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This chapter introduces the main aspects of surface gravity waves, initially considering linear waves and subsequently weakly nonlinear waves. For linear waves, the velocity field associated with a regular sinusoidal wave and the dispersion relation that links the angular frequency to the wave number are derived, delving into the two limits of deep water and shallow water waves and providing hints on the related phenomenology. The nonlinear extension for periodic waves is then considered. Finally, the solitonic solution for shallow water waves is discussed.

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Surface Gravity Waves: General Aspects

  • 章节

  • 发表日期：

    2025年

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  • Stefano Pierini

摘要

This chapter introduces the main aspects of surface gravity waves, initially considering linear waves and subsequently weakly nonlinear waves. For linear waves, the velocity field associated with a regular sinusoidal wave and the dispersion relation that links the angular frequency to the wave number are derived, delving into the two limits of deep water and shallow water waves and providing hints on the related phenomenology. The nonlinear extension for periodic waves is then considered. Finally, the solitonic solution for shallow water waves is discussed.