Numerical Study of the Influence of Weber and Reynolds Numbers on the Development of Kelvin-Helmholtz Instability

Sloshing model tests or wave impact tests in flumes show large variability of local impact pressure measurements. One of the reasons for such variability is the generation of free surface instabilities by the shearing gas flow at the free surface just before the impacts. To better understand the first steps of the development of free surface instabilities around the crest of breaking waves, a bi-fluid, high-fidelity front-tracking software based on the Navier-Stokes equations has been developed. Named CADYF, this software simulates separated two-phase incompressible viscous flows with surface tension. The numerical method uses adaptivity in space (adaptive remeshing) and time (hp-adaptivity) to yield accurate predictions while keeping computational cost low. As a first application, a simple experiment carried out by Thorpe, which enabled the generation of Kelvin-Helmholtz instability in a rectangular tube completely filled with two liquids of different densities, is simulated. Numerical results are compared with experimental results and other simulations. A parametric study is performed varying surface tension and fluid viscosities at a constant viscosity ratio. The evolutions of the main parameters describing the Kelvin-Helmholtz instability are provided in dimensionless form, giving some clues about the scaling process.