scholarly journals Dynamics of gravity–capillary solitary waves in deep water

2012 ◽  
Vol 708 ◽  
pp. 480-501 ◽  
Author(s):  
Zhan Wang ◽  
Paul A. Milewski
Keyword(s):  
Solitary Waves ◽  
Water Waves ◽  
Periodic Structures ◽  
Time Integration ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Full Potential ◽  
Numerical Time Integration ◽  
The Stability ◽  
Nonlinear Focusing

AbstractThe dynamics of solitary gravity–capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time-dependent solutions, we simplify the full potential flow problem by using surface variables and taking a particular cubic truncation possessing a Hamiltonian with desirable properties. This approximation agrees remarkably well with the full equations for the bifurcation curves, wave profiles and the dynamics of solitary waves for a two-dimensional fluid domain, and with higher-order truncations in three dimensions. Fully localized solitary waves are then computed in the three-dimensional problem and the stability and interaction of both line and localized solitary waves are investigated via numerical time integration of the equations. There are many solitary wave branches, indexed by their finite energy as their amplitude tends to zero. The dynamics of the solitary waves is complex, involving nonlinear focusing of wavepackets, quasi-elastic collisions, and the generation of propagating, spatially localized, time-periodic structures akin to breathers.

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.

Stability and instability of some nonlinear dispersive solitary waves in higher dimension

1996 ◽  
Vol 126 (1) ◽  
pp. 89-112 ◽  
Author(s):  
Anne de Bouard
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Ion Acoustic Waves ◽  
Stability And Instability ◽  
Ion Acoustic ◽  
De Vries ◽  
The Stability

We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.

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.

Combined Rayleigh–Taylor and Kelvin–Helmholtz instabilities on an annular liquid sheet

2016 ◽  
Vol 812 ◽  
pp. 152-177 ◽  
Author(s):  
M. Vadivukkarasan ◽  
Mahesh V. Panchagnula
Keyword(s):  
Total Energy ◽  
Time Integration ◽  
Three Dimensional ◽  
Liquid Sheet ◽  
Length Scale ◽  
Time Varying ◽  
Varying Coefficients ◽  
Flow Approximation ◽  
Time Varying Coefficients ◽  
Numerical Time Integration

This paper describes the three-dimensional destabilization characteristics of an annular liquid sheet when subjected to the combined action of Rayleigh–Taylor (RT) and Kelvin–Helmholtz (KH) instability mechanisms. The stability characteristics are studied using temporal linear stability analysis and by assuming that the fluids are incompressible, immiscible and inviscid. Surface tension is also taken into account at both the interfaces. Linearized equations governing the growth of instability amplitude have been derived. These equations involve time-varying coefficients and have been analysed using two approaches – direct numerical time integration and frozen-flow approximation. From the direct numerical time integration, we show that the time-varying coefficients evolve on a slow time scale in comparison with the amplitude growth. Therefore, we justify the use of the frozen-flow approximation and derive a closed-form dispersion relation from the appropriate governing equations and boundary conditions. The effect of flow conditions and fluid properties is investigated by introducing dimensionless numbers such as Bond number ($Bo$), inner and outer Weber numbers ($We_{i}$, $We_{o}$) and inner and outer density ratios ($Q_{i}$, $Q_{o}$). We show that four instability modes are possible – Taylor, sinuous, flute and helical. It is observed that the choice of instability mode is influenced by a combination of both $Bo$ as well as $We_{i}$ and $We_{o}$. However, the instability length scale calculated from the most unstable wavenumbers is primarily a function of $Bo$. We show a regime map in the $Bo,We_{i},We_{o}$ parameter space to identify regions where the system is susceptible to three-dimensional helical modes. Finally, we show an optimal partitioning of a given total energy ($\unicode[STIX]{x1D701}$) into acceleration-induced and shear-induced instability mechanisms in order to achieve a minimum instability length scale (${\mathcal{L}}_{m}^{\ast }$). We show that it is beneficial to introduce at least 90 % of the total energy into acceleration induced RT instability mechanism. In addition, we show that when the RT mechanism is invoked to destabilize an annular liquid sheet, ${\mathcal{L}}_{m}^{\ast }\sim \unicode[STIX]{x1D701}^{-3/5}$.

Stability and Robustness of a 3D Slip Model for Walking Using Lateral Leg Placement Control

2012 ◽  
Author(s):  
Dominik Budday ◽  
Fabian Bauer ◽  
Justin Seipel
Keyword(s):  
Humanoid Robot ◽  
Performance Test ◽  
Control Mechanism ◽  
Sagittal Plane ◽  
Control Strategies ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Slip Model ◽  
The Stability

The SLIP model has shown a way to easily represent the center of mass dynamics of human walking and running. For 2D motions in the sagittal plane, the model shows self-stabilizing effects that can be very useful when designing a humanoid robot. However, this self-stability could not be found in three-dimensional running, but simple control strategies achieved stabilization of running in three dimensions. Yet, 3D walking with SLIP has not been analyzed to the same extent. In this paper we show that three-dimensional humanoid SLIP walking is also unstable, but can be stabilized using the same strategy that has been successful for running. It is shown that this approach leads to the desired periodic solutions. Furthermore, the influence of different parameters on stability and robustness is examined. Using a performance test to simulate the transition from an upright position to periodic walking we show that the stability is robust. With a comparison of common models for humanoid walking and running it is shown that the simple control mechanism is able to achieve stable solutions for all models, providing a very general approach to this problem. The derived results point out preferable parameters to increase robustness promising the possibility of successfully realizing a humanoid walking robot based on 3D SLIP.

scholarly journals A Systematic Study of the Fracturing of Ronne - Filchner Ice Shelf, Antarctica, Using Multisource Satellite Data from 2001 to 2016

2017 ◽  
Author(s):  
Rongxing Li ◽  
Haifeng Xiao ◽  
Shijie Liu ◽  
Xiaohua Tong
Keyword(s):  
Satellite Data ◽  
Three Dimensional ◽  
Remote Sensing Data ◽  
Three Dimensions ◽  
Landsat 8 ◽  
Ice Shelf ◽  
Sar Imagery ◽  
The Stability ◽  
Fracture Mapping ◽  
New Framework

Abstract. We propose a new framework of systematic fracture mapping and major calving event prediction for the large ice shelves in Antarctica using multisource satellite data, including optical imagery, SAR imagery, altimetric data, and stereo mapping imagery. The new framework is implemented and applied for a comprehensive study of the fracturing of Ronne-Filchner Ice Shelf (RFIS), the second largest ice shelf in Antarctica, using a long time dataset dating back to 1957. New remote sensing data that have been made available in the past decade, including Landsat 8, WV-2, ZY-3 and others, greatly enhance our abilities to detect new fractures and monitor large rifts in three dimensions. Two large rifts, Rifts 1 and 2, were newly detected and are comparable to the Grand Chasm that caused a major calving event in the region in 1986. Three-dimensional rift models generated from quasi real-time stereo ZY-3 images revealed important topographic information about the large rifts that can be used to improve the reliability of ice shelf modeling and support enhanced analyses of ice shelf stability. Based on the results of the 2D and 3D fracture mapping, the spatial and temporal analyses of the overall fracture changes and large rift evolutions, i.e., the level of fracturing in RFIS, were slightly increased, particularly at the front of the ice sheet. The overall fracture observations do not seem to suggest immediate significant impacts on the stability of the shelf. However, the most active regional fracturing activities occurred at the front of Filchner Ice Shelf (FIS). A potential upcoming major calving event of FIS is estimated to occur in 2051. The stability of the ice shelf, particularly with regard to the developments of Rifts 1 and 2, should be closely monitored.

Structural Failure Mechanisms of Common Flexor Tendon Repairs

Hand Surgery ◽  
2015 ◽  
Vol 20 (03) ◽  
pp. 369-379 ◽  
Author(s):  
Tim Sebastian Peltz ◽  
Roger Haddad ◽  
Peter James Scougall ◽  
Sean Nicklin ◽  
Mark Peter Gianoutsos ◽  
...  
Keyword(s):  
Failure Mechanisms ◽  
Biomechanical Testing ◽  
Tendon Repair ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Biomechanical Stability ◽  
Repair Method ◽  
Before And After ◽  
The Stability ◽  
Repair Techniques

Background: This study investigated the exact failure mechanisms of the most commonly used conventional tendon repair techniques. A new method, radiographing repair constructs in antero-posterior and lateral projections before and after tensioning was used. This allowed to precisely analyse failure mechanisms in regards to geometrical changes in all three dimensions. Additionally the biomechanical stability focusing on gapping was tested. Methods: Sheep fore limb deep flexor tendons were harvested and divided in eight groups of ten tendons. Three common variants of the Kessler repair method and four common 4-strand repair techniques were tested. Additionally a new modification of the Adelaide repair was tested. Results: Biomechanical testing showed no significant differences in gapping for the three tested 2-strand Kessler repair groups. Once a double Kessler or 4-strand Kessler repair was performed the stability of the repair improved significantly. Further significant improvements in biomechanical stability could be achieved by using cross locks in the repair like in the Adelaide repair method. Qualitative analysis using radiographs showed that all Kessler repair variants unfolded via rotations around the transverse suturing component, no matter which variant was used. Conclusions: Additional to the commonly described constriction of the repair construct, the rotating deformation is the main reason for repair site gapping in Kessler tendon repair methods. The term “locking” in a Kessler repair is misleading. The cruciate repairs tended to loose grip and drag (cheese-wire) through the tendon and therefore lead to gapping. The most stable repair constructs in all three dimensions were the Adelaide repair and its interlocking modification. This is due to the superior anchoring qualities of its cross locks and three dimensional stability.

Spatial Distribution of Gravity-Dependent Gain Changes in the Vestibuloocular Reflex

2005 ◽  
Vol 93 (6) ◽  
pp. 3693-3698 ◽  
Author(s):  
Sergei B. Yakushin ◽  
Yongqing Xiang ◽  
Theodore Raphan ◽  
Bernard Cohen
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Head Tilt ◽  
Fundamental Property ◽  
Head Position ◽  
Three Dimensions ◽  
Vestibuloocular Reflex ◽  
Gain Adaptation ◽  
The Stability ◽  
Three Dimensional Space

This study determined whether dependence of angular vestibuloocular reflex (aVOR) gain adaptation on gravity is a fundamental property in three dimensions. Horizontal aVOR gains were adaptively increased or decreased in two cynomolgus monkeys in upright, side down, prone, and supine positions, and aVOR gains were tested in darkness by yaw rotation with the head in a wide variety of orientations. Horizontal aVOR gain changes peaked at the head position in which the adaptation took place and gradually decreased as the head moved away from this position in any direction. The gain changes were plotted as a function of head tilt and fit with a sinusoid plus a bias to obtain the gravity-dependent (amplitude) and gravity-independent (bias) components. Peak-to-peak gravity-dependent gain changes in planes containing the position of adaptation and the magnitude of the gravity-independent components were both ∼25%. We assumed that gain changes over three-dimensional space could be described by a sinusoid the amplitude of which also varied sinusoidally. Using gain changes obtained from the head position in which the gains were adapted, a three-dimensional surface was generated that was qualitatively similar to a surface obtained from the experimental data. This extends previous findings on vertical aVOR gain adaptation in one plane and introduces a conceptual framework for understanding plasticity in three dimensions: aVOR gain changes are composed of two components, one of which depends on head position relative to gravity. It is likely that this gravitational dependence optimizes the stability of retinal images during movement in three-dimensional space.

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