Influence of low-frequency vibration on thermocapillary instability in a binary mixture with the Soret effect: long-wave versus short-wave perturbations

2013 ◽  
Vol 714 ◽  
pp. 190-212 ◽  
Author(s):  
Irina S. Fayzrakhmanova ◽  
Sergey Shklyaev ◽  
Alexander A. Nepomnyashchy
Keyword(s):  
Binary Mixture ◽  
Soret Effect ◽  
Low Frequency ◽  
Short Wave ◽  
Pure Liquid ◽  
Long Wave ◽  
Empirical Criterion ◽  
Low Frequency Vibration ◽  
Thermocapillary Instability ◽  
Limiting Case

AbstractWe study the influence of low-frequency vibration on Marangoni instability in a layer of a binary mixture with the Soret effect. A linear stability analysis is performed numerically for perturbations of a finite wavelength (short-wave perturbations). Competition between long-wave and short-wave modes is found: the former ones are critical at smaller absolute values of the Soret number $\chi $, whereas the latter ones lead to instability at higher $\vert \chi \vert $. In both cases the vibration destabilizes the layer. Two variants of calculations are performed: via Floquet theory (linear asymptotic stability) and taking noise into consideration (empirical criterion). It is found that fluctuations substantially reduce the domains of stability. Further, while studying a limiting case within the empirical criterion, we have found a short-wave instability mode overlooked in former investigations of coupled Rayleigh–Marangoni convection in a layer of pure liquid.

Analysis on Low Frequency Heave, Roll and Pitch Motions of a Deepwater Semisubmersible

2009 ◽  
Author(s):  
Longfei Xiao ◽  
Jianmin Yang ◽  
Lijun Yang ◽  
Haining Lu
Keyword(s):  
Frequency Response ◽  
Low Frequency ◽  
Short Wave ◽  
Wind Drift ◽  
Viscous Forces ◽  
Wave Drift ◽  
Long Wave ◽  
Drift Force ◽  
Heave Motion ◽  
Survival Condition

Low frequency heave, roll and pitch motions of a semisubmersible should be evaluated carefully, since the air gap and the drilling operation are affected directly. A drilling semisubmersible in operating and survival conditions is investigated numerically and experimentally. Results of RAOs, power spectrums and statistic values are presented and analyzed. Viscous forces are significant for roll and pitch but negligible for heave. The natural periods of roll and pitch are relatively large and low frequency response exists due to excitations by the second order wave drift force. By comparison with the wave frequency response, the low frequency roll and pitch are dominative in operating condition and the same magnitude in survival condition. For heave motion, the low frequency response doesn’t exist in survival storm with long wave periods and exists obviously in operational storm with short wave periods. The effect of wind spectrum is small for heave but very significant for roll and pitch. The low frequency roll and pitch in wind spectrum are much larger than ones in steady wind. It indicated that the resonant roll and pitch induced by the slowly varying wind drift force are much larger than ones induced by the wave drift force.

Nonlinear low-frequency waves in dusty self-gravitating plasmas

2000 ◽  
Vol 64 (4) ◽  
pp. 359-370 ◽  
Author(s):  
VICTORIA V. YAROSHENKO ◽  
FRANK VERHEEST
Keyword(s):  
Solitary Waves ◽  
Modulational Instability ◽  
Low Frequency ◽  
Nonlinear Effects ◽  
Dusty Plasmas ◽  
Short Wave ◽  
Electrostatic Waves ◽  
Significant Difference ◽  
Dust Acoustic ◽  
Limiting Case

Nonlinear electrostatic waves in self-gravitating dusty plasmas are considered in two limiting cases, according to whether the charged-particle dynamics is governed mostly by electrostatic forces or mostly by gravitation. This shows a significant difference between these two plasma media with respect to the envelope dynamics in the nonlinear regime. In the former case, when ω2pα > ω2Jα, the amplitude perturbations are longitudinally unstable only in the short-wave range, and the nonlinear effects can result in the formation of longitudinal dust-acoustic solitary waves. But even weak self-gravitational effects can lead to the existence of a long-wavelength range, where self-gravitation prevents the formation of dust-acoustic solitons, and only transverse solitary structures are possible. In the other limiting case (ω2pα < ω2Jα), there is always a transverse modulational instability, which can lead to transverse solitary waves. In both cases, there is a threshold for solitary-wave formation.

scholarly journals Linear temporal and spatio-temporal stability analysis of a binary liquid film flowing down an inclined uniformly heated plate

2008 ◽  
Vol 599 ◽  
pp. 269-298 ◽  
Author(s):  
JUN HU ◽  
HAMDA BEN HADID ◽  
DANIEL HENRY ◽  
ABDELKADER MOJTABI
Keyword(s):  
Soret Effect ◽  
Short Wave ◽  
Heated Plate ◽  
Surface Mode ◽  
Wave Instability ◽  
Binary Liquid ◽  
Long Wave ◽  
Neutral Curves ◽  
Spatio Temporal ◽  
Boundary Curves

Temporal and spatio-temporal instabilities of binary liquid films flowing down an inclined uniformly heated plate with Soret effect are investigated by using the Chebyshev collocation method to solve the full system of linear stability equations. Seven dimensionless parameters, i.e. the Kapitza, Galileo, Prandtl, Lewis, Soret, Marangoni, and Biot numbers (Ka,G,Pr,L, χ,M,B), as well as the inclination angle (β) are used to control the flow system. In the case of pure spanwise perturbations, thermocapillary S- and P-modes are obtained. It is found that the most dangerous modes are stationary for positive Soret numbers (χ≥0), and oscillatory for χ<0. Moreover, the P-mode which is short-wave unstable for χ=0 remains so for χ<0, but becomes long-wave unstable for χ>0 and even merges with the long-wave S-mode. In the case of streamwise perturbations, a long-wave surface mode (H-mode) is also obtained. From the neutral curves, it is found that larger Soret numbers make the film flow more unstable as do larger Marangoni numbers. The increase of these parameters leads to the merging of the long-wave H- and S-modes, making the situation long-wave unstable for any Galileo number. It also strongly influences the short-wave P-mode which becomes the most critical for large enough Galileo numbers. Furthermore, from the boundary curves between absolute and convective instabilities (AI/CI) calculated for both the long-wave instability (S- and H-modes) and the short-wave instability (P-mode), it is shown that for small Galileo numbers the AI/CI boundary curves are determined by the long-wave instability, while for large Galileo numbers they are determined by the short-wave instability.

On the vibrational convective instability of a horizontal, binary-mixture layer with Soret effect

1997 ◽  
Vol 330 ◽  
pp. 251-269 ◽  
Author(s):  
G. Z. GERSHUNI ◽  
A. K. KOLESNIKOV ◽  
J.-C. LEGROS ◽  
B. I. MYZNIKOVA
Keyword(s):  
Binary Mixture ◽  
High Frequency ◽  
Soret Effect ◽  
Normal Modes ◽  
Quasi Equilibrium ◽  
Regular Perturbation ◽  
Wave Disturbances ◽  
Long Wave ◽  
Mean Fields ◽  
Parameter Values

A theoretical examination is made of the mechanical quasi-equilibrium stability of a horizontal, binary-mixture layer with Soret effect in the presence of a high-frequency vibrational field. The boundaries of the layer are assumed to be rigid, isothermal and impermeable. The axis of vibration is longitudinal. The study is based on the system of equations describing the behaviour of mean fields. The conditions of quasi-equilibrium are formulated. A linear stability analysis for normal modes is carried out. In the limit of long-wave disturbances the regular perturbation method is used with the wavenumber as a small parameter. For the case of an arbitrary wavenumber, the calculations are made using straight forward numerical integration. The boundaries of stability and the critical disturbance characteristics are determined for representative parameter values. Different instability mechanism and forms are discussed.

Nonlinear dynamics of long-wave Marangoni convection in a binary mixture with the Soret effect

2013 ◽  
Vol 25 (5) ◽  
pp. 052107 ◽  
Author(s):  
M. Morozov ◽  
A. Oron ◽  
A. A. Nepomnyashchy
Keyword(s):  
Nonlinear Dynamics ◽  
Binary Mixture ◽  
Marangoni Convection ◽  
Soret Effect ◽  
Long Wave

A Study on the Fine Structure of the Lateral Line Organ of the Sea Eel

1973 ◽  
Vol 31 ◽  
pp. 648-649
Author(s):  
K. Hama
Keyword(s):  
Fine Structure ◽  
Electron Microscope ◽  
Lateral Line ◽  
Low Frequency ◽  
Sensory Cells ◽  
Apical Surface ◽  
Voltage Electron ◽  
Sensory Epithelia ◽  
Low Frequency Vibration ◽  
Transmission Electron

The lateral line organs of the sea eel consist of canal and pit organs which are different in function. The former is a low frequency vibration detector whereas the latter functions as an ion receptor as well as a mechano receptor.The fine structure of the sensory epithelia of both organs were studied by means of ordinary transmission electron microscope, high voltage electron microscope and of surface scanning electron microscope.The sensory cells of the canal organ are polarized in front-caudal direction and those of the pit organ are polarized in dorso-ventral direction. The sensory epithelia of both organs have thinner surface coats compared to the surrounding ordinary epithelial cells, which have very thick fuzzy coatings on the apical surface.

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