Numerical study on internal waves generated by a submerged body moving in two types of stratified fluids

Abstract

A numerical model is employed to simulate the internal waves generated by a moving submerged body in stratified fluids through the joint solution of the Navier-Stokes equations and the density transport equation. It is found the generation of internal waves begins with the formation of elevation and depression regions at the front and rear ends of the submerged body. As the body moves, more pairs of elevation and depression regions emerge in the wake, progressively leading to the full evolution of divergent and transverse wave features. Internal waves generated in two types of stratified fluids are compared, inferring the similarity of internal waves between two stratified fluids is not restricted to a specific depth but is consistently observed across all depths, and this similarity encompasses main flow characteristics, including internal wave surface fluctuation, pressure, and velocity components. However, an equivalent of Froude number, Fr, is only a necessary condition for the similarity, which does not guarantee the similarity between cases with different density stratifications. A water depth-based Froude number, Fr’(z), is proposed in this paper to investigate similarity. It has been shown that similarity is ensured when the Fr’(z) values of these cases are equal at any water depth.