二维Oseen流中潜体产生的非定常表面波

本文考虑无限深不可压粘性流体中潜体产生的非定常表面波.受扰流动由非定常Oseen方程控制,对自由面上的波动则采用线性化边界条件,物体用具有周期振荡强度的Oseen极子模拟.通过Fourier变换,自由表面波的精确解表示为带复变色散函数的积分式,波动力学性质由Reynolds数和Strouhal数刻画.运用Lighthill定理,导出了亚临界和超临界Strouhal数时表面波的远场解的渐近式.结果显示,振荡Oseen极子生成的波动包含稳态和瞬态响应.对于亚临界Strouhal数粘性流动,存在四列波,三列在下游区域传播,一列在上游区域;对于超临界Strouhal数粘性流动,仅有在下游区域传播的二列波.

Unsteady Free-surface Waves Due to a Submerged Body in Two-dimensional Oseen Flows

The two-dimensional unsteady free-surface waves due to a submerged body moving in an incompressible viscous fluid of infinite depth is considered.The disturbed flow is governed by the unsteady Oseen equations with the kinematic and dynamic boundary conditions linearized for the free-surface waves.Accordingly, the body is mathematically simulated by an Oseenlet with a periodically oscillating strength.By means of Fourier transforms,the exact solution for the free-surface waves is expressed by an integral with a complex dispersion function, which explicitly shows that the wave dynamics is characterized by a Reynolds number and a Strouhal number.By applying Lighthill's theorem, asymptotic representations are derived for the far-field waves with a sub-critical and a super-critical Strouhal number. It is found that the generated waves due to the oscillating Oseenlet consist of the steady-state and transient responses. For the viscous flow with a sub-critical Strouhal number, there exist four waves: three propagate downstream while one propagates upstream.However, for the viscous flow with a super-critical Strouhal number, there exist two waves only, which propagate downstream.