Maxwell泥床上线性长波衰减的研究

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. 

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

In coastal area, the interactions between waves andmuddy seabed lead to energy dissipation. We use Maxwell model as theconstitutive equation of non-Newtonian mud and develope a new set ofBoussinesq-type equations to describe wave propagation under wave-mudinteraction. Based on these equations, the damping rate for one-dimensionallinear long waves is analytically obtained. The present result is consistentwith previous literatures when the model degenerates to Newtonian case. Whendimensionless relaxation time λ is large, extremums of the dampingrate appear quasi-periodically as the mud depth increases. These extremepoints correspond to the peaks of modal damping rates.