The nonlinear development of three-dimensional disturbances at hyperbolic stagnation points: A model of the braid region in mixing layers

2000 ◽  
Vol 12 (5) ◽  
pp. 1032-1043 ◽  
Author(s):  
C. P. Caulfield ◽  
R. R. Kerswell
Keyword(s):  
Three Dimensional ◽  
Mixing Layers ◽  
Nonlinear Development ◽  
Stagnation Points

Effects of the Coriolis force on the stability of Stuart vortices

1998 ◽  
Vol 356 ◽  
pp. 353-379 ◽  
Author(s):  
STÉPHANE LEBLANC ◽  
CLAUDE CAMBON
Keyword(s):  
Coriolis Force ◽  
Three Dimensional ◽  
Basic Mechanism ◽  
Short Wave ◽  
Stagnation Points ◽  
Floquet Modes ◽  
The Stability ◽  
Simple Flows ◽  
Stuart Vortices ◽  
Wave Breakdown

A detailed investigation of the effects of the Coriolis force on the three-dimensional linear instabilities of Stuart vortices is proposed. This exact inviscid solution describes an array of co-rotating vortices embedded in a shear flow. When the axis of rotation is perpendicular to the plane of the basic flow, the stability analysis consists of an eigenvalue problem for non-parallel versions of the coupled Orr–Sommerfeld and Squire equations, which is solved numerically by a spectral method. The Coriolis force acts on instabilities as a ‘tuner’, when compared to the non-rotating case. A weak anticyclonic rotation is destabilizing: three-dimensional Floquet modes are promoted, and at large spanwise wavenumber their behaviour is predicted by a ‘pressureless’ analysis. This latter analysis, which has been extensively discussed for simple flows in a recent paper (Leblanc & Cambon 1997) is shown to be relevant to the present study. The basic mechanism of short-wave breakdown is a competition between instabilities generated by the elliptical cores of the vortices and by the hyperbolic stagnation points in the braids, in accordance with predictions from the ‘geometrical optics’ stability theory. On the other hand, cyclonic or stronger anticyclonic rotation kills three-dimensional instabilities by a cut-off in the spanwise wavenumber. Under rapid rotation, the Stuart vortices are stabilized, whereas inertial waves propagate.

scholarly journals Coherent vortex simulation of three-dimensional turbulent mixing layers using orthogonal wavelets

2005 ◽  
Vol 534 ◽  
pp. 39-66 ◽  
Author(s):  
KAI SCHNEIDER ◽  
MARIE FARGE ◽  
GIULIO PELLEGRINO ◽  
MICHAEL M. ROGERS
Keyword(s):  
Turbulent Mixing ◽  
Three Dimensional ◽  
Mixing Layers ◽  
Orthogonal Wavelets ◽  
Coherent Vortex

Equilibrium and Stability of a Three-Dimensional Toroidal MHD Configuration Near its Magnetic Axis

1976 ◽  
Vol 31 (11) ◽  
pp. 1277-1288 ◽  
Author(s):  
D. Lortz ◽  
J. Nührenberg
Keyword(s):  
Three Dimensional ◽  
Magnetic Axis ◽  
Stability Criteria ◽  
Sufficient Criterion ◽  
Third Order ◽  
Stagnation Points ◽  
The Third ◽  
Longitudinal Current ◽  
The Stability

Abstract The expansion of a three-dimensional toroidal magnetohydrostatic equilibrium around its magnetic axis is reconsidered. Equilibrium and stability plasma-β estimates are obtained in connection with a discussion of stagnation points occurring in the third-order flux surfaces. The stability criteria entering the β-estimates are: (i) a necessary criterion for localized disturbances, (ii) a new sufficient criterion for configurations without longitudinal current. Hamada coordinates are used to evaluate these criteria.

Confined compressible mixing layers. I - Three-dimensional instabilities

1989 ◽  
Author(s):  
MOELJO SOETRISNO ◽  
JEFFREY GREENOUGH ◽  
D. EBERHARDT ◽  
JAMES RILEY
Keyword(s):  
Three Dimensional ◽  
Mixing Layers

The Effect of Angle and Flow Rate Upon Hemodynamics in Distal Vascular Graft Anastomoses: A Numerical Model Study

1994 ◽  
Vol 116 (3) ◽  
pp. 331-336 ◽  
Author(s):  
Ding-Yu Fei ◽  
James D. Thomas ◽  
Stanley E. Rittgers
Keyword(s):  
Numerical Model ◽  
Stagnation Point ◽  
Arterial Wall ◽  
Artery Bypass ◽  
Three Dimensional ◽  
Separated Flow ◽  
Reynolds Numbers ◽  
In Vivo Studies ◽  
Stagnation Points

Flow in distal end-to-side anastomoses of iliofemoral artery bypass grafts was simulated using a steady flow, three-dimensional numerical model. With the proximal artery occluded, anastomotic angles were varied over 20, 30, 40, 45, 50, 60 and 70 deg while the inlet Reynolds numbers were 100 and 205. Fully developed flow in the graft became somewhat skewed toward the inner wall with increasing angle for both Reynolds numbers. Separated flow regions were seen along the inner arterial wall (toe region) for angles ≥ 60 deg at Re = 100 and for angles ≥ 45 deg at Re = 205 while a stagnation point existed along the outer arterial wall (floor region) for all cases which moved downstream relative to the toe of the anastomosis with decreasing angles. Normalized shear rates (NSR) along the arterial wall varied widely throughout the anastomotic region with negative values seen in the separation zones and upstream of the stagnation points which increased in magnitude with angle. The NSR increased with distance downstream of the stagnation point and with magnitudes which increased with the angle. Compared with observations from chronic in vivo studies, these results appear to support the hypothesis of greater intimal hyperplasia occurring in regions of low fluid shear.

Lagrangian transport in a class of three-dimensional buoyancy-driven flows

2017 ◽  
Vol 832 ◽  
pp. 5-40 ◽  
Author(s):  
P. S. Contreras ◽  
M. F. M. Speetjens ◽  
H. J. H. Clercx
Keyword(s):  
Temperature Gradient ◽  
Three Dimensional ◽  
Global Temperature ◽  
Cavity Flows ◽  
Fluid Inertia ◽  
Lagrangian Dynamics ◽  
Flow Topology ◽  
Generic Structure ◽  
Driven Cavity ◽  
Stagnation Points

The present study concerns the Lagrangian dynamics of three-dimensional (3D) buoyancy-driven cavity flows under steady and laminar conditions due to a global temperature gradient imposed via an opposite hot and cold sidewall. This serves as the archetypal configuration for natural-convection flows in which (contrary to the well-known Rayleigh–Bénard flow) gravity is perpendicular (instead of parallel) to the global temperature gradient. Limited insight into the Lagrangian properties of this class of flows, despite its relevance to observed flow phenomena as well as scalar transport, motivates this study. The 3D Lagrangian dynamics are investigated in terms of the generic structure and associated transport properties of the global streamline pattern (‘Lagrangian flow topology’) by both theoretical and computational analyses. The Grashof number $Gr$ is the principal control parameter for the flow topology: limit $Gr=0$ yields a trivial state of closed streamlines; $Gr>0$ induces symmetry breaking by fluid inertia and buoyancy and thus causes formation of toroidal coherent structures (‘primary tori’) embedded in chaotic streamlines governed by Hamiltonian mechanisms. Fluid inertia prevails for ‘smaller’ $Gr$ and gives behaviour that is dynamically entirely analogous to 3D lid-driven cavity flows. Buoyancy-induced bifurcation of the flow topology occurs for ‘larger’ $Gr$ and underlies the emergence of ‘secondary rolls’ observed in the literature and to date unreported secondary tori for ‘larger’ Prandtl numbers $Pr$. Key to these dynamics are stagnation points and corresponding heteroclinic manifold interactions.

scholarly journals A pancake droplet translating in a Hele-Shaw cell: lubrication film and flow field

2016 ◽  
Vol 798 ◽  
pp. 955-969 ◽  
Author(s):  
Lailai Zhu ◽  
François Gallaire
Keyword(s):  
Flow Field ◽  
Three Dimensional ◽  
Streamwise Vortex ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Symmetric Pair ◽  
Lubrication Film ◽  
Stagnation Points ◽  
Interior Flow ◽  
Hele Shaw Cell

We adopt a boundary integral method to study the dynamics of a translating droplet confined in a Hele-Shaw cell in the Stokes regime. The droplet is driven by the motion of the ambient fluid with the same viscosity. We characterize the three-dimensional (3D) nature of the droplet interface and of the flow field. The interface develops an arc-shaped ridge near the rear-half rim with a protrusion in the rear and a laterally symmetric pair of higher peaks; this pair of protrusions has been identified by recent experiments (Huerre et al., Phys. Rev. Lett., vol. 115 (6), 2015, 064501) and predicted asymptotically (Burgess & Foster, Phys. Fluids A, vol. 2 (7), 1990, pp. 1105–1117). The mean film thickness is well predicted by the extended Bretherton model (Klaseboer et al., Phys. Fluids, vol. 26 (3), 2014, 032107) with fitting parameters. The flow in the streamwise wall-normal middle plane is featured with recirculating zones, which are partitioned by stagnation points closely resembling those of a two-dimensional droplet in a channel. Recirculation is absent in the wall-parallel, unconfined planes, in sharp contrast to the interior flow inside a moving droplet in free space. The preferred orientation of the recirculation results from the anisotropic confinement of the Hele-Shaw cell. On these planes, we identify a dipolar disturbance flow field induced by the travelling droplet and its $1/r^{2}$ spatial decay is confirmed numerically. We pinpoint counter-rotating streamwise vortex structures near the lateral interface of the droplet, further highlighting the complex 3D flow pattern.

On the Weis-Fogh mechanism of lift generation

1973 ◽  
Vol 60 (1) ◽  
pp. 1-17 ◽  
Author(s):  
M. J. Lighthill
Keyword(s):  
Stokes Equations ◽  
Separation Bubble ◽  
Three Dimensional ◽  
Leading Edge ◽  
The Body ◽  
Navier Stokes ◽  
Encarsia Formosa ◽  
Concentrated Force ◽  
Stagnation Points ◽  
Wing Tips

Weis-Fogh (1973) proposed a new mechanism of lift generation of fundamental interest. Surprisingly, it could work even in inviscid two-dimensional motions starting from rest, when Kelvin's theorem states that the total circulation round a body must vanish, but does not exclude the possibility that if the body breaks into two pieces then there may be equal and opposite circulations round them, each suitable for generating the lift required in the pieces’ subsequent motions! The ‘fling’ of two insect wings of chord c (figure 1) turning with angular velocity Ω generates irrotational motions associated with the sucking of air into the opening gap which are calculated in § 2 as involving circulations −0·69Ωc2 and + 0.69Ωc2 around the wings when their trailing edges, which are stagnation points of those irrotational motions, break apart (position (f)). Viscous modifications to this irrotational flow pattern by shedding of vorticity at the boundary generate (§ 3) a leading-edge separation bubble, and tend to increase slightly the total bound vorticity. Its role in a three-dimensional picture of the Weis-Fogh mechanism of lift generation, involving formation of trailing vortices at the wing tips, and including the case of a hovering insect like Encarsia formosa moving those tips in circular paths, is investigated in § 4. The paper ends with the comment that the far flow field of such very small hovering insects should take the form of the exact solution (Landau 1944; Squire 1951) of the Navier-Stokes equations for the effect of a concentrated force (the weight mg of the animal) acting on a fluid of kinematic viscosity v and density p, whenever the ratio mg/pv2 is small enough for that jet-type induced motion to be stable.

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