scholarly journals Nonlinear Stage of the Benjamin-Feir Instability: Three-Dimensional Coherent Structures and Rogue Waves

2007 ◽  
Vol 99 (4) ◽  
Author(s):  
V. P. Ruban
Keyword(s):  
Coherent Structures ◽  
Three Dimensional ◽  
Rogue Waves ◽  
Nonlinear Stage

scholarly journals Experimental Study on Coherent Structures by Particles Suspended in Half-Zone Thermocapillary Liquid Bridges: Review

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 105
Author(s):  
Ichiro Ueno
Keyword(s):  
Coherent Structures ◽  
Three Dimensional ◽  
Wave Number ◽  
Flow Structures ◽  
Liquid Bridges ◽  
Thermocapillary Effect ◽  
Particle Accumulation ◽  
Azimuthal Wave Number ◽  
Experimental Approaches ◽  
Particle Behaviour

Coherent structures by the particles suspended in the half-zone thermocapillary liquid bridges via experimental approaches are introduced. General knowledge on the particle accumulation structures (PAS) is described, and then the spatial–temporal behaviours of the particles forming the PAS are illustrated with the results of the two- and three-dimensional particle tracking. Variations of the coherent structures as functions of the intensity of the thermocapillary effect and the particle size are introduced by focusing on the PAS of the azimuthal wave number m=3. Correlation between the particle behaviour and the ordered flow structures known as the Kolmogorov–Arnold—Moser tori is discussed. Recent works on the PAS of m=1 are briefly introduced.

Experiments on the stability of sinusoidal flow over a circular cylinder

2002 ◽  
Vol 457 ◽  
pp. 157-180 ◽  
Author(s):  
TURGUT SARPKAYA
Keyword(s):  
Stokes Flow ◽  
Coherent Structures ◽  
High Speed ◽  
Three Dimensional ◽  
Separated Flow ◽  
Circular Cylinders ◽  
Centrifugal Forces ◽  
Complex Interactions ◽  
Sinusoidal Flow ◽  
The Stability

The instabilities in a sinusoidally oscillating non-separated flow over smooth circular cylinders in the range of Keulegan–Carpenter numbers, K, from about 0.02 to 1 and Stokes numbers, β, from about 103 to 1.4 × 106 have been observed from inception to chaos using several high-speed imagers and laser-induced fluorescence. The instabilities ranged from small quasi-coherent structures, as in Stokes flow over a flat wall (Sarpkaya 1993), to three-dimensional spanwise perturbations because of the centrifugal forces induced by the curvature of the boundary layer (Taylor–Görtler instability). These gave rise to streamwise-oriented counter-rotating vortices or mushroom-shaped coherent structures as K approached the Kh values theoretically predicted by Hall (1984). Further increases in K for a given β led first to complex interactions between the coherent structures and then to chaotic motion. The mapping of the observations led to the delineation of four states of flow in the (K, β)-plane: stable, marginal, unstable, and chaotic.

Localized waves and interaction solutions to an extended (3+1)-dimensional Kadomtsev–Petviashvili equation

2020 ◽  
Vol 34 (06) ◽  
pp. 2050076 ◽  
Author(s):  
Han-Dong Guo ◽  
Tie-Cheng Xia ◽  
Wen-Xiu Ma
Keyword(s):  
Three Dimensional ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Dark Soliton ◽  
Complex Conjugate ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Parameter Constraints ◽  
Localized Waves

In this paper, an extended (3[Formula: see text]+[Formula: see text]1)-dimensional Kadomtsev–Petviashvili (KP) equation is studied via the Hirota bilinear derivative method. Soliton, breather, lump and rogue waves, which are four types of localized waves, are obtained. N-soliton solution is derived by employing bilinear method. Then, line or general breathers, two-order line or general breathers, interaction solutions between soliton and line or general breathers are constructed by complex conjugate approach. These breathers own different dynamic behaviors in different planes. Taking the long wave limit method on the multi-soliton solutions under special parameter constraints, lumps, two- and three-lump and interaction solutions between dark soliton and dark lump are constructed, respectively. Finally, dark rogue waves, dark two-order rogue waves and related interaction solutions between dark soliton and dark rogue waves or dark lump are also demonstrated. Moreover, dynamical characteristics of these localized waves and interaction solutions are further vividly demonstrated through lots of three-dimensional graphs.

NESTED INVARIANT 3-TORI EMBEDDED IN A SEA OF CHAOS IN A QUASIPERIODIC FLUID FLOW

2009 ◽  
Vol 19 (07) ◽  
pp. 2181-2191 ◽  
Author(s):  
HOPE L. WEISS ◽  
ANDREW J. SZERI
Keyword(s):  
Fixed Point ◽  
Fluid Flow ◽  
Cross Sections ◽  
Coherent Structures ◽  
Three Dimensional ◽  
Elliptic Type ◽  
Two Phase ◽  
Dimensional Phase Space ◽  
Hyperbolic Fixed Point ◽  
Stream Functions

Nested invariant 3-tori surrounding a torus braid of elliptic type are found to exist in a model of a fluid flow with quasiperiodic forcing. The Hamiltonian describing the system is given by the superposition of two steady stream functions, one with an elliptic fixed point and the other with a coincident hyperbolic fixed point. The superposition, modulated by two incommensurate frequencies, yields an elliptic torus braid at the location of the fixed point. The system is suspended in a four-dimensional phase space (two space and two phase directions). To analyze this system we define two three-dimensional, global, Poincaré sections of the flow. The coherent structures (cross-sections of nested 2 tori) are found each to have a fractal dimensional of two, in each Poincaré cross-section. This framework has applications to tidal and other mixing problems of geophysical interest.

NONLINEAR EVOLUTION OF TURBULENT COHERENT STRUCTURES IN CHANNEL FLOWS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1539-1542
Author(s):  
ZHANG LI ◽  
DENGBIN TANG ◽  
LINLIN GUO
Keyword(s):  
Coherent Structures ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Channel Flows ◽  
Navier Stokes ◽  
Theoretic Model ◽  
Compact Difference Scheme ◽  
Navier Stokes Equation ◽  
Turbulent Coherent Structures ◽  
Dimensional Coupling

The generation and the development of turbulent coherent structures in channel flows are investigated by using numerical simulation of Navier-Stokes equation and the theoretic model of turbulent coherent structures built up by the flow stability theories. The three-dimensional coupling compact difference scheme with high accuracy and resolution developed can be applied to the calculative region including points near the boundary. The results computed show nonlinear evolution process and characteristics of Reynolds stress, stream-wise vortices and span-wise vorticities, especially the nonlinear interactions between different coherent structures.

Line Rogue Waves in the Mel’nikov Equation

2017 ◽  
Vol 72 (7) ◽  
pp. 609-615 ◽  
Author(s):  
Yongkang Shi
Keyword(s):  
Three Dimensional ◽  
Rogue Waves ◽  
Higher Order ◽  
Matrix Elements ◽  
Bilinear Method ◽  
Algebraic Expressions ◽  
General Line ◽  
Free Parameters ◽  
Hirota Bilinear ◽  
Fundamental Line

AbstractGeneral line rogue waves in the Mel’nikov equation are derived via the Hirota bilinear method, which are given in terms of determinants whose matrix elements have plain algebraic expressions. It is shown that fundamental rogue waves are line rogue waves, which arise from the constant background with a line profile and then disappear into the constant background again. By means of the regulation of free parameters, two subclass of nonfundamental rogue waves are generated, which are called as multirogue waves and higher-order rogue waves. The multirogue waves consist of several fundamental line rogue waves, which arise from the constant background and then decay back to the constant background. The higher-order rogue waves start from a localised lump and retreat back to it. The dynamical behaviours of these line rogue waves are demonstrated by the density and the three-dimensional figures.

Coherent structures and dominant frequencies in a turbulent three-dimensional diffuser

2012 ◽  
Vol 699 ◽  
pp. 320-351 ◽  
Author(s):  
Johan Malm ◽  
Philipp Schlatter ◽  
Dan S. Henningson
Keyword(s):  
Coherent Structures ◽  
Large Scale ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Low Frequency ◽  
Bulk Velocity ◽  
Time Signal ◽  
Mean Flow ◽  
The Mean ◽  
Dominant Frequencies

AbstractDominant frequencies and coherent structures are investigated in a turbulent, three-dimensional and separated diffuser flow at $\mathit{Re}= 10\hspace{0.167em} 000$ (based on bulk velocity and inflow-duct height), where mean flow characteristics were first studied experimentally by Cherry, Elkins and Eaton (Intl J. Heat Fluid Flow, vol. 29, 2008, pp. 803–811) and later numerically by Ohlsson et al. (J. Fluid Mech., vol. 650, 2010, pp. 307–318). Coherent structures are educed by proper orthogonal decomposition (POD) of the flow, which together with time probes located in the flow domain are used to extract frequency information. The present study shows that the flow contains multiple phenomena, well separated in frequency space. Dominant large-scale frequencies in a narrow band $\mathit{St}\equiv fh/ {u}_{b} \in [0. 0092, 0. 014] $ (where $h$ is the inflow-duct height and ${u}_{b} $ is the bulk velocity), yielding time periods ${T}^{\ensuremath{\ast} } = T{u}_{b} / h\in [70, 110] $, are deduced from the time signal probes in the upper separated part of the diffuser. The associated structures identified by the POD are large streaks arising from a sinusoidal oscillating motion in the diffuser. Their individual contributions to the total kinetic energy, dominated by the mean flow, are, however, small. The reason for the oscillating movement in this low-frequency range is concluded to be the confinement of the flow in this particular geometric set-up in combination with the high Reynolds number and the large separated zone on the top diffuser wall. Based on this analysis, it is shown that the bulk of the streamwise root mean square (r.m.s.) value arises due to large-scale motion, which in turn can explain the appearance of two or more peaks in the streamwise r.m.s. value. The weak secondary flow present in the inflow duct is shown to survive into the diffuser, where it experiences an imbalance with respect to the upper expanding corners, thereby giving rise to the asymmetry of the mean separated region in the diffuser.

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