Structures and Mechanisms of Air-Entraining Quasi-Steady Breaking Ship Waves

Abstract

The overall objective of this study is to develop a fundamental understanding of the quasi-steady breaking wave regions present in surface ship wakes. Our approach uses direct numerical simulation (DNS) and implicit large eddy simulation. Building on our previous efforts looking at three-dimensional canonical dry transom sterns, we focus on the flow structure, air entrainment, and incompressible highly variable density turbulent characteristics in the wake of a fully submerged lifting body. This article represents the first steps of this study. Here, we perform DNS of the wake of a fully submerged lifting body with constant forward speed. Depending on the geometry and flow conditions, the wake of the submerged body contains a quasi-steady breaking-wave region downstream of the body that entrains air. We show that the simulations accurately predict the force and vortex wake frequency of the submerged body. Lagrangian analysis of the wake shows a frequency of peak entrainment that aligns with the frequency of the vortex wake. Finally, we establish that the power law of the air cavity density spectrum during the peak entrainment periods is predicted by r−10/3, consistent with experiments and theory. 1. Introduction Air-entraining quasi-steady breaking waves are prominent and highly observable features associated with surface ships and (nearsurface) submarines. They are important to the overall understanding of ship hydrodynamics with significant implications to the design operations of naval vessels. A systematic research effort elucidated many aspects of the complex three-dimensional highly mixed flows for a canonical dry transom stern (Weymouth et al. 2010; Hendrickson et al. 2012, 2016). In particular, we 1) identified wake and flow characteristics and obtained scaling with ship-scale parameters; 2) quantified the volume and scaling of the entrained air in the near wake; 3) characterized nature of the incompressible highly variable density turbulence (IHVDT) in the wake; and 4) developed explicit turbulent mass flux closure models (Hendrickson et al. under review; Hendrickson and Yue under review). Despite recent advances in large-scale state-of-the-art simulations of these flows, there remain fundamental issues and gaps in our knowledge and modeling capabilities. The main challenge of the canonical stern flow is that it contains regional complexity (convergent corner waves, rooster tails, diverging breaking waves) and many concurrent entrainment mechanisms and processes that limit our ability to isolate and address them fundamentally with sufficient numerical resolution.