Dynamic response of soft poroelastic bed to nonlinear water wave - Boundary layer correction approach

When an oscillatory water wave propagates over a soft poroelastic bed, a bo undary layer exists within the porous bed and near the homogeneous water/po rous bed interface. Owing to the effect of the boundary layer, the conventi onal evaluation of the second kind of longitudinal wave inside the soft por oelastic bed by one parameter, E-1 = k(0)a, is very inaccurate so that a bo undary layer correction approach for a soft poroelastic bed is proposed to solve the nonlinear water wave problem. Hence a perturbation expansion for the boundary layer correction approach based on two small parameters, epsil on(1) and epsilon(2) = k(0)/k(2), is proposed and then solved. The solution s carried out to the first three terms are valid for the first kind and the third kind of waves throughout the whole domain. The second kind of wave i s solved systematically inside the boundary layer, whereas it disappears ou tside the boundary layer. The result is compared with the linear wave solut ion of Huang and Song in order to show the nonlinearity effect. The present study is very helpful to formulate a simplified boundary-value problem in numerical computation for soft poroelastic medium with irregular geometry. When an oscillatory water wave propagates over a soft poroelastic bed, a bo undary layer exists within the porous bed and near the homogeneous water/po rous bed interface. Owing to the effect of the boundary layer, the conventi onal evaluation of the second kind of longitudinal wave inside the soft por oelastic bed by one parameter, epsilon(1) = k(0)a, is very inaccurate so th at a boundary layer correction approach for a soft poroelastic bed is propo sed to solve the nonlinear water wave problem. Hence a perturbation expansi on for the boundary layer correction approach based on two small parameters , epsilon(1) and epsilon(2) = k(0)/k(2), is proposed and then solved. The s olutions carried out to the first three terms are valid for the first kind and the third kind of waves throughout the whole domain. The second kind of wave is solved systematically inside the boundary layer, whereas it disapp ears outside the boundary layer. The result is compared with the linear wav e solution of Huang and Song in order to show the nonlinearity effect. The present study is very helpful to formulate a simplified boundary-value prob lem in numerical computation for soft poroelastic medium with irregular geo metry.