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.

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.

Three-dimensional destabilization of Stuart vortices: the influence of rotation and ellipticity

1999 ◽  
Vol 387 ◽  
pp. 205-226 ◽  
Author(s):  
P. G. POTYLITSIN ◽  
W. R. PELTIER
Keyword(s):  
Cross Sections ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Steady State Solution ◽  
Vorticity Distribution ◽  
Columnar Vortex ◽  
Elliptical Instability ◽  
The Stability ◽  
Dimensional Instability ◽  
Stuart Vortices

We investigate the influence of the ellipticity of a columnar vortex in a rotating environment on its linear stability to three-dimensional perturbations. As a model of the basic-state vorticity distribution, we employ the Stuart steady-state solution of the Euler equations. In the presence of background rotation, an anticyclonic vortex column is shown to be strongly destabilized to three-dimensional perturbations when background rotation is weak, while rapid rotation strongly stabilizes both anticyclonic and cyclonic columns, as might be expected on the basis of the Taylor–Proudman theorem. We demonstrate that there exist three distinct forms of three-dimensional instability to which strong anticyclonic vortices are subject. One form consists of a Coriolis force modified form of the ‘elliptical’ instability, which is dominant for vortex columns whose cross-sections are strongly elliptical. This mode was recently discussed by Potylitsin & Peltier (1998) and Leblanc & Cambon (1998). The second form of instability may be understood to constitute a three-dimensional inertial (centrifugal) mode, which becomes the dominant mechanism of instability as the ellipticity of the vortex column decreases. Also evident in the Stuart model of the vorticity distribution is a third ‘hyperbolic’ mode of instability that is focused on the stagnation point that exists between adjacent vortex cores. Although this short-wavelength cross-stream mode is much less important in the spectrum of the Stuart model than it is in the case of a true homogeneous mixing layer, it nevertheless does exist even though its presence has remained undetected in most previous analyses of the stability of the Stuart solution.

Zonal approach to centrifugal, elliptic and hyperbolic instabilities in Stuart vortices with external rotation

2001 ◽  
Vol 449 ◽  
pp. 1-37 ◽  
Author(s):  
FABIEN S. GODEFERD ◽  
CLAUDE CAMBON ◽  
S. LEBLANC
Keyword(s):  
Stability Analysis ◽  
External Rotation ◽  
Short Wave ◽  
Rotating Flows ◽  
Mean Flow ◽  
Mode Decomposition ◽  
Centrifugal Instability ◽  
The Mean ◽  
The Stability ◽  
Stuart Vortices

The stability analysis of a street of Stuart vortices in a rotating frame is performed by integrating the Kelvin–Townsend equations along the mean flow trajectories, using the geometrical optics technique (Lifschitz & Hameiri 1991) for short-wave perturbations. A parallel is drawn between the formulations of this zonal approach and that of rapid distortion theory, better known to the turbulence community. The results presented confirm those obtained by the standard stability analysis based on normal-mode decomposition: depending on the rotation parameter and the oblique mode considered, three unstable zones are identified, related to the centrifugal, elliptic and hyperbolic instabilities, as observed for Taylor–Green cells (Sipp et al. 1999). Anticyclonic rotation is shown to destabilize Stuart vortices through a combination of the elliptical and centrifugal instability mechanisms, depending on the ratio of its rate to the structure core vorticity. Available stability criteria are discussed in the general case of two-dimensional rotating flows, in relation to their streamline topology and the values of the local Rossby number or vorticity.

Three-dimensional instabilities of quasi-solitary waves in a falling liquid film

2014 ◽  
Vol 757 ◽  
pp. 854-887 ◽  
Author(s):  
N. Kofman ◽  
S. Mergui ◽  
C. Ruyer-Quil
Keyword(s):  
Travelling Waves ◽  
Three Dimensional ◽  
Water Film ◽  
Short Wave ◽  
Wave Mode ◽  
Long Wave ◽  
Wave Patterns ◽  
Inclination Angles ◽  
Rayleigh Taylor Instability ◽  
The Stability

AbstractThe stability of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\gamma _2$ travelling waves at the surface of a film flow down an inclined plane is considered experimentally and numerically. These waves are fast, one-humped and quasi-solitary. They undergo a three-dimensional secondary instability if the flow rate (or Reynolds number) is sufficiently high. Rugged or scallop wave patterns are generated by the interplay between a short-wave and a long-wave instability mode. The short-wave mode arises in the capillary region of the wave, with a mechanism of capillary origin which is similar to the Rayleigh–Plateau instability, whereas the long-wave mode deforms the entire wave and is triggered by a Rayleigh–Taylor instability. Rugged waves are observed at relatively small inclination angles. At larger angles, the long-wave mode predominates and scallop waves are observed. For a water film the transition between rugged and scallop waves occurs for an inclination angle around 12°.

Strato-hyperbolic instability: a new mechanism of instability in stably stratified vortices

2018 ◽  
Vol 854 ◽  
pp. 293-323
Author(s):  
Shota Suzuki ◽  
Makoto Hirota ◽  
Yuji Hattori
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Local Stability ◽  
Underlying Mechanism ◽  
Internal Gravity Waves ◽  
Stagnation Points ◽  
Local Stability Analysis ◽  
The Stability ◽  
Parameter Values ◽  
Stuart Vortices

The stability of stably stratified vortices is studied by local stability analysis. Three base flows that possess hyperbolic stagnation points are considered: the two-dimensional (2-D) Taylor–Green vortices, the Stuart vortices and the Lamb–Chaplygin dipole. It is shown that the elliptic instability is stabilized by stratification; it is completely stabilized for the 2-D Taylor–Green vortices, while it remains and merges into hyperbolic instability near the boundary or the heteroclinic streamlines connecting the hyperbolic stagnation points for the Stuart vortices and the Lamb–Chaplygin dipole. More importantly, a new instability caused by hyperbolic instability near the hyperbolic stagnation points and phase shift by the internal gravity waves is found; it is named the strato-hyperbolic instability; the underlying mechanism is parametric resonance as unstable band structures appear in contours of the growth rate. A simplified model explains the mechanism and the resonance curves. The growth rate of the strato-hyperbolic instability is comparable to that of the elliptic instability for the 2-D Taylor–Green vortices, while it is smaller for the Stuart vortices and the Lamb–Chaplygin dipole. For the Lamb–Chaplygin dipole, the tripolar instability is found to merge with the strato-hyperbolic instability as stratification becomes strong. The modal stability analysis is also performed for the 2-D Taylor–Green vortices. It is shown that global modes of the strato-hyperbolic instability exist; the structure of an unstable eigenmode is in good agreement with the results obtained by local stability analysis. The strato-hyperbolic mode becomes dominant depending on the parameter values.

A Liquid Metal Flow Between Two Coaxial Cylinders System

2019 ◽  
Vol 11 (1) ◽  
pp. 79-86
Author(s):  
Abdelkrim Merah ◽  
Ridha Kelaiaia ◽  
Faiza Mokhtari
Keyword(s):  
Couette Flow ◽  
Metal Flow ◽  
Three Dimensional ◽  
Liquid Sodium ◽  
Taylor Vortex ◽  
Turbulent Regime ◽  
Coaxial Cylinders ◽  
Concentric Cylinders ◽  
Ideal Tool ◽  
The Stability

Abstract The Taylor-Couette flow between two rotating coaxial cylinders remains an ideal tool for understanding the mechanism of the transition from laminar to turbulent regime in rotating flow for the scientific community. We present for different Taylor numbers a set of three-dimensional numerical investigations of the stability and transition from Couette flow to Taylor vortex regime of a viscous incompressible fluid (liquid sodium) between two concentric cylinders with the inner one rotating and the outer one at rest. We seek the onset of the first instability and we compare the obtained results for different velocity rates. We calculate the corresponding Taylor number in order to show its effect on flow patterns and pressure field.

Handheld Laser Scanner Research

2019 ◽  
Vol 952 (10) ◽  
pp. 47-54
Author(s):  
A.V. Komissarov ◽  
A.V. Remizov ◽  
M.M. Shlyakhova ◽  
K.K. Yambaev
Keyword(s):  
Point Cloud ◽  
Three Dimensional ◽  
Laser Scanner ◽  
Test Site ◽  
Optical Systems ◽  
Advantages And Disadvantages ◽  
Site Survey ◽  
Laser Scanners ◽  
Three Dimensional Models ◽  
The Stability

The authors consider hand-held laser scanners, as a new photogrammetric tool for obtaining three-dimensional models of objects. The principle of their work and the newest optical systems based on various sensors measuring the depth of space are described in detail. The method of simultaneous navigation and mapping (SLAM) used for combining single scans into point cloud is outlined. The formulated tasks and methods for performing studies of the DotProduct (USA) hand-held laser scanner DPI?8X based on a test site survey are presented. The accuracy requirements for determining the coordinates of polygon points are given. The essence of the performed experimental research of the DPI?8X scanner is described, including scanning of a test object at various scanner distances, shooting a test polygon from various scanner positions and building point cloud, repeatedly shooting the same area of the polygon to check the stability of the scanner. The data on the assessment of accuracy and analysis of research results are given. Fields of applying hand-held laser scanners, their advantages and disadvantages are identified.

scholarly journals Gum Tragacanth (GT): A Versatile Biocompatible Material beyond Borders

Molecules ◽  
2021 ◽  
Vol 26 (6) ◽  
pp. 1510 ◽  
Author(s):  
Mohammad Ehsan Taghavizadeh Yazdi ◽  
Simin Nazarnezhad ◽  
Seyed Hadi Mousavi ◽  
Mohammad Sadegh Amiri ◽  
Majid Darroudi ◽  
...  
Keyword(s):  
Tissue Engineering ◽  
Food Packaging ◽  
Three Dimensional ◽  
Great Promise ◽  
Anionic Polymer ◽  
Gum Tragacanth ◽  
New Horizons ◽  
Tissue Healing ◽  
The Stability ◽  
Therapeutic Substance

The use of naturally occurring materials in biomedicine has been increasingly attracting the researchers’ interest and, in this regard, gum tragacanth (GT) is recently showing great promise as a therapeutic substance in tissue engineering and regenerative medicine. As a polysaccharide, GT can be easily extracted from the stems and branches of various species of Astragalus. This anionic polymer is known to be a biodegradable, non-allergenic, non-toxic, and non-carcinogenic material. The stability against microbial, heat and acid degradation has made GT an attractive material not only in industrial settings (e.g., food packaging) but also in biomedical approaches (e.g., drug delivery). Over time, GT has been shown to be a useful reagent in the formation and stabilization of metal nanoparticles in the context of green chemistry. With the advent of tissue engineering, GT has also been utilized for the fabrication of three-dimensional (3D) scaffolds applied for both hard and soft tissue healing strategies. However, more research is needed for defining GT applicability in the future of biomedical engineering. On this object, the present review aims to provide a state-of-the-art overview of GT in biomedicine and tries to open new horizons in the field based on its inherent characteristics.

scholarly journals Emergent chiral symmetry in a three-dimensional interacting Dirac liquid

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
András L. Szabó ◽  
Bitan Roy
Keyword(s):  
Fixed Points ◽  
Chiral Symmetry ◽  
Rotational Symmetry ◽  
Three Dimensional ◽  
Spatial Dimension ◽  
Dirac Fermions ◽  
Electronic Interactions ◽  
Emergent Phenomena ◽  
Ordered Phases ◽  
The Stability

Abstract We compute the effects of strong Hubbardlike local electronic interactions on three-dimensional four-component massless Dirac fermions, which in a noninteracting system possess a microscopic global U(1) ⊗ SU(2) chiral symmetry. A concrete lattice realization of such chiral Dirac excitations is presented, and the role of electron-electron interactions is studied by performing a field theoretic renormalization group (RG) analysis, controlled by a small parameter ϵ with ϵ = d−1, about the lower-critical one spatial dimension. Besides the noninteracting Gaussian fixed point, the system supports four quantum critical and four bicritical points at nonvanishing interaction couplings ∼ ϵ. Even though the chiral symmetry is absent in the interacting model, it gets restored (either partially or fully) at various RG fixed points as emergent phenomena. A representative cut of the global phase diagram displays a confluence of scalar and pseudoscalar excitonic and superconducting (such as the s-wave and p-wave) mass ordered phases, manifesting restoration of (a) chiral U(1) symmetry between two excitonic masses for repulsive interactions and (b) pseudospin SU(2) symmetry between scalar or pseudoscalar excitonic and superconducting masses for attractive interactions. Finally, we perturbatively study the effects of weak rotational symmetry breaking on the stability of various RG fixed points.

Sign in / Sign up

Export Citation Format

Share Document