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Two different air-water interfacial flows are studied including plunging wave breaking and flow past a vertical surface-piercing circular cylinder using complementary CFDShip-Iowa version 6 including Cartesian grid solver and orthogonal curvilinear grid solver. The plunging wave-breaking process for impulsive flow over a bump in a shallow water flume has been simulated using the exact experimental initial and boundary conditions. The overall plunging wave breaking process is described with major wave breaking events identified: jet plunge, oblique splash and vertical jet. These major events repeat up to four times before entering the chaotic breaking. The simulations show a similar time line as the experiments consisting of startup, steep wave formation, plunging wave, and chaotic wave breaking swept downstream time phases. Detailed wave breaking processes, including wave profile at maximum height, first plunge, entrapped air bubble trajectories and diameters, kinetic, potential, and total energy, and bottom pressures are discussed along with the experimental results. The simulations show differences and similarities with other experimental and computational studies for wave breaking in deep water and sloping beaches. The geometry and conditions in the present study are relevant to ship hydrodynamics since it includes effects of wave-body interactions and wave breaking direction is opposite to the mean flow. Large-eddy simulation with the Lagrangian dynamic subgrid-scale model has been performed to study the flow past a surface-piercing circular cylinder for Re and Fr effect. The flow features near the air-water interface show significant changes with different Reynolds numbers from sub-critical to critical regime. It is shown that the interface makes the separation point more delayed for all regime of Re. Remarkably reduced separated region below the interface is observed for critical Re regime and it is responsible for much reduced wake and recirculation region behind the cylinder and it recovers in the deep flow. At different Fr, significant changes are shown on the air-water interface structures. At lower Fr, relatively smaller bow waves are observed in front of the cylinder with Kelvin waves behind the cylinder and small amount of free-surface roughness and turbulence are also seen in the wake region. For higher Fr, the bow wave increases remarkably with the larger wake region and deeper depression and it breaks with similar features of plunging breakers. Much more small air-water interface structures including splashes and bubbles are observed behind the cylinder. It is hard to distinguish the Kelvin waves behind the cylinder due to much larger free-surface oscillations and turbulence. As Fr increases, the Kelvin wave angle decreases and deeper and narrower depression region behind the cylinder are observed. The flow features around the cylinder are significantly changed due to this cavity region behind the cylinder.