The simulation of surface ship micro-bubble wakes

A method in which the transport and evolution of the bubble population in a surface ship wake is numerically simulated is presented. The simulation is accomplished by constructing an advective-diffusive transport model for the scalar bubble field and solving this model for late times after ship passage. The bubble population model requires convection velocities and turbulent diffusion information that is supplied by solving the Reynolds-averaged parabolized Navier-Stokes equations with a k - ∊ turbulence model. The mean flow equations are solved by approximating the differential equations with a second order accurate finite difference scheme. The resulting large, sparse, banded matrix is solved by applying a version of the conjugate gradient method. The method has proven to be efficient and robust for the free shear flow problems of interest here. The simulation is initiated with given information in a plane at some point downstream of the ship from which the solution is propagated. The model is executed for a single and a twin propeller ship at 15 knots. The simulation shows that the development of the hydrodynamic and bubble near wake is dominated by ship geometry via strong advective transport. The far wake is dominated by diffusion and bubble rise and dissolution. Thus relatively large changes in geometry have a limited influence on the far wake.