimuthal velocity, U, and corresponding radius, R, of the strongest vortex, i.e. the principal vortex, and buoyancy frequency N. For Fr>1, both vortices are elliptically unstable while the instability is suppressed for Fr<1. In an asymmetric vortex pair, the principal vortex is less – and the secondary vortex more – elliptical than the vortices in an equivalent symmetric dipolar vortex. The far more unstable secondary vortex interacts with the principal vortex and increases the strain on the latter, thus increasing its ellipticity and its instability growth rate. The nonlinear interactions render the elliptical instability more relevant. An asymmetric dipole can be more unstable than an equivalent symmetric dipole. Further, the wavelength of the instability is shown to be a function of the Froude number for strong stratifications corresponding to small Froude numbers, whereas it remains constant in the limit of a homogenous fluid.

Suppression of Baroclinic Instabilities in Buoyancy-Driven Flow over Sloping Bathymetry

2017 ◽  
Vol 47 (1) ◽  
pp. 49-68 ◽  
Author(s):  
Robert D. Hetland
Keyword(s):  
Growth Rate ◽  
Linear Instability ◽  
Linear Stability Theory ◽  
Buoyancy Frequency ◽  
Bottom Slope ◽  
Coriolis Parameter ◽  
Plume Front ◽  
Instability Theory ◽  
Instability Growth ◽  
Flow Configurations

AbstractBaroclinic instabilities are ubiquitous in many types of geostrophic flow; however, they are seldom observed in river plumes despite strong lateral density gradients within the plume front. Supported by results from a realistic numerical simulation of the Mississippi–Atchafalaya River plume, idealized numerical simulations of buoyancy-driven flow are used to investigate baroclinic instabilities in buoyancy-driven flow over a sloping bottom. The parameter space is defined by the slope Burger number S = Nf−1α, where N is the buoyancy frequency, f is the Coriolis parameter, and α is the bottom slope, and the Richardson number Ri = N2f2M−4, where M2 = |∇Hb| is the magnitude of the lateral buoyancy gradients. Instabilities only form in a subset of the simulations, with the criterion that SH ≡ SRi−1/2 = Uf−1W−1 = M2f−2α 0.2, where U is a horizontal velocity scale and SH is a new parameter named the horizontal slope Burger number. Suppression of instability formation for certain flow conditions contrasts linear stability theory, which predicts that all flow configurations will be subject to instabilities. The instability growth rate estimated in the nonlinear 3D model is proportional to ωImaxS−1/2, where ωImax is the dimensional growth rate predicted by linear instability theory, indicating that bottom slope inhibits instability growth beyond that predicted by linear theory. The constraint SH 0.2 implies a relationship between the inertial radius Li = Uf−1 and the plume width W. Instabilities may not form when 5Li > W; that is, the plume is too narrow for the eddies to fit.

scholarly journals On annihilation of the relativistic electron vortex pair in collisionless plasmas

2018 ◽  
Vol 84 (6) ◽  
Author(s):  
K. V. Lezhnin ◽  
F. F. Kamenets ◽  
T. Zh. Esirkepov ◽  
S. V. Bulanov
Keyword(s):  
Magnetic Field ◽  
Collisionless Plasma ◽  
Vortex Formation ◽  
Vortex Pair ◽  
Skin Depth ◽  
Secondary Vortex ◽  
Vortex System ◽  
Collisionless Plasmas ◽  
Secondary Vortices ◽  
The Magnetic Field

In contrast to hydrodynamic vortices, vortices in a plasma contain an electric current circulating around the centre of the vortex, which generates a magnetic field localized inside. Using computer simulations, we demonstrate that the magnetic field associated with the vortex gives rise to a mechanism of dissipation of the vortex pair in a collisionless plasma, leading to fast annihilation of the magnetic field with its energy transforming into the energy of fast electrons, secondary vortices and plasma waves. Two major contributors to the energy damping of a double vortex system, namely, magnetic field annihilation and secondary vortex formation, are regulated by the size of the vortex with respect to the electron skin depth, which scales with the electron$\unicode[STIX]{x1D6FE}$factor,$\unicode[STIX]{x1D6FE}_{e}$, as$R/d_{e}\propto \unicode[STIX]{x1D6FE}_{e}^{1/2}$. Magnetic field annihilation appears to be dominant in mildly relativistic vortices, while for the ultrarelativistic case, secondary vortex formation is the main channel for damping of the initial double vortex system.

Asymmetric vortex pair induces secondary traveling wave vibration of a flexible cylinder from still water to incoming flow

2021 ◽  
Vol 33 (12) ◽  
pp. 125115
Author(s):  
Zhicheng Wang ◽  
Ang Li ◽  
Baiheng Wu ◽  
Dixia Fan ◽  
Michael S. Triantafyllou ◽  
...  
Keyword(s):  
Traveling Wave ◽  
Vortex Pair ◽  
Incoming Flow ◽  
Flexible Cylinder ◽  
Asymmetric Vortex

Excitation of superharmonics by internal modes in non-uniformly stratified fluid

2016 ◽  
Vol 793 ◽  
pp. 335-352 ◽  
Author(s):  
Bruce R. Sutherland
Keyword(s):  
Single Mode ◽  
Stratified Fluid ◽  
Buoyancy Frequency ◽  
Nonlinear Interactions ◽  
Initial State ◽  
Weakly Nonlinear ◽  
Resonant Wave ◽  
Vertical Scale ◽  
Scale Structures ◽  
Parametric Subharmonic Instability

Theory and numerical simulations show that the nonlinear self-interaction of internal modes in non-uniform stratification results in energy being transferred to superharmonic disturbances forced at twice the horizontal wavenumber and frequency of the parent mode. These disturbances are not in themselves a single mode, but a superposition of modes such that the disturbance amplitude is largest where the change in the background buoyancy frequency with depth is largest. Through weakly nonlinear interactions with the parent mode, the disturbances evolve to develop vertical-scale structures that distort and modulate the parent mode. Because pure resonant wave triads do not exist in non-uniformly stratified fluid, parametric subharmonic instability (PSI) is not evident even though noise is superimposed upon the initial state. The results suggest a new mechanism for energy transfer to dissipative scales (from large to small vertical scale and with frequencies larger and smaller than that of the parent mode) through forcing superharmonic rather than subharmonic disturbances.

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.

An Experimental Study of Streamwise Vortices in a Compressor Cascade

1988 ◽  
Author(s):  
Chen Fang ◽  
Chen Mao-Zhang ◽  
Jiang Hao-Kang
Keyword(s):  
Experimental Study ◽  
Vortex Pair ◽  
Secondary Vortex ◽  
Streamwise Vortices ◽  
Reynolds Stresses ◽  
Compressor Cascade ◽  
Suction Surface ◽  
Mean Velocity ◽  
Passage Vortex ◽  
Corner Vortex

An experimental study on the production and development of streamwise vortices in a compressor cascade is reported. At four locations inside and one location outside the blade passage, the mean velocity components, three turbulent intensities and three Reynolds stresses were measured with a “x” hot wire probe. The results obtained describe the flow structure in the corner between the end-wall and blade suction surface in detail. Besides a passage vortex within the passage, there exist a shed corner vortex pair and a secondary vortex pair in the corner. The characteristics of two vortex pairs were different from that of the passage vortex. The mechanism causing the shed corner vortex pair and secondary vortex pair and the effect of these vortices on the cascade losses are discussed.

Three-dimensional vortex dynamics in oscillatory flow separation

2011 ◽  
Vol 674 ◽  
pp. 408-432 ◽  
Author(s):  
MIGUEL CANALS ◽  
GENO PAWLAK
Keyword(s):  
Time Scale ◽  
Oscillatory Flow ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Outer Region ◽  
Vortex Pair ◽  
Propagation Distance ◽  
Oscillation Period ◽  
Number Range ◽  
Elliptical Instability

The dynamics of coherent columnar vortices and their interactions in an oscillatory flow past an obstacle are examined experimentally. The main focus is on the low Keulegan–Carpenter number range (0.2 < KC < 2), where KC is the ratio between the fluid particle excursion during half an oscillation cycle and the obstacle size, and for moderate Reynolds numbers (700 < Rev < 7500). For this parameter range, a periodic unidirectional vortex pair ejection regime is observed, in which the direction of vortex propagation is set by the initial conditions of the oscillations. These vortex pairs provide a direct mechanism for the transfer of momentum and enstrophy to the outer region of rough oscillating boundary layers. Vortices are observed to be short-lived relative to the oscillation time scale, which limits their propagation distance from the boundary. The instability mechanisms leading to vortex decay are elucidated via flow visualizations and digital particle image velocimetry (DPIV). Dye visualizations reveal complex three-dimensional vortex interactions resulting in rapid vortex destruction. These visualizations suggest that one of the instabilities affecting the spanwise vortices is an elliptical instability of the strained vortex cores. This is supported by DPIV measurements which identify the spatial structure of the perturbations associated with the elliptical instability in the divergence field. We also identify regions in the periphery of the vortex cores which are unstable to the centrifugal instability. Vortex longevity is quantified via a vortex decay time scale, and the results indicate that vortex pair lifetimes are of the order of an oscillation period T.

PLASMA FLOW CONTROL OVER FOREBODY AT HIGH ANGLES OF ATTACK

2010 ◽  
Vol 24 (13) ◽  
pp. 1405-1408 ◽  
Author(s):  
ZIJIE ZHAO ◽  
CHAO GAO ◽  
FENG LIU ◽  
SHIJUN LUO
Keyword(s):  
Wind Tunnel ◽  
Flow Control ◽  
Plasma Flow ◽  
Vortex Pair ◽  
Apex Angle ◽  
Plasma Actuators ◽  
Pressure Measurements ◽  
Asymmetric Vortex ◽  
Plasma Flow Control ◽  
High Angles Of Attack

Forward blowing from a pair of plasma actuators on the leeward surface and near the apex is used to switch the asymmetric vortex pair over a cone of semi-apex angle 10° at high angles of attack. Wind tunnel pressure measurements show that by appropriate design of the actuators and appropriate choice of the AC voltage and frequency, side forces and yawing moments of opposite signs can be obtained at a given angle of attack by activating one of the plasma actuators. Further work is suggested.

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).

Experimental studies of strongly stratified flow past three-dimensional orography

1999 ◽  
Vol 390 ◽  
pp. 223-249 ◽  
Author(s):  
S. B. VOSPER ◽  
I. P. CASTRO ◽  
W. H. SNYDER ◽  
S. D. MOBBS
Keyword(s):  
Flow Visualization ◽  
Froude Number ◽  
Vortex Shedding ◽  
Wave Amplitude ◽  
Wave Train ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Stratified Flow ◽  
Finite Depth ◽  
Buoyancy Frequency

Stably stratified flows past three-dimensional orography have been investigated using a stratified towing tank. Flows past idealized axisymmetric orography in which the Froude number, Fh=U/Nh (where U is the towing speed, N is the buoyancy frequency and h is the height of the obstacle) is less than unity have been studied. The orography considered consists of two sizes of hemisphere and two cones of different slope. For all the obstacles measurements show that as Fh decreases, the drag coefficient increases, reaching between 2.8 and 5.4 times the value in neutral flow (depending on obstacle shape) for Fh[les ]0.25. Local maxima and minima in the drag also occur. These are due to the finite depth of the tank and can be explained by linear gravity-wave theory. Flow visualization reveals a lee wave train downstream in which the wave amplitude is O(Fhh), the smallest wave amplitude occurring for the steepest cone. Measurements show that for all the obstacles, the dividing-streamline height, zs, is described reasonably well by the formula zs/h=1−Fh. Flow visualization and acoustic Doppler velocimeter measurements in the wake of the obstacles show that vortex shedding occurs when Fh[les ]0.4 and that the period of the vortex shedding is independent of height. Based on velocity measurements in the wake of both sizes of hemisphere (plus two additional smaller hemispheres), it is shown that a blockage-corrected Strouhal number, S2c =fL2/Uc, collapses onto a single curve when plotted against the effective Froude number, Fhc=Uc/Nh. Here, Uc is the blockage-corrected free-stream speed based on mass-flux considerations, f is the vortex shedding frequency and L2 is the obstacle width at a height zs/2. Collapse of the data is also obtained for the two different shapes of cone and for additional measurements made in the wake of triangular and rectangular at plates. Indeed, the values of S2c for all these obstacles are similar and this suggests that despite the fact that the obstacle widths vary with height, a single length scale determines the vortex-street dynamics. Experiments conducted using a splitter plate indicate that the shedding mechanism provides a major contribution to the total drag (∼25%). The addition of an upstream pointing ‘verge region’ to a hemisphere is also shown to increase the drag significantly in strongly stratified flow. Possible mechanisms for this are discussed.

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