Numerical investigation of mixing in stratified waters induced by ship navigation using the lattice Boltzmann method

Vertical density stratification frequently occurs in estuaries and coastal waterways. However, ship navigation induces vertical mixing that can significantly modify stratified water masses. Therefore, this study developed a coupled lattice Boltzmann model (LBM) to simulate the mixing of saltwater and freshwater by ships in a density-stratified environment. The model was validated against published results for lock-exchange flows, propeller wakes, and particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) experiments. The simulations showed that coherent wake vortices generated within the ship wake propagated downstream and continuously interacted with the density interface, causing interfacial deformation and promoting vertical transport of saltwater and freshwater. Regions with Richardson numbers below 0.25 were identified near the density interface, indicating enhanced mixing driven by local dynamic instabilities and turbulence. The evolution of the stratification coefficient revealed a sequence of rapid mixing immediately after ship passage, followed by partial re-stratification driven by buoyancy effects. However, the final stratification intensity remained lower than its initial state, indicating a persistent weakening of the density stratification after ship passage. Further analysis of the turbulence characteristics showed that more intensive coupled vessel operating conditions led to stronger mixing and a greater reduction in density stratification.