布拉格共振条件下的高阶谐波特性研究

Investigation of higher harmonics induced by periodically submerged obstacles at Bragg resonance

为了考虑波浪在周期性地形上传播时诱发的布拉格共振现象和高阶谐波之间的相互影响,本文基于时域高阶边界元方法,建立二维完全非线性数值波浪水槽,数值研究布拉格共振条件下周期性地形诱发的高阶谐波特性。研究发现:随着潜体高度增加,二阶自由波透射系数呈现先增大后减小的趋势,而其反射系数则持续增大。同时,随着潜体长度增加,二阶自由波透反射系数均呈现增大的趋势,并最终各自稳定于一定值附近振荡。在布拉格共振条件下,除了普遍认为的自由波,二阶锁定波也将发生共振反射现象;此外,在布拉格共振条件下,周期性地形迎浪侧的二阶谐波波幅会出现“拍”和“寄生拍”的组合现象,使得迎浪侧波浪场更为复杂,并增加极端大波出现的概率。

To consider the interaction between higher harmonics and Bragg resonance induced by waves propagating on a periodic terrain,two-dimensional fully nonlinear numerical wave flumes have been established based on a time-domain higher-order boundary element method(HOBEM).HOBEM has been used to investigate higher harmonic waves generated over an array of submerged obstacles at Bragg resonance.It has been found that with an increase in the height of obstacles,the transmission coefficient for second-order harmonic free wave also increases initially and decreases thereafter,while the corresponding reflection coefficients continue to increase.Both transmission and reflection coefficients increase with increment in obstacle length and eventually saturate at certain values with marginal oscillation.When Bragg resonance occurs,the phenomenon of resonant reflection also takes place for the second-order locked wave,in addition to the well-recognized free waves.It has also been found that under the Bragg resonant condition,the second-order harmonic amplitude on the weather side of the bars shows the so-called“beat”and“parasitic beat”phenomena,which may increase the occurrence of extreme waves.