On the Downshift of Wave Frequency for Bragg Resonance

Ji, Peng; Tao, Aifeng; Fan, Jun; Zheng, Jinhai; Liu, Yuming

doi:10.1007/s13344-022-0006-y

Cited by 12 publications

(6 citation statements)

References 36 publications

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“…This is different to class I Bragg resonance for which a downshift by bottom nonlinearity and an upshift by surface wave nonlinearity are found (Peng et al. 2022). Note that for class I Bragg resonance, and for class III Bragg resonance; the plus signs are taken for the transmitted waves and the minus sign for the reflected waves.…”

Section: Nonlinear Behaviours Of Class III Bragg Resonancecontrasting

confidence: 63%

“…class III sub-harmonic resonant waves (open symbols in the figures), as now k b = 2k (1) + k p ; recall that the wavenumber in this work is a scalar, and hence no information on its direction is provided. This is different to class I Bragg resonance for which a downshift by bottom nonlinearity and an upshift by surface wave nonlinearity are found (Peng et al 2022). Note that 2k (1) /k b = 1 for class I Bragg resonance, and (2k (1) ± k b )/k…”

Section: Actual Class III Bragg Resonance Conditionsmentioning

confidence: 63%

“…The resonant wave frequency/number shifting (either upshifting or downshifting) can in general be attributed to the nonlinear effects involved. Peng et al (2022) derived the theoretical solutions of frequency downshifting for class I Bragg resonance based on a regular perturbation analysis up to third order, and found that the frequency shifting has a quadratic dependence on the bottom/surface wave steepness. Hence, the variations in the actual class III Bragg resonance conditions are plotted against (k (1) a (1) ) 2 (representing the surface wave nonlinearity) and (k b b) 2 (representing the bottom nonlinearity) in figures 7 and 8, respectively.…”

Section: Actual Class III Bragg Resonance Conditionsmentioning

confidence: 99%

“…According to Peng et al. (2022), the nonlinear frequency correction introduced by the inclusion of third-order bottom and surface nonlinearities consists of three components. The first two, associated with the third-order interactions of bottom ripples with the second-order wave components that have wavenumbers of () and (), respectively, cause the surface wave frequency to shift downwards when compared with the linear solutions.…”

Section: Nonlinear Behaviours Of Class III Bragg Resonancementioning

confidence: 99%

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Nonlinear Bragg scattering of surface waves over a two-dimensional periodic structure

et al. 2022

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Bragg scattering of nonlinear surface waves over a wavy bottom is studied using two-dimensional fully nonlinear numerical wave tanks (NWTs). In particular, we consider cases of high nonlinearity which lead to complex wave generation and transformations, hence possible multiple Bragg resonances. The performance of the NWTs is well verified by benchmarking experiments. Classic Bragg resonances associated with second-order triad interactions among two surface (linear incident and reflected waves) and one bottom wave components (class I), and third-order quartet interactions among three surface (linear incident and reflected waves, and second-order reflected/transmitted waves) and one bottom wave components (class III) are observed. In addition, class I Bragg resonance occurring for the second-order (rather than linear) transmitted waves, and Bragg resonance arising from quintet interactions among three surface and two bottom wave components, are newly captured. The latter is denoted class IV Bragg resonance which magnifies bottom nonlinearity. It is also found that wave reflection and transmission at class III Bragg resonance have a quadratic rather than a linear relation with the bottom slope if the bottom size increases to a certain level. The surface wave and bottom nonlinearities are found to play opposite roles in shifting the Bragg resonance conditions. Finally, the results indicate that Bragg resonances are responsible for the phenomena of beating and parasitic beating, leading to a significantly large local free surface motion in front of the depth transition.

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Section: Nonlinear Behaviours Of Class III Bragg Resonancecontrasting

confidence: 63%

Section: Actual Class III Bragg Resonance Conditionsmentioning

confidence: 63%

Section: Actual Class III Bragg Resonance Conditionsmentioning

confidence: 99%

Section: Nonlinear Behaviours Of Class III Bragg Resonancementioning

confidence: 99%

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Nonlinear Bragg scattering of surface waves over a two-dimensional periodic structure

et al. 2022

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“…Although CFD can simulate the particleliquid two-phase flow, it cannot accurately calculate the behavior of mixed slurry that contains nodules inside the pump. Dong et al [11] proposed a two-phase flow calculation model for the research of smooth slurry that contained large nodules and distinguished the particle sizes. Nevertheless, a two-phase flow calculation model was essentially the DPM method that ignored particle interactions and disturbances that occurred during the flows.…”

Section: Introductionmentioning

confidence: 99%

Effect of Particle Factors on the Reflux and Blockage of a Deep‐Sea Six‐Stage Pump Based on CFD‐DEM

Hu,

Zhu,

Deng

et al. 2023

Advcd Theory and Sims

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The deep‐sea six‐stage centrifugal pump is an essential power source of the lifting system that conveys slurry containing coarse particles. Emergency failure of the electric system can easily lead to pump blockage because of slurry reflux. The reflux movement of particles in a six‐stage pump under emergency power failure is investigated using the verified computation fluid dynamics and discrete element method (CFD‐DEM) simulation. The JKR contact model is used to perform particle simulation. Simultaneously, shaped particles are added to realistically simulate the reflux characteristics under deep‐sea mining conditions. The effect of particle size, shape, and size distribution in the reflux is investigated. The blockage behavior of the particles during reflux and the blockage mechanism is clarified. Particles with less shape and size below 30 mm are more conducive to safe slurry transportation. The experimental results verify the credibility of the CFD‐DEM simulation results.

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Erratum to: On the Downshift of Wave Frequency for Bragg Resonance

Tao

Fan

et al. 2022

China Ocean Eng

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On the Downshift of Wave Frequency for Bragg Resonance

Cited by 12 publications

References 36 publications

Nonlinear Bragg scattering of surface waves over a two-dimensional periodic structure

Nonlinear Bragg scattering of surface waves over a two-dimensional periodic structure

Effect of Particle Factors on the Reflux and Blockage of a Deep‐Sea Six‐Stage Pump Based on CFD‐DEM

Erratum to: On the Downshift of Wave Frequency for Bragg Resonance

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