Marangoni waves in two-layer films under the action of spatial temperature modulation

2016 ◽  
Vol 805 ◽  
pp. 322-354 ◽  
Author(s):  
Alexander A. Nepomnyashchy ◽  
Ilya B. Simanovskii
Keyword(s):  
Wave Equations ◽  
Travelling Waves ◽  
Three Dimensional ◽  
Standing Waves ◽  
Solid Substrate ◽  
Temperature Modulation ◽  
Stationary Flows ◽  
Long Wave ◽  
Dynamical Regimes ◽  
Spatial Temperature

The nonlinear dynamics of waves generated by the deformational oscillatory Marangoni instability in a two-layer film under the action of a spatial temperature modulation on the solid substrate is considered. A system of long-wave equations governing the deformations of the upper surface and the interface between the liquids is derived. The nonlinear simulations reveal the existence of numerous dynamical regimes, including two-dimensional stationary flows and standing waves, three-dimensional standing waves with different spatial periods, and three-dimensional travelling waves. The general diagram of the flow regimes is constructed.

The influence of two-dimensional temperature modulation on nonlinear Marangoni waves in two-layer films

2018 ◽  
Vol 846 ◽  
pp. 944-965 ◽  
Author(s):  
Alexander A. Nepomnyashchy ◽  
Ilya B. Simanovskii
Keyword(s):  
Nonlinear Dynamics ◽  
Wave Equations ◽  
Flow Regimes ◽  
Solid Substrate ◽  
Temperature Modulation ◽  
Two Dimensional ◽  
Periodic Flows ◽  
Long Wave ◽  
Nonlinear Simulations ◽  
Time Periodic

The nonlinear dynamics of waves generated by the deformational oscillatory Marangoni instability in a two-layer film under the action of a two-dimensional temperature modulation on the solid substrate is considered. A system of long-wave equations governing the deformations of the upper surface and the interface between the liquids is presented. The long-wave approach is applied. The nonlinear simulations reveal the existence of different dynamic regimes, including stationary, time-periodic and quasi-periodic flows. The general diagrams of the flow regimes are constructed.

scholarly journals On nonlinear convection in mushy layers Part 1. Oscillatory modes of convection

2002 ◽  
Vol 467 ◽  
pp. 331-359 ◽  
Author(s):  
D. N. RIAHI
Keyword(s):  
Flow Instability ◽  
Travelling Waves ◽  
Three Dimensional ◽  
Standing Waves ◽  
Lower Boundary ◽  
Small Range ◽  
Nonlinear Convection ◽  
Mushy Layers ◽  
The Stability ◽  
Parameter Values

We consider the problem of nonlinear convection in horizontal mushy layers during the solidification of binary alloys. We analyse the oscillatory modes of convection in the form of two- and three-dimensional travelling and standing waves. Under a near-eutectic approximation and the limit of large far-field temperature, we determine the solutions to the nonlinear problem by using a perturbation technique, and the stability of two- and three-dimensional solutions in the form of simple travelling waves, general travelling waves and standing waves is investigated. The results of the stability and the nonlinear analyses indicate that supercritical simple travelling rolls are stable over most of the studied range of parameter values, while supercritical standing rolls can be stable only over some small range of parameter values, where the simple travelling rolls are unstable. The results of the investigation of the onset of plume convection and chimney formation leading to the occurrence of freckles in the alloy crystal indicate that the chimney of the plume can be generated internally or near the lower boundary of the mushy layer. The roles of a Stefan number, a permeability parameter and a concentration ratio on the flow instability in both linear and nonlinear regimes are also determined.

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 Generalisation of Integrable (2+1)-Dimensional Dispersive Long-Wave Equations

1997 ◽  
Vol 66 (5) ◽  
pp. 1288-1290 ◽  
Author(s):  
Thangavel Alagesan ◽  
Ambigapathy Uthayakumar ◽  
Kuppusamy Porsezian
Keyword(s):  
Wave Equations ◽  
Long Wave

scholarly journals Experimental travelling waves identification in mechanical structures

2017 ◽  
Vol 24 (1) ◽  
pp. 152-167
Author(s):  
Izhak Bucher ◽  
Ran Gabai ◽  
Harel Plat ◽  
Amit Dolev ◽  
Eyal Setter
Keyword(s):  
Energy Flux ◽  
Power Flow ◽  
Reactive Power ◽  
Mechanical Energy ◽  
Travelling Waves ◽  
Electrical Power ◽  
Normal Modes ◽  
Standing Waves ◽  
Amplitude Curve ◽  
Physical Point

Vibrations are often represented as a sum of standing waves in space, i.e. normal modes of vibration. While this can be mathematically accurate, the representation as travelling waves can be compact and more appropriate from a physical point of view, in particular when the energy flux along the structure is meaningful. The quantification of travelling waves assists in computing the energy being transferred and propagated along a structure. It can provide local as well as global information about the structure through which the mechanical energy flows. Presented in this paper is a new method to quantify the fraction of mechanical power being transmitted in a vibration cycle at a specific direction in space using measured data. It is shown that the method can detect local defects causing slight non-uniformity of the energy flux. Equivalence is being made with the electrical power factor and electromagnetic standing waves ratio, commonly employed in such cases. Other methods to perform experiment based wave identification in one-dimension are compared with the power flow based identification. Including a signal processing approach that fits an ellipse to the complex amplitude curve and Hilbert transform for obtaining the local phase and amplitude. A new representation of the active and reactive power flow is developed and its relationship to standing waves ratio is demonstrated analytically and experimentally.

scholarly journals Existence and linearized stability of solitary waves for a quasilinear Benney system

2016 ◽  
Vol 146 (3) ◽  
pp. 547-564 ◽  
Author(s):  
João-Paulo Dias ◽  
Mário Figueira ◽  
Filipe Oliveira
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Compact Support ◽  
Travelling Waves ◽  
Standing Waves ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Linearized Stability ◽  
Stability Of Solitary Waves ◽  
Image Position

We prove the existence of solitary wave solutions to the quasilinear Benney systemwhere , –1 < p < +∞ and a, γ > 0. We establish, in particular, the existence of travelling waves with speed arbitrarily large if p < 0 and arbitrarily close to 0 if . We also show the existence of standing waves in the case , with compact support if – 1 < p < 0. Finally, we obtain, under certain conditions, the linearized stability of such solutions.

The two-sided lid-driven cavity: experiments on stationary and time-dependent flows

2002 ◽  
Vol 450 ◽  
pp. 67-95 ◽  
Author(s):  
CH. BLOHM ◽  
H. C. KUHLMANN
Keyword(s):  
Three Dimensional ◽  
Standing Waves ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Flow State ◽  
Incompressible Fluid Flow ◽  
Velocity Measurements ◽  
Driven Cavity ◽  
Rectangular Container ◽  
Hot Film

The incompressible fluid flow in a rectangular container driven by two facing sidewalls which move steadily in anti-parallel directions is investigated experimentally for Reynolds numbers up to 1200. The moving sidewalls are realized by two rotating cylinders of large radii tightly closing the cavity. The distance between the moving walls relative to the height of the cavity (aspect ratio) is Γ = 1.96. Laser-Doppler and hot-film techniques are employed to measure steady and time-dependent vortex flows. Beyond a first threshold robust, steady, three-dimensional cells bifurcate supercritically out of the basic flow state. Through a further instability the cellular flow becomes unstable to oscillations in the form of standing waves with the same wavelength as the underlying cellular flow. If both sidewalls move with the same velocity (symmetrical driving), the oscillatory instability is found to be tricritical. The dependence on two sidewall Reynolds numbers of the ranges of existence of steady and oscillatory cellular flows is explored. Flow symmetries and quantitative velocity measurements are presented for representative cases.

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