The evolution of upper ocean currents involves a set of complex, poorly understood interactions between submesoscale turbulence (e.g. density fronts and filaments and coherent vortices) and smaller-scale boundary-layer turbulence. Here we simulate the lifecycle of a cold (dense) filament undergoing frontogenesis in the presence of turbulence generated by surface stress and/or buoyancy loss. This phenomenon is examined in large-eddy simulations with resolved turbulent motions in large horizontal domains using${\sim}10^{10}$grid points. Steady winds are oriented in directions perpendicular or parallel to the filament axis. Due to turbulent vertical momentum mixing, cold filaments generate a potent two-celled secondary circulation in the cross-filament plane that is frontogenetic, sharpens the cross-filament buoyancy and horizontal velocity gradients and blocks Ekman buoyancy flux across the cold filament core towards the warm filament edge. Within less than a day, the frontogenesis is arrested at a small width,${\approx}100~\text{m}$, primarily by an enhancement of the turbulence through a small submesoscale, horizontal shear instability of the sharpened filament, followed by a subsequent slow decay of the filament by further turbulent mixing. The boundary-layer turbulence is inhomogeneous and non-stationary in relation to the evolving submesoscale currents and density stratification. The occurrence of frontogenesis and arrest are qualitatively similar with varying stress direction or with convective cooling, but the detailed evolution and flow structure differ among the cases. Thus submesoscale filament frontogenesis caused by boundary-layer turbulence, frontal arrest by frontal instability and frontal decay by forward energy cascade, and turbulent mixing are generic processes in the upper ocean.