Rapid expansions of the offshore wind industry have stimulated a renewed interest in the behavior of offshore wind turbines. Monopile, tripod, and jack-up wind turbines support most offshore wind turbines. These foundations are sensitive to scour, reducing their ultimate capacity and altering their dynamic response. However, the existing approaches ignore the seabed’s rheological properties in the scour process. This study focuses on the scour development around the wind turbine foundation in the Changhua wind farm in Taiwan. The simulation results explain the influence of different hydrodynamic mechanisms on the local scours in a cohesive fluid, such as regular waves, random waves, and constant currents. A newly non-Newtonian fluid model, the Discontinuous Bi-viscous Model (DBM), reproduces closet mud material nature without many empirical coefficients and an empirical formula. This new rheology model is integrated and coupled into the Splash3D model, which resolves the Navier–Stokes equations with a PLIC-VOF surface-tracking algorithm. The deformation of the scour hole, the backfilling, and the maximum scour depth are exhibited around the wind turbines. Waves, including regular and irregular waves, do not increase the scour depth compared with currents only. In the case of random wave–current coupling, the results present a signal of scour evolution. However, the scour depth is shallow at (Formula presented.).