Maxwell泥床上线性长波衰减的研究

A STUDY OF LINEAR LONG WAVE ATTENUATION OVER A MAXWELL MUD BED

用Maxwell模型作为非牛顿泥床本构,建立了一组新的Boussinesq型方程组,以描述波-泥相互作用下水波的传播.基于该方程,解析给出了一维线性长波衰减率的表达式.当泥层模型退化到牛顿流体时,该结果与前人文献的结果一致.当无量纲松弛时间λ较大时,衰减率随泥深近似地出现周期性的极值现象,这些极值位置对应泥层中各阶模态的衰减率峰值.

In coastal area,the interactions between waves and muddy seabed lead to energy dissipation.We use Maxwell model as the constitutive equation of non-Newtonian mud and develope a new set of Boussinesq-type equations to describe wave propagation under wave-mud interaction.Based on these equations,the damping rate for one-dimensional linear long waves is analytically obtained.The present result is consistent with previous literatures when the model degenerates to Newtonian case.When dimensionless relaxation timeλis large, extremums of the damping rate appear quasi-periodically as the mud depth increases.These extreme points correspond to the peaks of modal damping rates.