Abstract
Under the assumption of weak shear current with varying vorticity in water and weak air pressure the Zakharov theory is extended to include the effects of vorticity and air pressure on the modulation of water waves. This new equation is used to examine the influence of current and wind on the Benjamin-Feir sideband instability and long-time evolution of wavetrain. As strength of the current increases the bandwidth is found broadened, and the maximum growth rate of sidebands decreased. Periodic solution of sidebands in the presence of current is indicated, which means that shear current does not affect the downshift of wave spectrum peak. Energy input by imposing the air pressure leads to the enhancement of the lower sideband, which is in agreement with the finding of Hara and Mei (1991).
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The project supported by the National Natural Science Foundation of China
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Qingpu, Z. Nonlinear instability of wavetrain under influences of shear current with varying vorticity and air pressure. Acta Mech Sinica 12, 24–38 (1996). https://doi.org/10.1007/BF02486759
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DOI: https://doi.org/10.1007/BF02486759