China Ocean Engineering

, Volume 33, Issue 1, pp 86–93 | Cite as

Study on Energy Spectrum Instability in the Processes of Propagating and Breaking of Focusing Waves

  • Yi-hui ZhangEmail author
  • Shu-xiu LiangEmail author
  • Zhao-chen Sun


Based on phase focusing theory, focusing waves with different spectral types and breaking severities were generated in a wave flume. The time series of surface elevation fluctuation along the flume were obtained by utilizing 22 wave probes mounted along the mid-stream of the flume. Based on the wave spectrum obtained using fast Fourier transform (FFT), the instability characteristics of the energy spectrum were reported in this paper. By analyzing the variation of total spectral energy, the total spectral energy after wave breaking was found to clearly decrease, and the loss value and ratio gradually increased and tended to stabilize with the enhancement of breaking severity for different spectral types. When wave breaking occurred, the energy loss was primarily in a high-frequency range of f/fp>1.0, and energy gain was primarily in a low-frequency range of f/fp<1.0. As the breaking severity increased, the energy gain-loss ratio decreased gradually, which demonstrates that the energy was mostly dissipated. For plunging waves, the energy gain-loss ratio reached 24% for the constant wave steepness (CWS) spectrum, and was slightly larger at approximately 30% for the constant wave amplitude (CWA) spectrum, and was the largest at approximately 42% for the Pierson-Moskowitz (PM) spectrum.

Key words

phase focusing wave breaking wave surface wave steepness 


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Copyright information

© Chinese Ocean Engineering Society and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Lake Science and Environment, Nanjing Institute of Geography and LimnologyChinese Academy of SciencesNanjingChina
  2. 2.State Key Laboratory of Coastal and Offshore EngineeringDalian University of TechnologyDalianChina

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