  In this manuscript we perform an extensive numerical study of the long wave
interaction problem with a fixed partially immersed body into a fluid layer.
The incident wave is assumed to be an isolated solitary wave. The body in this
study is assumed to be fixed with a rectangular section which is not touching
the bottom of the channel. The mathematical modelling of this problem is based
on Part I (Khakimzyanov and Dutykh 2020) of this series and considered models
include the Nonlinear Shallow Water Equations (NSWE), fully nonlinear weakly
dispersive Serre-Green-Naghdi Equations (SGN equations) (completed with
appropriate compatibility conditions on solid/fluid boundaries) and the free
surface irrotational full Euler equations (FEE). We study the influence of the
floating body elongation, immersion depth and incident wave amplitude on the
wave field before and after the obstacle. The comparison of all three models
predictions and the data of small-scale laboratory experiments is performed.
Moreover, in the framework of the FEE model we investigate the anomalous wave
run-up behind the floating body in the close presence of a vertical wall. We
demonstrate the cases where the vertical wall creates extreme wave amplitudes
behind the body, but also we show the cases where the wall attenuates wave
amplitudes comparing to the wave field without a wall.
