scholarly journals Benjamin–Feir instability of waves in the presence of current

2014 ◽  
Vol 1 (2) ◽  
pp. 1803-1832
Author(s):  
I. V. Shugan ◽  
H. H. Hwung ◽  
R. Y. Yang
Keyword(s):  
Nonlinear Waves ◽  
Wave Interaction ◽  
Experimental Results ◽  
Initial State ◽  
Resonance Model ◽  
Freak Waves ◽  
Energy Peak ◽  
Stokes Waves ◽  
Moving Media ◽  
Nonlinear Focusing

Abstract. The development of Benjamin–Feir instability of Stokes waves in the presence of variable current is presented. We employ a model of a resonance system having three coexisting nonlinear waves and nonuniform current. The model is free from the narrow-band approximation for surface waves and relatively weak adverse current. The modulation instability of Stokes waves in nonuniform moving media has special properties. Interaction with countercurrent accelerates the growth of sideband modes on a short spatial scale. An increase in initial wave steepness intensifies the wave energy exchange accompanied by wave breaking dissipation, results in asymmetry of sideband modes and a frequency downshift with an energy transfer jump to the lower sideband mode, and depresses the higher sideband and carrier wave. Nonlinear waves may even overpass the blocking barrier produced by strong adverse current. The frequency downshift of the energy peak is permanent and the system does not revert to its initial state. We find reasonable correspondence between the results of model simulations and available experimental results for wave interaction with blocking opposing current. Large transient or freak waves with amplitude and steepness several times those of normal waves may form during temporal nonlinear focusing of the resonant waves accompanied by energy income from sufficiently strong opposing current. We employ the resonance model for the estimation of the maximum amplification of wave amplitudes as a function of gradually increasing opposing current and compare the result obtained with recently published experimental results and modeling results obtained with the nonlinear Schrödinger equation.

scholarly journals An analytical model of the evolution of a Stokes wave and its two Benjamin–Feir sidebands on nonuniform unidirectional current

2015 ◽  
Vol 22 (3) ◽  
pp. 313-324 ◽  
Author(s):  
I. V. Shugan ◽  
H. H. Hwung ◽  
R. Y. Yang
Keyword(s):  
Schrödinger Equation ◽  
Spatial Scale ◽  
Schrodinger Equation ◽  
Wave Interaction ◽  
Experimental Results ◽  
Stokes Wave ◽  
Initial State ◽  
Weakly Nonlinear ◽  
Resonant Interactions ◽  
Cubic Schrödinger Equation

Abstract. An analytical weakly nonlinear model of the Benjamin–Feir instability of a Stokes wave on nonuniform unidirectional current is presented. The model describes evolution of a Stokes wave and its two main sidebands propagating on a slowly varying steady current. In contrast to the models based on versions of the cubic Schrödinger equation, the current variations could be strong, which allows us to examine the blockage and consider substantial variations of the wave numbers and frequencies of interacting waves. The spatial scale of the current variation is assumed to have the same order as the spatial scale of the Benjamin–Feir (BF) instability. The model includes wave action conservation law and nonlinear dispersion relation for each of the wave's triad. The effect of nonuniform current, apart from linear transformation, is in the detuning of the resonant interactions, which strongly affects the nonlinear evolution of the system. The modulation instability of Stokes waves in nonuniform moving media has special properties. Interaction with countercurrent accelerates the growth of sideband modes on a short spatial scale. An increase in initial wave steepness intensifies the wave energy exchange accompanied by wave breaking dissipation, resulting in asymmetry of sideband modes and a frequency downshift with an energy transfer jump to the lower sideband mode, and depresses the higher sideband and carrier wave. Nonlinear waves may even overpass the blocking barrier produced by strong adverse current. The frequency downshift of the energy peak is permanent and the system does not revert to its initial state. We find reasonable correspondence between the results of model simulations and available experimental results for wave interaction with blocking opposing current. Large transient or freak waves with amplitude and steepness several times those of normal waves may form during temporal nonlinear focusing of the waves accompanied by energy income from sufficiently strong opposing current. We employ the model for the estimation of the maximum amplification of wave amplitudes as a function of opposing current value and compare the result obtained with recently published experimental results and modeling results obtained with the nonlinear Schrödinger equation.

Benjamin-Feir Wave Instability on the Opposite Current

2016 ◽  
Author(s):  
Igor V. Shugan ◽  
Hwung-Hweng Hwung ◽  
Ray-Yeng Yang
Keyword(s):  
Wave Interaction ◽  
Stokes Wave ◽  
Initial State ◽  
Weakly Nonlinear ◽  
Initial Wave ◽  
Steady Current ◽  
Cubic Schrödinger Equation ◽  
Energy Peak ◽  
Waves Interaction ◽  
Weakly Nonlinear Model

An analytical weakly nonlinear model of Benjamin–Feir instability of a Stokes wave on nonuniform unidirectional current is presented. The model describes evolution of a Stokes wave and its two main sidebands propagating on a slowly-varying steady current. In contrast to the models based on versions of the cubic Schrodinger equation the current variations could be strong, which allows us to examine the blockage and consider substantial variations of the wave numbers and frequencies of interacting waves. Interaction with countercurrent accelerates the growth of sideband modes on a short spatial scale. An increase in initial wave steepness intensifies the wave energy exchange accompanied by wave breaking dissipation, results in asymmetry of sideband modes and a frequency downshift with an energy transfer jump to the lower sideband mode, and depresses the higher sideband and carrier wave. Nonlinear waves may even overpass the blocking barrier produced by strong adverse current. The frequency downshift of the energy peak is permanent and the system does not revert to its initial state. We find reasonable correspondence between the results of model simulations and available experimental results for wave interaction with blocking opposing current.

scholarly journals EQUILIBRIUM CONDITIONS IN BEACH WAVE INTERACTION

1972 ◽  
Vol 1 (13) ◽  
pp. 62 ◽  
Author(s):  
H. Raman
Keyword(s):  
Wave Interaction ◽  
Experimental Results ◽  
Laboratory Studies ◽  
Regular Waves ◽  
Equilibrium Conditions ◽  
Wave Characteristics ◽  
New Criterion ◽  
Constant Characteristics ◽  
Stable Points

Laboratory studies were conducted in an attempt to find out a relationship between beach and wave characteristics when equilibrium conditions are reached in beach wave interaction for the simple case of regular waves acting normal to the beach. Experimental results indicate the existence of stable points on beach profiles where the coordinates of the profile do not change with time when waves of constant characteristics act on the beach. Emperical relationship between the wave and beach properties are proposed. A new criterion for classification of beach profiles is indicated.

Quantum circuits for calculating the squared sum of the inner product of quantum states and its application

2019 ◽  
Vol 17 (05) ◽  
pp. 1950043
Author(s):  
Panchi Li ◽  
Jiahui Guo ◽  
Bing Wang ◽  
Mengqi Hao
Keyword(s):  
Quantum Circuit ◽  
Quantum States ◽  
Experimental Results ◽  
Quantum Circuits ◽  
Inner Product ◽  
Superposition State ◽  
Initial State ◽  
Control Rules ◽  
Control Qubit ◽  
Classical Computer

In this paper, we propose a quantum circuit for calculating the squared sum of the inner product of quantum states. The circuit is designed by the multi-qubits controlled-swapping gates, in which the initial state of each control qubit is [Formula: see text] and they are in the equilibrium superposition state after passing through some Hadamard gates. Then, according to the control rules, each basis state in the superposition state controls the corresponding quantum states pair to swap. Finally, the Hadamard gates are applied to the control qubits again, and the squared sum of the inner product of many pairs of quantum states can be obtained simultaneously by measuring only one control qubit. We investigate the application of this method in quantum images matching on a classical computer, and the experimental results verify the correctness of the proposed method.

Investigating the Use of the Hilbert-Huang Transform for the Analysis of Freak Waves

2012 ◽  
Author(s):  
Jan Maris ◽  
Marios Christou ◽  
René Huijsmans
Keyword(s):  
Empirical Mode Decomposition ◽  
Nonlinear Waves ◽  
Freak Waves ◽  
Hilbert Huang Transform ◽  
Mode Decomposition ◽  
Conventional Methods ◽  
New Perspective ◽  
Stockwell Transform

This paper presents the Hilbert-Huang Transform (HHT) with Empirical Mode Decomposition (EMD), which is an opportune method to analyse non-stationary traces of nonlinear waves, with freak waves as a case in point. Comparison to conventional methods such as the Fourier, Wavelet and Stockwell Transform is undertaken. Furthermore, an investigation of different EMD schemes (Ensemble EMD or Smoothed EMD) is undertaken to improve the interpretability of the results. Ultimately the Draupner New Year Wave is examined by using the HHT. After all, on successfully applying the HHT, a new perspective on analysing waves is suggested.

A Fast Approach of Locating Complex System Design Errors

2013 ◽  
Vol 572 ◽  
pp. 115-118
Author(s):  
Zhi Yuan Chen ◽  
Shao Bin Huang ◽  
Li Li Han
Keyword(s):  
Complex System ◽  
Genetic Algorithm ◽  
Model Checking ◽  
System Design ◽  
Experimental Results ◽  
Initial State ◽  
Craig Interpolation ◽  
Fast Approach ◽  
Complex System Design ◽  
Model Failure

Model checking technique can give a specific counterexample which explains how the system violates some assertion when model does not satisfy the specification. However, it is a tedious work to understand the long counterexamples. We propose a genetic algorithm to enhance the efficiency of understanding long counterexample by computing the minimal unsatisfiable subformula. Besides, we also propose a Craig interpolation computation-based method to understand counterexample. The causes which are responsible for model failure are extracted by deriving interpolation from the proof of the nonsatisfiability of the initial state and the weakest precondition of counterexample. Experimental results show that our methods improve the efficiency of understanding counterexamples and debugging significantly.

scholarly journals Effect of Initial State and Deformation Conditions on the Hot Deformation Behavior of M50NiL Steel

Materials ◽  
2020 ◽  
Vol 13 (23) ◽  
pp. 5367
Author(s):  
Yan Zhang ◽  
Ming Yang ◽  
Shaolei Long ◽  
Bo Li ◽  
Yilong Liang ◽  
...  
Keyword(s):  
Dynamic Recrystallization ◽  
Hot Deformation ◽  
Deformation Behavior ◽  
Experimental Results ◽  
Coarse Grained ◽  
Case Hardening ◽  
Compression Tests ◽  
Hot Deformation Behavior ◽  
Initial State ◽  
Fine Grained

M50NiL steel, which belongs to a new generation of case-hardening steels used in aerospace bearing applications, is used mainly for the manufacturing of aerospace transmission components that operate under high temperatures. In this study, the effects of the hot deformation parameters and the initial microstructure on the hot deformation behavior of M50NiL steel were investigated through Gleeble-3500 isothermal hot compression tests. The experimental results demonstrated that the critical stain of dynamic recrystallization and the deformation activation energy of the coarse-grained samples were higher than those of the fine-grained samples. This is attributed to the difficulty of deformation and the dynamic recrystallization behavior of coarse-grained samples. Moreover, fine-grained samples contain a large number of dispersed phases, which can pin the grain boundaries and inhibit the growth of recrystallized grains. Such phenomena are beneficial for obtaining finer and more uniform microstructures in M50NiL steel. The experimental results can provide a useful reference for preparing M50NiL steel with excellent mechanical properties.

Research of ASM Object Tracking Method Combining Kalman Estimation

2014 ◽  
Vol 1049-1050 ◽  
pp. 1595-1598
Author(s):  
Li Guo Zhang ◽  
Mei Jin ◽  
Ju Jin ◽  
Guo Hui Yu
Keyword(s):  
Kalman Filter ◽  
Statistical Model ◽  
Object Tracking ◽  
Experimental Results ◽  
Initial Contour ◽  
Initial State ◽  
Current Frame ◽  
Rigid Object ◽  
Tracking Method ◽  
Actual Contour

ASM is a statistical model applied to match contours of non-rigid object. The actual contour may much different from the initial contour and the result is likely to converge to an error contour. Kalman filter is adopted to track the current frame for the prediction and acts as the initial state of the ASM, and then applies the ASM to correct the contour of the object. Experimental results show that the method proposed in this paper allows the model to converge to the target contour quickly and accurately. It has good stability and robustness.

The Mechanical Properties for the Attenuation of Shock Wave Interaction with Watery Foam Material

2013 ◽  
Vol 815 ◽  
pp. 558-566 ◽  
Author(s):  
Jie Zhou ◽  
Gang Tao
Keyword(s):  
Mechanical Properties ◽  
Shock Wave ◽  
Internal Friction ◽  
Dynamic Behavior ◽  
Wave Interaction ◽  
Experimental Results ◽  
Foam Material ◽  
Reflection And Transmission ◽  
Shock Wave Interaction ◽  
Water Atomization

For understanding the dynamic behavior of watery cellular foam subject to a shock wave, this paper through experiments, to gain a deeper understanding of the incidence, reflection and transmission of a shock wave when it interacted with watery foam. Moreover, by analyzing the loss of the peak overpressure and positive impulse, we were able to respectively know the positive impulse of the incidence, reflection and transmission shock wave. The experimental results indicated that the attenuation capability for watery foam to the shock wave was caused by the internal friction and the water atomization, which would absorb the energy of the shock wave. Therein, the higher percentage of water in the cellular foam, the more obvious attenuation phenomenon for the shock wave was presented. However, the mechanical processes of cellular foam with different water percentages subject to the shock wave were not completely consistent.

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