,A nonlinear Schr(o)dinger equation for gravity waves slowly modulated by linear shear flow

• 作 者: Shaofeng Li Juan Chen Anzhou Cao Jinbao Song
• 机 构: Ocean College, Zhejiang University, Zhoushan 316000, China
• 出 处: 中国物理B（英文版）
• 发表日期: 2019年12期
• 关键词: nonlinear Schr(o)dinger equation gravity waves linear shear flow modulational in

Assume that a fluid is inviscid,incompressible,and irrotational.A nonlinear Schr(o)dinger 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.