An analytical solution to the soil’s dynamic response induced by wave interaction with a marine current characterized by a non-uniform vertical profile

Abstract

In this work, we obtain an analytical solution to the soil’s dynamic response induced by wave interaction with a marine current with a prescribed non-uniform vertical profile. The control volume used to analyze the present problem is divided into a water region and another composed of a poroelastic soil region. The governing equations for the water hydrodynamics are presented in its dimensionless version and they are simplified for the limit of linear water waves. The velocity field in the water region is determined from the continuity equation and the “inviscid Orr-Sommerfeld linear equation”. We obtain a dispersion equation for wave-current interaction. For modeling the soil’s dynamics response, we adopt the u-p approximation. Considering a characteristic criterion for soil liquefaction, the maximum liquefaction depth is obtained as an eigenvalue problem. The analytical estimations, valid for the limit of linear water waves, provided by the present analysis show that, marine currents traveling in the same direction to the wave propagation induces larger values of the liquefaction depth than those obtained for currents opposite to wave propagation. As a first approximation, the present analysis may help understand the dynamic response of poroelastic soil induced by the wave-non-uniform marine current interaction.