The stability of an expanding circular vortex layer

1981 ◽  
Vol 375 (1762) ◽  
pp. 443-451 ◽  
Keyword(s):  
Layer Thickness ◽  
Short Wave ◽  
Wave Analysis ◽  
Short Waves ◽  
Vortex Layer ◽  
Vortex Lines ◽  
Cylindrical Vortex ◽  
The Stability ◽  
Small Disturbances

The stability of a circular cylindrical vortex layer against small disturbances that do not bend the vortex lines is examined. A short-wave analysis of the equations governing the growth of disturbances for a thin vortex layer reveals the stabilizing influence of the vortex-layer thickness when the layer is undergoing stretching. Also, the onset of amplification of very short waves is found to be delayed. Certain experimental observations due to Crow & Barker (1977) are discussed in view of the results of the analysis.

The stability of short waves on a straight vortex filament in a weak externally imposed strain field

1976 ◽  
Vol 73 (4) ◽  
pp. 721-733 ◽  
Author(s):  
Chon-Yin Tsai ◽  
Sheila E. Widnall
Keyword(s):  
Strain Field ◽  
Circular Cross Section ◽  
Short Wave ◽  
Vortex Filament ◽  
Linear Stability Theory ◽  
Short Waves ◽  
Constant Vorticity ◽  
Long Wave ◽  
Intersection Points ◽  
The Stability

The stability of short-wave displacement perturbations on a vortex filament of constant vorticity in a weak externally imposed strain field is considered. The circular cross-section of the vortex filament in this straining flow field becomes elliptical. It is found that instability of short waves on this strained vortex can occur only for wavelengths and frequencies at the intersection points of the dispersion curves for an isolated vortex. Numerical results show that the vortex is stable at some of these points and unstable at others. The vortex is unstable at wavelengths for which ω = 0, thus giving some support to the instability mechanism for the vortex ring proposed recently by Widnall, Bliss & Tsai (1974). The growth rate is calculated by linear stability theory. The previous work of Crow (1970) and Moore & Saffman (1971) dealing with long-wave instabilities is discussed as is the very recent work of Moore & Saffman (1975).

On the modulation of water waves on shear flows

1976 ◽  
Vol 347 (1651) ◽  
pp. 537-546 ◽  
Keyword(s):  
Water Waves ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vries Equation ◽  
Harmonic Wave ◽  
Short Wave ◽  
Long Wave ◽  
Stokes Waves ◽  
The Stability ◽  
Wave Limit

The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here.

scholarly journals Structure and dynamical behavior of non-normal networks

2018 ◽  
Vol 4 (12) ◽  
pp. eaau9403 ◽  
Author(s):  
Malbor Asllani ◽  
Renaud Lambiotte ◽  
Timoteo Carletti
Keyword(s):  
Network Science ◽  
Wide Spectrum ◽  
Dynamical Behavior ◽  
Transient Phase ◽  
The Stability ◽  
Normal Networks ◽  
Empirical Networks ◽  
Peculiar Behavior ◽  
Potential Use ◽  
Small Disturbances

We analyze a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behavior, as initial small disturbances may undergo a transient phase and be strongly amplified in linearly stable systems. In addition, eigenvalues may become extremely sensible to noise and have a diminished physical meaning. We identify structural properties of networks that are associated with non-normality and propose simple models to generate networks with a tunable level of non-normality. We also show the potential use of a variety of metrics capturing different aspects of non-normality and propose their potential use in the context of the stability of complex ecosystems.

scholarly journals On some short-wave equivalent height measurements of the ionized regions of the upper atmosphere

1930 ◽  
Vol 128 (807) ◽  
pp. 159-178 ◽  
Keyword(s):  
Wave Length ◽  
Good Deal ◽  
Short Wave ◽  
Wave Intensity ◽  
Upper Atmosphere ◽  
Frequency Change ◽  
Electronic Density ◽  
Short Waves ◽  
F Region ◽  
E Region

The present paper continues the account of wireless investigations of the ionized regions of the upper atmosphere given in two previous papers. The results discussed in it consist chiefly of measurements of the equivalent heights of the ionized regions made simultaneously at two or three receiving stations with wave-lengths of the order of 100 metres. The frequency-change method of measuring the equivalent height was used throughout. 2. Extension of Equivalent Height Measurements to the Use of Short Waves . The experiments described previously were continued with shorter wave-lengths with two objects in view. In the first place it had been found that 400-metre waves penetrated the lower ionized region (E region) only on certain nights, and then only during the few hours before dawn. This result clearly showed that penetration of this region was most likely when the density of ionization was least. But, according to most theories of wireless propagation, a greater electronic density is required to reflect or refract short waves than is the case with long waves, so that it was anticipated that by reducing the wave-length below 400 metres it might be possible to penetrate E region over a longer period of time during the night than had been possible when 400-metre waves had been used. In this way it was hoped to make a more detailed study of the variation of the equivalent height of the upper region (F region) which had been found to reflect 400-metre waves on the occasion when they had penetrated the normal E region. Secondly, since it is known that the attenuation of the ground waves increases rapidly as the wave-length is reduced below, say, 400 metres, it was expected that, with the use of shorter waves, the ratio of the values of downcoming wave intensity and ground wave intensity would be much increased at all stations. Such an increase, it was expected, would make it possible to continue the measurements of equivalent heights, in general, a good deal further into the daylight hours. Such daylight measurements on longer waves had previously been found difficult, because of the relative weakness of the intensity of the downcoming waves as compared with that of the ground waves.

Radiation of short waves from the resonantly excited capillary–gravity waves

2016 ◽  
Vol 810 ◽  
pp. 5-24 ◽  
Author(s):  
M. Hirata ◽  
S. Okino ◽  
H. Hanazaki
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Gravity Waves ◽  
Wave Pattern ◽  
Short Wave ◽  
Bond Number ◽  
Linear Wave ◽  
Cnoidal Wave ◽  
Short Waves ◽  
Long Wave

Capillary–gravity waves resonantly excited by an obstacle (Froude number: $Fr=1$) are investigated by the numerical solution of the Euler equations. The radiation of short waves from the long nonlinear waves is observed when the capillary effects are weak (Bond number: $Bo<1/3$). The upstream-advancing solitary wave radiates a short linear wave whose phase velocity is equal to the solitary waves and group velocity is faster than the solitary wave (soliton radiation). Therefore, the short wave is observed upstream of the foremost solitary wave. The downstream cnoidal wave also radiates a short wave which propagates upstream in the depression region between the obstacle and the cnoidal wave. The short wave interacts with the long wave above the obstacle, and generates a second short wave which propagates downstream. These generation processes will be repeated, and the number of wavenumber components in the depression region increases with time to generate a complicated wave pattern. The upstream soliton radiation can be predicted qualitatively by the fifth-order forced Korteweg–de Vries equation, but the equation overestimates the wavelength since it is based on a long-wave approximation. At a large Bond number of $Bo=2/3$, the wave pattern has the rotation symmetry against the pattern at $Bo=0$, and the depression solitary waves propagate downstream.

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 Antibubbles and fine cylindrical sheets of air

2015 ◽  
Vol 779 ◽  
pp. 87-115 ◽  
Author(s):  
D. Beilharz ◽  
A. Guyon ◽  
E. Q. Li ◽  
M.-J. Thoraval ◽  
S. T. Thoroddsen
Keyword(s):  
Layer Thickness ◽  
Stability Theory ◽  
Extended Period ◽  
Viscous Drops ◽  
Pool Surface ◽  
Lower Viscosity ◽  
Air Layers ◽  
The Stability ◽  
Air Film ◽  
The Way

Drops impacting at low velocities onto a pool surface can stretch out thin hemispherical sheets of air between the drop and the pool. These air sheets can remain intact until they reach submicron thicknesses, at which point they rupture to form a myriad of microbubbles. By impacting a higher-viscosity drop onto a lower-viscosity pool, we have explored new geometries of such air films. In this way we are able to maintain stable air layers which can wrap around the entire drop to form repeatable antibubbles, i.e. spherical air layers bounded by inner and outer liquid masses. Furthermore, for the most viscous drops they enter the pool trailing a viscous thread reaching all the way to the pinch-off nozzle. The air sheet can also wrap around this thread and remain stable over an extended period of time to form a cylindrical air sheet. We study the parameter regime where these structures appear and their subsequent breakup. The stability of these thin cylindrical air sheets is inconsistent with inviscid stability theory, suggesting stabilization by lubrication forces within the submicron air layer. We use interferometry to measure the air-layer thickness versus depth along the cylindrical air sheet and around the drop. The air film is thickest above the equator of the drop, but thinner below the drop and up along the air cylinder. Based on microbubble volumes, the thickness of the cylindrical air layer becomes less than 100 nm before it ruptures.

Basin of Attraction of the Simplest Walking Model

2001 ◽  
Author(s):  
A. L. Schwab ◽  
M. Wisse
Keyword(s):  
Equations Of Motion ◽  
Basin Of Attraction ◽  
Mapping Method ◽  
Walking Robots ◽  
Natural Energy ◽  
Walking Motion ◽  
The Stability ◽  
The Basin Of Attraction ◽  
General Method ◽  
Small Disturbances

Abstract Passive dynamic walking is an important development for walking robots, supplying natural, energy-efficient motions. In practice, the cyclic gait of passive dynamic prototypes appears to be stable, only for small disturbances. Therefore, in this paper we research the basin of attraction of the cyclic walking motion for the simplest walking model. Furthermore, we present a general method for deriving the equations of motion and impact equations for the analysis of multibody systems, as in walking models. Application of the cell mapping method shows the basin of attraction to be a small, thin area. It is shown that the basin of attraction is not directly related to the stability of the cyclic motion.

scholarly journals Thrust Prediction of an Active Flapping Foil in Waves Using CFD

2019 ◽  
Vol 7 (11) ◽  
pp. 396
Author(s):  
Rupesh Kumar ◽  
Hyunkyoung Shin
Keyword(s):  
Wave Energy ◽  
Thrust Force ◽  
Short Wave ◽  
Floating Structures ◽  
Flapping Foil ◽  
Short Waves ◽  
Computational Fluid Dynamics Cfd ◽  
Numerical Tool ◽  
Flapping Foils ◽  
Ansys Workbench

A horizontally submerged passive flapping foil can generate thrust force against the wave propagation using wave energy. This renewable method has been used for the design of propulsion and maneuvering systems of ships and other floating structures. Recently, the passive flapping foils were applied to design the station-keeping system of deep-water floaters. Studies proved that the passively flapping foil system was ineffective in short waves and drift of the floater beyond the design limit was recorded. Therefore, an active flapping foil was investigated as a potential solution to this problem. A computational fluid dynamics (CFD) numerical tool “ANSYS Workbench 19.2” was used to predict the thrust force generated by the active flapping foil in a short wave. Results proved that the active flapping foil can effectively convert wave energy into propulsive energy in short waves and the magnitude of the thrust force depends on the flapping frequency.

scholarly journals Analysis of Factors Influencing Stability of Overlying Soil Layer on Thin Bedrock Based on Crack Development-Closure Test

2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
Guangming Wu ◽  
Haibo Bai ◽  
Luyuan Wu ◽  
Shixin He ◽  
Bin Du
Keyword(s):  
Water Content ◽  
Layer Thickness ◽  
Crack Width ◽  
Soil Layer ◽  
Crack Development ◽  
Sand Content ◽  
Particle Composition ◽  
Thin Bedrock ◽  
The Stability ◽  
Seam Mining

The water-blocking properties of the clay layer at the bottom of the Cenozoic overburden in China are an important factor influencing the safety of thin bedrock coal seam mining. Clay has remolding properties that are unlike the nonreversible characteristics of cracks in brittle rock, and failure cracks in clay can reclose or continue to expand under the influence of different external factors. In this work, the soil layer on top of thin bedrock is the research object, and the influences of the particle composition, water content, soil layer thickness, and crack width on the crack development-closure state of soil layer are analyzed by the orthogonal test method. Visual analysis shows that the order of influence of each factor on the stability of soil layer is the crack width, particle composition, soil layer thickness, and water content. The stability of soil layer decreases with increasing crack width and sand content and decreasing soil layer thickness; in addition, soil layer stability decreases first and then increases with increasing water content. Further variance analysis shows that the crack width and particle composition are key factors that impact the stability of soil layer and that the soil layer thickness has some influence, while the water content has little effect on the stability of soil layer. In addition, the crack will reclose when the sand content in soil is less than 50% and the crack width is less than or equal to 1.0 mm, and the soil layer is prone to further failure when the sand content in soil is more than 50% and the crack width is greater than or equal to 3.0 mm; when the soil layer thickness is 15.0 cm, its stability is better than when the soil layer thickness is 10.0 cm or 5.0 cm.

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