A non-boundary-conforming formulation for simulating transitional and turbulent flows with complex geometries and dynamically moving boundaries on fixed orthogonal grids is developed. The underlying finite-difference solver for the filtered incompressible Navier-Stokes equations in both Cartesian and cylindrical coordinates is based on a second-order fractional step method on staggered grid. To satisfy the boundary conditions on an arbitrary immersed interface, the velocity field at the grid points near the interface is reconstructed locally without smearing the sharp interface. The complications caused by the Eulerian grid points emerging from a moving solid body into the fluid phase are treated with a novel "field-extension" strategy. To treat the two-way interactions between the fluid and structure, a strong coupling scheme based on Hamming's fourth-order predictor-corrector method has • attack angle at Re = 10, 000. Then, the turbulent flow over a traveling wavy wall at Re = 10, 170 are simulated are compared with the detailed DNS using bodyfitted grid in the literature. Finally, the simulation of the transitional flow past a prosthetic mechanical heart valve with moving leaflets at Re = 4, 000 has been performed. All results are in good agreement with the available reference data.

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High-fidelity simulations of wave breaking processes are performed with a focus on the small-scale structures of breaking waves, such as bubble/droplet size distributions. Very large grids (up to 12 billion grid points) are used in order to resolve the bubbles/droplets in breaking waves at the scale of hundreds of micrometres. Wave breaking processes and spanwise three-dimensional interface structures are identified. It is speculated that the Görtler type centrifugal instability is likely more relevant to the plunging wave breaking instabilities. Detailed air entrainment and spray formation processes are shown. The bubble size distribution shows power-law scaling with two different slopes which are separated by the Hinze scale. The droplet size distribution also shows power-law scaling. The computational results compare well with the available experimental and computational data in the literature. Computational difficulties and challenges for large grid simulations are addressed.