中国物理B ›› 2019, Vol. 28 ›› Issue (12): 124701-124701.doi: 10.1088/1674-1056/ab53cf
• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇 下一篇
Shaofeng Li(李少峰), Juan Chen(陈娟), Anzhou Cao(曹安州), Jinbao Song(宋金宝)
Shaofeng Li(李少峰), Juan Chen(陈娟), Anzhou Cao(曹安州), Jinbao Song(宋金宝)
摘要: Assume that a fluid is inviscid, incompressible, and irrotational. A nonlinear Schrödinger equation (NLSE) describing the evolution of gravity waves in finite water depth is derived using the multiple-scale analysis method. The gravity waves are influenced by a linear shear flow, which is composed of a uniform flow and a shear flow with constant vorticity. The modulational instability (MI) of the NLSE is analyzed, and the region of the MI for gravity waves (the necessary condition for existence of freak waves) is identified. In this work, the uniform background flows along or against wave propagation are referred to as down-flow and up-flow, respectively. Uniform up-flow enhances the MI, whereas uniform down-flow reduces it. Positive vorticity enhances the MI, while negative vorticity reduces it. Hence, the influence of positive (negative) vorticity on MI can be balanced out by that of uniform down (up) flow. Furthermore, the Peregrine breather solution of the NLSE is applied to freak waves. Uniform up-flow increases the steepness of the free surface elevation, while uniform down-flow decreases it. Positive vorticity increases the steepness of the free surface elevation, whereas negative vorticity decreases it.
中图分类号: (Ocean waves and oscillations)