Nonlinear waves of the oscillatory instability on finite convective rolls

Croquette, Vincent; Williams, Hugh

doi:10.1016/0167-2789(89)90138-3

Cited by 49 publications

(50 citation statements)

References 29 publications

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“…We have yet no way to estimate µ. The small value of λ denotes a moderate destructive interaction between right-and left-propagating waves compared, for example, to oscillatory instability in Argon where λ = 2 [43]. Although standing hydrothermal waves have never been observed in onedimensional systems, complex states involving both right and left waves are common in the rectangular cell, close to onset, and in the annular cell, for chaotic regimes at large ǫ: once the amplitude of the major wave is attenuated -and whatever the cause-the opposite wave is much less damped and starts growing.…”

Section: Experimentally Known Cgl Coefficientsmentioning

confidence: 99%

“…CGL model equation describe correctly most non-linear wave systems such as low-Prandtl-number oscillatory instability [43,7,8], binary fluid convection [4,5], convection with rotation [9], cylinder wake [10] and so on. A single equation is enough for systems with broken x → −x symmetry, i.e., when a single wave is present.…”

Section: Complex Ginzburg-landau Envelope Equation Modelingmentioning

confidence: 99%

“…This pattern is saturated by non-linearities, because all quantities are constant along time. As far as the amplitude of the modulation is large on all fields, we tried to determine the group velocity and some CGL coefficients from the frequencywavenumber and amplitude-wavenumber relation extracted from local values over the whole data set [43,34]. We thus get:…”

Section: Modulations Of Large Period At Small ǫmentioning

confidence: 99%

“…In order to demodulate the signal, we apply Hilbert transform. Real data are complexified by the three following operations [43,14]: a Fourier transform of θ r in x or t, a wide band-pass filtering around the positive fundamental frequency in Fourier space and then the inverse Fourier transform; this creates the complex signal θ c . In this complex signal, the right-and left-propagating waves data are mixed:…”

Section: Experimental Demodulation Technique and Cgl Modelingmentioning

confidence: 99%

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Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II. Convective/absolute transitions

Garnier¹,

Chiffaudel²,

Daviaud³

2003

Physica D: Nonlinear Phenomena

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We present experimental results on hydrothermal traveling-waves dynamics in long and narrow 1D channels. The onset of primary traveling-wave patterns is briefly presented for different fluid heights and for annular or bounded channels, i.e., within periodic or non-periodic boundary conditions. For periodic boundary conditions, by increasing the control parameter or changing the discrete mean-wavenumber of the waves, we produce modulated waves patterns. These patterns range from stable periodic phase-solutions, due to supercritical Eckhaus instability, to spatio-temporal defect-chaos involving traveling holes and/or counter-propagating-waves competition, i.e., traveling sources and sinks. The transition from non-linearly saturated Eckhaus modulations to transient pattern-breaks by traveling holes and spatiotemporal defects is documented. Our observations are presented in the framework of coupled complex Ginzburg-Landau equations with additional fourth and fifth order terms which account for the reflection symmetry breaking at high wave-amplitude far from onset. The second part of this paper [1] extends this study to spatially non-periodic patterns observed in both annular and bounded channel.

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Section: Experimentally Known Cgl Coefficientsmentioning

confidence: 99%

Section: Complex Ginzburg-landau Envelope Equation Modelingmentioning

confidence: 99%

Section: Modulations Of Large Period At Small ǫmentioning

confidence: 99%

Section: Experimental Demodulation Technique and Cgl Modelingmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II. Convective/absolute transitions

Garnier¹,

Chiffaudel²,

Daviaud³

2003

Physica D: Nonlinear Phenomena

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show abstract

“…That instability is of interest in many physical problems and has been observed experimentally in, e.g. binary ñuid convection [2][3][4][5], isothermal double diffusive convection [6], puré Rayleigh-Bénard convection (as a secondary instability of rolls) [7][8][9], the Taylor-Couette system [10,11], several thermocapillary flows [12][13][14], electrodynamic convection in nematic liquid crystals [15][16][17][18], and several combustión systems [19][20][21].…”

Section: Introductionmentioning

confidence: 99%