化学波在对流介质中的折射与反射

Refraction and reflection of chemical waves in media with convection

以含有对流项的二维布鲁塞尔子为模型,导出化学波的波速随介质对流速度变化的关系式,用之说明化学波在对流介质中的折射与反射规律.结果表明:在对流介质中,尽管化学波在两种介质分界面上的折射与回折射(反射)仍然遵从波矢量切向分量连续定律,但折射角和反射角随入射角变化的规律与在静止介质中有所不同.当平面化学波从低速介质射向高速介质时,若介质对流速度方向与化学波的入射方向一致,在入射角大于临界角时,化学波在两种介质的边界上发生反常折射和反射现象,反常折射角随入射角的增大而增大,反射角随入射角变化,而且小于临界角;当平面化学波从高速介质射向低速介质时,若介质对流速度方向与化学波的入射方向一致,化学波在两种介质的边界上发生折射现象,折射角随入射角变化,先增大后减小.数值模拟结果进一步验证了理论结果.

The two-dimensional Brusselator model with convection was used to deduce the relation between wave speed and convective speed, and to study the refraction and reflection of chemical waves. It was found that the refraction and reflection of chemical waves obey the law of continuity of tangential wave vector, that the relation between the angle of incidence and angle of refraction and the relation between the angle of incidence and angle of reflection in media with convection are different from the relation in static media. When the direction of convection is parallel to the direction of incident wave vector, unusual refraction and reflection of chemical waves can occur simultaneously and the angle of unusual refraction increases with the increase of incident angle, and the angle of reflection is lesser than the critical angle and changes with incident angle if the plane wave goes from a medium with a lower speed to a medium with a higher speed. Provided the incident angle is larger than the critical angle, refraction occur and the angle of refraction changes with incident angle, first increasing with the increase of incident angle and then decreasing with the increase of incident angle if the plane wave goes from a medium with a higher speed to a medium with a lower speed.The numerical results testified the theoretical results.