In recent decades, global climate change has strongly affected the Arctic region, leading to a rapid decline in sea ice extent. This decline affects the interactions between sea ice, the atmosphere, and the ocean, driven by complex thermodynamic and dynamical processes. The Arctic mixed layer (ML), located in the upper ocean, plays a key role in regulating the interactions between the deep ocean, sea ice, and the atmosphere. This region is strongly affected by exchanges of mass (such as freshwater and saltwater fluxes) and momentum driven by various forces like ocean currents, tides, waves, and winds. Here, we study the ad-hoc vertical turbulent kinetic energy (TKE) mixing scheme within the NEMO-SI3 model. Specifically, we focus on the influence of surface and internal wave breaking in sea ice-covered regions. The critical parameters are the fraction of surface TKE that penetrates below the ML, the nature of the exponential TKE penetration decrease beneath the ML, and the damping effect on Langmuir and surface wave breaking beneath the ice cover. We aim to assess how these parameters affect the ML and various sea ice properties.