水滑坡体产生的涌浪特性

Characteristics of waves generated by sub-aerial landslides

入水滑坡体所产生涌浪的波峰高度及传播时间是此类灾害预警和风险评估最为关注的特性参数。本文通过对滑坡体和水波相互作用的耦合数学模型进行数值求解,研究了以上2个特性参数与滑坡体形状及运动过程的关系。数学模型中假设滑坡体兴波区域内水波横向能量扩散可忽略,在立面二维的简化下应用非线性浅水方程描述水波过程;假设滑坡体底部流体法向流速为零,应用简化的Novier-Stokes方程描述底部流动;在滑坡体的运动方程中考虑了惯性力、水波波动压力、底部流体对滑坡体的阻力和浮托力以及滑坡体和滑动面间的摩擦力等。数值结果表明:滑坡体水平速度越大,涌浪传播越快;当滑坡体水平速度接近波速时,滑坡体具体形状对波峰高度有显著影响;当滑坡体水平速度大于波速时,波峰高度随滑坡体速度的增大而减小。因此,以往数学模型中对滑坡体具体形状的忽视,或者设定过大的滑坡体速度,都有可能导致波峰高度的低估,不利于防灾减灾。

Crest heights and arrival times of water waves generated by sub-aerial landslides are essential in Tsunami early warning systems and engineering risk assessment. The interaction between the water waves and the landslide is analyzed numerically to study the effect of landslide shape and landslide motion on the waves. The wave energy propagation in the transverse direction can be neglected in the landslide disturbance zone. Two dimensional nonlinear shallow water wave equations are then used to describe the wave generation process. Since the fluid velocity in the normal direction can be neglected, the Navier-Stokes equations can be simplified to describe the flow underneath the landslide, the inertial force, the water wave pressure along the landslide surface, the lubrication resistance, the buoyancy and the drag on the bottom. The results show that a faster landslide will cause a faster Tsunami wave. When the landslide horizontal velocity is approximately equals to the wave celerity, the crest height becomes sensitive to the landslide shape. When the landslide horizontal velocity is larger than wave celerity, a faster landslide creates a smaller crest height. Thus, the wave crest may be underestimated by previous models which ignore the specific shape of the landslide or the estimated landslide velocity is higher than in reality.