Gravity–capillary multi-component wave patterns generated by a single-frequency wave-maker oscillation and subsequent resonances

2021 ◽  
Vol 926 ◽  
Author(s):  
Chang Xu ◽  
Marc Perlin
Keyword(s):  
Surface Tension ◽  
Wavelet Transforms ◽  
Fourier Transforms ◽  
Single Frequency ◽  
Two Dimensional ◽  
Frequency Wave ◽  
Wave Patterns ◽  
Surface Patterns ◽  
Wave Maker ◽  
Cross Waves

Cross-waves are standing waves with crests perpendicular to a wave-maker; they are subharmonic waves excited by parametric instability. The modulational and chaotic behaviours of nonlinear cross-waves have been studied widely since the 1970s. Most of the previous work has focused on gravity waves where surface tension can be neglected. In this work we study cross-waves that are highly dependent on surface tension as well as gravity. By oscillating a planar wave-maker either vertically or horizontally with frequencies of 25 Hz through 40 Hz at one end of a rectangular basin, two-dimensional multi-component surface patterns are realized. Using the free-surface synthetic Schlieren technique to measure the surface elevations, multi-dimensional Fourier transforms are utilized to track the evolutionary spectrum of the water surface in both the temporal and spatial domains. Wavelet transforms are implemented to show the development of the various frequency components. Three-wave resonances with and without first subharmonics are observed for small nonlinearity. Three-dimensional oblique propagating cross-waves are generated at higher nonlinearity; unlike most previous cross-wave experiments, this staggered pattern propagates far downstream. Experimental evidence shows that two oblique propagating waves form a two-dimensional short-crested pattern, and that the lateral component of the waves develops into parametric sloshing modes corresponding to the width of the tank. Two regimes of nonlinear wave patterns, resonant triads and oblique propagating cross-waves, are delineated.

Phase saddles and dislocations in two-dimensional waves such as the tides

1988 ◽  
Vol 417 (1852) ◽  
pp. 7-20 ◽  
Keyword(s):  
Three Dimensional ◽  
Single Frequency ◽  
External Parameter ◽  
Two Dimensional ◽  
Basic Pattern ◽  
Fixed Frequency ◽  
Frequency Wave ◽  
Tidal Theory ◽  
The Antarctic ◽  
Three Dimensional Vector Field

A two-dimensional scalar wavefield of fixed frequency contains, in general, points where the amplitude is zero and the phase is indeter­minate. On a map of contours of equal phase these wave dislocations (interference nulls) are accompanied by saddles. When an external parameter is changed dislocations can be created in pairs or a pair can meet and destroy one another. For the simplest single-frequency wave equation it is a topological necessity that two saddles should participate in this event; moreover, they have to lie, in the final stage before annihilation, on the circle whose diameter is the line joining the dislocations. Examples are given to show how this basic pattern is always ultimately attained even when initially the configuration is quite different. In tidal theory, where the dislocations are amphidromic points, the external parameter that moves them can be the frequency. An example of an annihilation event occurs in the South Atlantic, and a close pair of amphidromic points may explain anomalous tidal observations from the Antarctic Peninsula. The tidal current, as distinct from the tidal rise and fall, provides an example of a two or three-dimensional vector field, and it is pointed out that the singularities in this field are precisely the same as those to be found in the polarization field of an electromagnetic wave.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

Tuning Molecular Superlattice by Charge-Density-Wave Patterns in Two-Dimensional Monolayer Crystals

2021 ◽  
pp. 3545-3551
Author(s):  
Quanzhen Zhang ◽  
Zeping Huang ◽  
Yanhui Hou ◽  
Peiwen Yuan ◽  
Ziqiang Xu ◽  
...  
Keyword(s):  
Charge Density ◽  
Charge Density Wave ◽  
Density Wave ◽  
Two Dimensional ◽  
Wave Patterns

Surface Roughness Identification in End Milling Using Vibration Signals and Fuzzy Clustering

2016 ◽  
Author(s):  
Issam Abu-Mahfouz ◽  
Amit Banerjee ◽  
A. H. M. Esfakur Rahman
Keyword(s):  
Surface Roughness ◽  
Fuzzy Clustering ◽  
Wavelet Transforms ◽  
Fourier Transforms ◽  
End Milling ◽  
Cutting Conditions ◽  
Depth Of Cut ◽  
Cutting Condition ◽  
Machined Surface ◽  
Vibration Signals

The study presented involves the identification of surface roughness in Aluminum work pieces in an end milling process using fuzzy clustering of vibration signals. Vibration signals are experimentally acquired using an accelerometer for varying cutting conditions such as spindle speed, feed rate and depth of cut. Features are then extracted by processing the acquired signals in both the time and frequency domain. Techniques based on statistical parameters, Fast Fourier Transforms (FFT) and the Continuous Wavelet Transforms (CWT) are utilized for feature extraction. The surface roughness of the machined surface is also measured. In this study, fuzzy clustering is used to partition the feature sets, followed by a correlation with the experimentally obtained surface roughness measurements. The fuzzifier and the number of clusters are varied and it is found that the partitions produced by fuzzy clustering in the vibration signal feature space are related to the partitions based on cutting conditions with surface roughness as the output parameter. The results based on limited simulations are encouraging and work is underway to develop a larger framework for online cutting condition monitoring system for end milling.

Data Acquisition and Processing of Weak Low-Frequency Magnetic Signals

2011 ◽  
Vol 65 ◽  
pp. 299-302 ◽  
Author(s):  
Shou Qiang Men ◽  
Christian Resagk
Keyword(s):  
Magnetic Field ◽  
Data Acquisition ◽  
Fourier Transforms ◽  
Low Frequency ◽  
Fast Fourier Transforms ◽  
Two Dimensional ◽  
Calibration System ◽  
Magnetic Field Sensors ◽  
Data Acquisition And Processing

A simple calibration system for magnetic field sensors was designed, and experiments were carried out to calibrate two-dimensional fluxgate sensors and a sensor ring composed of eight fluxgate sensors. Fast Fourier Transforms and trapezoidal numerical integrals were applied to deal with the raw signals. It is found that it is not suitable to apply fast Fourier Transforms only to deal with signals with several peaks close to each other, but trapezoidal numerical integrals should also be used in combination with the FFT method.

scholarly journals Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids in a horizontal magnetic field

2008 ◽  
Vol 12 (3) ◽  
pp. 103-110 ◽  
Author(s):  
Aiyub Khan ◽  
Neha Sharma ◽  
P.K. Bhatia
Keyword(s):  
Magnetic Field ◽  
Surface Tension ◽  
Growth Rate ◽  
Unstable Mode ◽  
Two Dimensional ◽  
Horizontal Magnetic Field ◽  
Streaming Velocity ◽  
The Stability ◽  
Conducting Fluids ◽  
Streaming Motion

The Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids has been investigated in the taking account of effects of surface tension, when the whole system is immersed in a uniform horizontal magnetic field. The streaming motion is assumed to be two-dimensional. The stability analysis has been carried out for two highly viscous fluid of uniform densities. The dispersion relation has been derived and solved numerically. It is found that the effect of viscosity, porosity and surface tension have stabilizing influence on the growth rate of the unstable mode, while streaming velocity has a destabilizing influence on the system.

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