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°.

The observation of the simultaneous development of a long- and a short-wave instability mode on a vortex pair

1994 ◽  
Vol 265 ◽  
pp. 289-302 ◽  
Author(s):  
P. J. Thomas ◽  
D. Auerbach
Keyword(s):  
Vortex Pair ◽  
Short Wave ◽  
Wave Mode ◽  
Core Diameter ◽  
Vortex Pairs ◽  
Long Wave ◽  
Instability Modes ◽  
Bending Mode ◽  
Theoretical Predictions ◽  
The Stability

Experiments on the stability of vortex pairs are described. The vortices (ratio of length to core diameter L/c of up to 300) were generated at the edge of a flat plate rotating about a horizontal axis in water. The vortex pairs were found to be unstable, displaying two distinct modes of instability. For the first time, as far as it is known to the authors, a long-wave as well as a short-wave mode of instability were observed to develop simultaneously on such a vortex pair. Experiments involving single vortices show that these do not develop any instability whatsoever. The wavelengths of the developing instability modes on the investigated vortex pairs are compared to theoretical predictions. Observed long wavelengths are in good agreement with the classic symmetric long-wave bending mode identified by Crow (1970). The developing short waves, on the other hand, appear to be less accurately described by the theoretical results predicted, for example, by Windnall, Bliss & Tsai (1974).

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.

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 Nonlinear stage in the development of hydrodynamic instability in laser targets

1990 ◽  
Vol 8 (1-2) ◽  
pp. 173-182 ◽  
Author(s):  
E. G. Gamaly ◽  
I. G. Lebo ◽  
V. B. Rozanov ◽  
A. P. Favorsky ◽  
A. O. Fedyanin ◽  
...  
Keyword(s):  
Growth Rate ◽  
Laser Irradiation ◽  
Hydrodynamic Instability ◽  
Short Wave ◽  
Numerical Code ◽  
Linear Stage ◽  
Long Wave ◽  
Nonlinear Stage ◽  
Rayleigh Taylor Instability ◽  
Image Position

The development of a hydrodynamic instability in laser targets is studied by means of a 2-D numerical code “ATLANT”. During the linear stage, the perturbations grow as:In the nonlinear stage the growth rate of the Rayleigh-Taylor instability is reduced, and new harmonics are generated. The effect of the nonuniformity of the laser irradiation has been investigated for long-wave and short-wave perturbations. The growth rate of short-wave perturbations may be effectively decreased by means of symmetrical pre-pulses.

The instability of a pinched fluid with a longitudinal magnetic field

1958 ◽  
Vol 245 (1241) ◽  
pp. 222-237 ◽  
Keyword(s):  
Magnetic Field ◽  
Longitudinal Magnetic Field ◽  
Short Wave ◽  
Longitudinal Field ◽  
Plasma Equilibrium ◽  
Azimuthal Magnetic Field ◽  
Long Wave ◽  
Pinched Plasma ◽  
Pinch Current ◽  
The Stability

The stability of a pinched plasma equilibrium with a longitudinal magnetic field superimposed on the characteristic azimuthal magnetic field of the pinch current is studied theoretically. The linearized solutions are developed as helical perturbations of the plasma surface, and the behaviour of these is given for the different cases of uniform longitudinal, longitudinal field zero inside the plasma, and for helices of the same and opposite sense to the helix which describes the total magnetic field. Approximately, the conclusions are: that the longitudinal field has the effect of stabilizing short-wave perturbations, but that some long-wave perturbations remain unstable no matter how large the externally imposed longitudinal magnetic field.

On the stability of nonlinear waves coexisting with plasma beams

1975 ◽  
Vol 13 (1) ◽  
pp. 173-187 ◽  
Author(s):  
E. Infeld ◽  
G. Rowlands
Keyword(s):  
Nonlinear Wave ◽  
Growth Rates ◽  
Three Dimensional ◽  
Stationary Waves ◽  
One Dimensional ◽  
Long Wavelength ◽  
Long Wave ◽  
Set Up ◽  
The Stability ◽  
The One

In this paper we consider the stability of one-dimensional stationary waves set up by two counter-streaming beams of electrons in a background of stationary ions. The perturbations considered are long-wave in a direction perpendicular to the wave. The presence of a uniform magnetic field in the direction of the wave and the effect of a perpendicular pressure are taken into account. In the long-wavelength limit growth rates are diminished by the nonlinear wave. When the amplitude of this wave tends to its maximum value, the growth rates tend to zero. Thus the wave has a stabilizing effect for long-wave perturbations. Three- dimensional effects lead to additional instabilities which are also quenched by the nonlinear wave, but not as fast as the one-dimensional calculation indicates.

scholarly journals On the porosity influence on stability of flow over porous medium

2020 ◽  
Vol 30 (1) ◽  
pp. 134-144
Author(s):  
K.B. Tsiberkin
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Short Wave ◽  
Wave Instability ◽  
Plane Parallel ◽  
Long Wave ◽  
The Stability ◽  
Critical Wavenumber

The stability of incompressible fluid plane-parallel flow over a layer of a saturated porous medium is studied. The results of a linear stability analysis are described at different porosity values. The considered system is bounded by solid wall from the porous layer bottom. Top fluid surface is free and rigid. A linear stability analysis of plane-parallel stationary flow is presented. It is realized for parameter area where the neutral stability curves are bimodal. The porosity variation effect on flow stability is considered. It is shown that there is a transition between two main instability modes: long-wave and short-wave. The long-wave instability mechanism is determined by inflection points within the velocity profile. The short-wave instability is due to the large transverse gradient of flow velocity near the interface between liquid and porous medium. Porosity decrease stabilizes the long wave perturbations without significant shift of the critical wavenumber. Simultaneously, the short-wave perturbations destabilize, and their critical wavenumber changes in wide range. When the porosity is less than 0.7, the inertial terms in filtration equation and magnitude of the viscous stress near the interface increase to such an extent that the Kelvin-Helmholtz analogue of instability becomes the dominant mechanism for instability development. The stability band realizes in narrow porosity area. It separates the two branches of the neutral curve.

Three-dimensional Rayleigh-Taylor instability Part 1. Weakly nonlinear theory

1988 ◽  
Vol 187 ◽  
pp. 329-352 ◽  
Author(s):  
J. W. Jacobs ◽  
I. Catton
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Taylor Instability ◽  
Initial Surface ◽  
Surface Slope ◽  
Cross Sectional ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Rayleigh Taylor Instability ◽  
The Stability

Three-dimensional weakly nonlinear Rayleigh-Taylor instability is analysed. The stability of a confined inviscid liquid and an overlying gas with density much less than that of the liquid is considered. An asymptotic solution for containers of arbitrary cross-sectional geometry, valid up to order ε3 (where ε is the root-mean-squared initial surface slope) is obtained. The solution is evaluated for the rectangular and circular geometries and for various initial modes (square, hexagonal, axisymmetric, etc.). It is found that the hexagonal and axisymmetric instabilities grow faster than any other shapes in their respective geometries. In addition it is found that, sufficiently below the cutoff wavenumber, instabilities that are equally proportioned in the lateral directions grow faster than those with longer, thinner shape. However, near the cutoff wavenumber this trend reverses with instabilities having zero aspect ratio growing faster than those with aspect ratio near 1.

scholarly journals Transversally periodic solitary gravity–capillary waves

2014 ◽  
Vol 470 (2161) ◽  
pp. 20130537 ◽  
Author(s):  
Paul A. Milewski ◽  
Zhan Wang
Keyword(s):  
Solitary Waves ◽  
Water Waves ◽  
Travelling Waves ◽  
Plane Waves ◽  
Three Dimensional ◽  
Capillary Waves ◽  
Propagation Direction ◽  
The Stability ◽  
Dirichlet To Neumann Operator ◽  
The Waves

When both gravity and surface tension effects are present, surface solitary water waves are known to exist in both two- and three-dimensional infinitely deep fluids. We describe here solutions bridging these two cases: travelling waves which are localized in the propagation direction and periodic in the transverse direction. These transversally periodic gravity–capillary solitary waves are found to be of either elevation or depression type, tend to plane waves below a critical transverse period and tend to solitary lumps as the transverse period tends to infinity. The waves are found numerically in a Hamiltonian system for water waves simplified by a cubic truncation of the Dirichlet-to-Neumann operator. This approximation has been proved to be very accurate for both two- and three-dimensional computations of fully localized gravity–capillary solitary waves. The stability properties of these waves are then investigated via the time evolution of perturbed wave profiles.

scholarly journals Geometric- and Optimization-Based Registration Methods for Long-Wave Infrared Hyperspectral Images

2021 ◽  
Vol 13 (13) ◽  
pp. 2465
Author(s):  
Alper Koz ◽  
Ufuk Efe
Keyword(s):  
Hyperspectral Image ◽  
Three Dimensional ◽  
Average Energy ◽  
Short Wave ◽  
Hyperspectral Images ◽  
Spectral Radiance ◽  
Global Registration ◽  
Long Wave ◽  
Image Pixels ◽  
Long Wave Infrared

Registration of long-wave infrared (LWIR) hyperspectral images with their thermal and emissivity components has until now received comparatively less attention with respect to the visible near and short wave infrared hyperspectral images. In this paper, the registration of LWIR hyperspectral images is investigated to enhance applications of LWIR images such as change detection, temperature and emissivity separation, and target detection. The proposed approach first searches for the best features of hyperspectral image pixels for extraction and matching in the LWIR range and then performs a global registration over two-dimensional maps of three-dimensional hyperspectral cubes. The performances of temperature and emissivity features in the thermal domain along with the average energy and principal components of spectral radiance are investigated. The global registration performed over whole 2D maps is further improved by blockwise local refinements. Among the two proposed approaches, the geometric refinement seeks the best keypoint combination in the neighborhood of each block to estimate the transformation for that block. The alternative optimization-based refinement iteratively finds the best transformation by maximizing the similarity of the reference and transformed blocks. The possible blocking artifacts due to blockwise mapping are finally eliminated by pixelwise refinement. The experiments are evaluated with respect to the (i) utilized similarity metrics in the LWIR range between transformed and reference blocks, (ii) proposed geometric- and optimization-based methods, and (iii) image pairs captured on the same and different days. The better performance of the proposed approach compared to manual, GPU-IMU-based, and state-of-the-art image registration methods is verified.

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