Experiments on nonlinear gravity–capillary waves

1999 ◽  
Vol 380 ◽  
pp. 205-232 ◽  
Author(s):  
LEV SHEMER ◽  
MELAD CHAMESSE
Keyword(s):  
Narrow Band ◽  
Numerical Study ◽  
Three Dimensional ◽  
Capillary Waves ◽  
Carrier Wave ◽  
Nls Equation ◽  
Zakharov Equation ◽  
The Stability ◽  
Nonlinear Gravity

Benjamin–Feir instability of nonlinear gravity–capillary waves is studied experimentally. The experimental results are compared with computations performed for values of wavelength and steepness identical to those employed in the experiments. The theoretical approach is based on the Zakharov nonlinear equation which is modified here to incorporate weak viscous dissipation. Experiments are performed in a wave ume which has an accurately controlled wavemaker for generation of the carrier wave, as well as an additional independent conical wavemaker for generation of controlled three-dimensional disturbances. The approach adopted in the present experimental investigation allows therefore the determination of the actual boundaries of the instability domain, and not just the most unstable disturbances. Instantaneous surface elevation measurements are performed with capacitance-type wave gauges. Multipoint measurements make it possible to determine the angular dependence of the amplitude of the forced and unforced disturbances, as well as their variation along the tank. The limits of the instability domains obtained experimentally for each set of carrier wave parameters agree favourably with those computed numerically using the model equation. The numerical study shows that application of the Zakharov equation, which is free of the narrow-band approximation adopted in the derivation of the nonlinear Schrödinger (NLS) equation, may lead to qualitatively different results regarding the stability of nonlinear gravity–capillary waves. The present experiments support the results of the numerical investigation.

scholarly journals Evolution of a narrow-band spectrum of random surface gravity waves

2003 ◽  
Vol 478 ◽  
pp. 1-10 ◽  
Author(s):  
KRISTIAN B. DYSTHE ◽  
KARSTEN TRULSEN ◽  
HARALD E. KROGSTAD ◽  
HERVÉ SOCQUET-JUGLARD
Keyword(s):  
Three Dimensional ◽  
Low Frequency ◽  
Three Dimensions ◽  
Band Spectrum ◽  
Nls Equation ◽  
Random Surface ◽  
Narrow Bandwidth ◽  
Quasi Stationary State ◽  
The Stability ◽  
Three Dimensional Simulations

Numerical simulations of the evolution of gravity wave spectra of fairly narrow bandwidth have been performed both for two and three dimensions. Simulations using the nonlinear Schrödinger (NLS) equation approximately verify the stability criteria of Alber (1978) in the two-dimensional but not in the three-dimensional case. Using a modified NLS equation (Trulsen et al. 2000) the spectra ‘relax’ towards a quasi-stationary state on a timescale (ε2ω0)−1. In this state the low-frequency face is steepened and the spectral peak is downshifted. The three-dimensional simulations show a power-law behaviour ω−4 on the high-frequency side of the (angularly integrated) spectrum.

scholarly journals Modeling inflatable fabric with undevelopable surfaces by motion folding method

2019 ◽  
Vol 14 ◽  
pp. 155892501988640
Author(s):  
Xiao-Shun Zhao ◽  
He Jia ◽  
Zhihong Sun ◽  
Li Yu
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Numerical Study ◽  
Technical Problem ◽  
Three Dimensional ◽  
Element Model ◽  
Model Errors ◽  
Folding Model ◽  
Study Results ◽  
The Stability

At present, most space inflatable structures are composed of flexible inflatable fabrics with complex undevelopable surfaces. It is difficult to establish a multi-dimensional folding model for this type of structure. To solve this key technical problem, the motion folding method is proposed in this study. First, a finite element model with an original three-dimensional surface was flattened with a fluid structure interaction algorithm. Second, the flattened surface was folded based on the prescribed motion of the node groups, and the final folding model was obtained. The fold modeling process of this methodology was consistent with the actual folding processes. Because the mapping relationship between the original finite element model and the final folding model was unchanged, the initial stress was used to modify the model errors during folding process of motion folding method. The folding model of an inflatable aerodynamic decelerator, which could not be established using existing folding methods, was established by using motion folding method. The folding model of the inflatable aerodynamic decelerator showed that the motion folding method could achieve multi-dimensional folding and a high spatial compression rate. The stability and regularity of the inflatable aerodynamic decelerator numerical inflation process and the consistency of the inflated and design shapes indicated the reliability, applicability, and feasibility of the motion folding method. The study results could provide a reference for modeling complex inflatable fabrics and promote the numerical study of inflatable fabrics.

Potential Flow Field Generated by Downstream Moving Bars and Propagated on a Turbine Blade at Low Reynolds Number

2011 ◽  
Author(s):  
Ve´ronique Penin ◽  
Pascale Kulisa ◽  
Franc¸ois Bario
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Numerical Study ◽  
Three Dimensional ◽  
Potential Effect ◽  
Navier Stokes ◽  
Turbine Cascade ◽  
Wake Interaction ◽  
Rotor Stator Interaction ◽  
The Stability

During the last few decades, the size and weight of turbo-machinery have been continuously reduced. However, by decreasing the distance between rows, rotor-stator interaction is strengthened. Two interactions now have the same magnitude: wake interaction and potential effect. Studying this effect is essential to understand rotor-stator interactions. Indeed, this phenomenon influences the whole flow, including the boundary layer of the upstream and downstream blades, ergo the stability of the flow and the efficiency of the machine. A large scale turbine cascade followed by a specially designed rotating cylinder system is used. Synchronised velocity LDA measurements on the vane profile show the flow and boundary layer behavior due to the moving bars. To help the general understanding and to corroborate our experimental results, numerical investigations are carried out with an unsteady three dimensional Navier-Stokes code. Moreover, the numerical study informs about the potential disturbance to the whole flow of the cascade.

Numerical Investigation of the Three-Dimensional Flow Structure About a Revolving Wing

2012 ◽  
Author(s):  
Daniel J. Garmann ◽  
Miguel R. Visbal ◽  
Paul D. Orkwis
Keyword(s):  
Turbulent Flows ◽  
Numerical Study ◽  
Three Dimensional ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Vortex System ◽  
Aerodynamic Loads ◽  
Eddy Simulation ◽  
Data Reduction Technique ◽  
The Stability

A numerical study is conducted to examine the vortex structure about a revolving wing in quiescent flow employing a high-fidelity, implicit large eddy simulation (ILES) technique found to be effective in simulating flows that exhibit interspersed regions of laminar, transitional, and turbulent flows. The revolving wing configuration consists of a single, aspect ratio one rectangular plate extended out a distance of 0.5 chords from the origin. Shortly after the onset of the motion, the rotating wing generates a stable and coherent vortex system across the leading edge and wing root that remains throughout the motion. The aerodynamic loads are also analyzed and found to remain mostly constant during the maneuver. Transitional effects on the vortex system are investigated over a range of Reynolds numbers (3,000 < Re < 15,000). It is found that higher Reynolds numbers promote more breakdown of the leading edge and root vortices, but do not alter the stability of the vortex system. The aerodynamic loads also show little sensitivity to Reynolds number with the higher Reynolds numbers producing only moderately higher forces. Comparisons with recent experimental PIV measurements using a PIV-like data reduction technique applied to the computational solution show very favorable agreement with the mid-span velocity and vorticity contours.

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.

A Numerical Study of Flutter in a Transonic Fan

1998 ◽  
Vol 120 (3) ◽  
pp. 500-507 ◽  
Author(s):  
K. Isomura ◽  
M. B. Giles
Keyword(s):  
Cfd Simulation ◽  
Numerical Study ◽  
Three Dimensional ◽  
Third Order ◽  
Blade Vibration ◽  
Pressure Surface ◽  
Dominant Component ◽  
Bending Mode ◽  
The Stability ◽  
Transonic Fan

The bending mode Flutter of a modern transonic fan has been studied using a quasi-three-dimensional viscous unsteady CFD code. The type of flutter in this research is that of a highly loaded blade with a tip relative Mach number just above unity, commonly referred to as transonic stall flutter. This type of Flutter is often encountered in modern wide chord fans without a part span shroud. The CFD simulation uses an upwinding scheme with Roe’s third-order flux differencing, and Johnson and King’s turbulence model with the later modification due to Johnson and Coakley. A dynamic transition point model is developed using the en method and Schubauer and Klebanoff’s experimental data. The calculations of the flow in this fan reveal that the source of the flutter of IHI transonic fan is an oscillation of the passage shock, rather than a stall. As the blade loading increases, the passage shock moves forward. Just before the passage shock unstarts, the stability of the passage shock decreases, and a small blade vibration causes the shock to oscillate with a large amplitude between unstarted and started positions. The dominant component of the blade excitation force is due to the foot of the oscillating passage shock on the blade pressure surface.

scholarly journals Enhanced Energy Dissipation by Parasitic Capillaries on Short Gravity–Capillary Waves

2010 ◽  
Vol 40 (11) ◽  
pp. 2435-2450 ◽  
Author(s):  
Wu-ting Tsai ◽  
Li-ping Hung
Keyword(s):  
Energy Dissipation ◽  
Dissipation Rate ◽  
Capillary Wave ◽  
Wave Train ◽  
Three Dimensional ◽  
Local Maximum ◽  
Finite Amplitude ◽  
Capillary Waves ◽  
Carrier Wave ◽  
Order Of Magnitude

Abstract The increased energy dissipation caused by the formation of parasitic capillary wavelets on moderately short, steep gravity–capillary waves is studied numerically. This study focuses on understanding the mechanism leading to dissipation enhancement and on exploring the possible correlation between the enhanced dissipation rate and the characteristic parameters of the parasitic capillaries. The interaction between the parasitic capillary wave train and the underlying dominant flow of the carrier wave induces strong vortex shedding and imposes large straining immediately underneath the troughs of the capillary ripples. These localized strains are very effective in dissipating energy of the carrier gravity–capillary wave. The attenuation rate of the carrier wave can increase by more than one order of magnitude in the presence of capillary wavelets. Systematic simulations for various carrier wavelengths and steepnesses reveal that the enhanced dissipation rate can be quantified well by a simple parameter: the average of all the difference between the local maximum and minimum slopes along the entire carrier wave surface, which is equivalent to the mean slope of the parasitic capillary wave train. The enhanced dissipation rate increases approximately linearly with the carrier gravity–capillary wavenumber for a given mean slope of the capillary wave train. The increased energy dissipation caused by the formation of parasitic capillaries is also found to significantly impact on the characteristics of three-dimensional instabilities of finite-amplitude, uniform gravity–capillary waves.

On the stability of weakly-nonlinear gravity-capillary waves

Wave Motion ◽  
1986 ◽  
Vol 8 (5) ◽  
pp. 439-454 ◽  
Author(s):  
Jun Zhang ◽  
W.K. Melville
Keyword(s):  
Capillary Waves ◽  
Weakly Nonlinear ◽  
The Stability ◽  
Nonlinear Gravity

Evaluation of Pile Application for Slopes on Bedrock Stability

2015 ◽  
Vol 744-746 ◽  
pp. 479-484
Author(s):  
Mudthir Bakri ◽  
Yuan You Xia ◽  
Chun Shu Chen ◽  
Hua Bin Wang
Keyword(s):  
Failure Mode ◽  
Failure Modes ◽  
Numerical Study ◽  
Soil Layer ◽  
Three Dimensional ◽  
Single Pile ◽  
Stability Of Slopes ◽  
Maximum Value ◽  
The Stability ◽  
Sliding Soil

This paper presents a numerical study that performs the stability of slopes on bedrock reinforced with single pile row at different locations. The slope is formed of top sliding soil layer that underlies over rock. The numerical analysis has been implemented by employing the three dimensional analysis using FLAC3D. The results indicate that as the pile location is moved towards the slope crest the displacement increases.In the single row of pile application, the factor of safety reached its maximum value when the pile located at the top middle of the slope. Considering the failure mode the results has conclude three failure modes; above, in front, and through the pile according to the location of the pile. Failure mode is also affected by socketed length of pile in bedrock layer. It is believed that the findings of this study contribute to the engineers performing slope stability analysis in practice.

Three-dimensional instabilities of nonlinear gravity-capillary waves

1987 ◽  
Vol 174 ◽  
pp. 187-208 ◽  
Author(s):  
Jun Zhang ◽  
W. K. Melville
Keyword(s):  
Three Dimensional ◽  
Capillary Waves ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Pure Gravity ◽  
Weakly Nonlinear Waves ◽  
Steep Waves ◽  
The Stability ◽  
Dimensional Instability ◽  
Eigenvalue System

Linear three-dimensional instabilities of nonlinear two-dimensional uniform gravitycapillary waves are studied using numerical methods. The eigenvalue system for the stability problem is generated using a Galerkin method and differs in detail from techniques used to study the stability of pure gravity waves (McLean 1982) and pure capillary waves (Chen & Saffman 1985). It is found that instabilities develop in the neighbourhood of the linear (triad, quartet and quintet) resonance curves. Further, both sum and difference triad ressonances are unstable for sufficiently steep waves in consequence of which Hasselmann's (1967) theorem is restricted to weakly nonlinear waves. The appearance of a superharmonic two-dimensional instability and bifurcation to three-dimensional waves are noted.

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