In this paper we present a stabilized finite element method for three-dimensional, non-hydrostatic, turbulent coastal ocean flows. The model we have developed, named HELIKE, incorporates also surface wind stress, bottom friction, Coriolis forces and several closure models for both the horizontal and the vertical turbulent eddy vis- cosity coefficients. Unstructured meshes are employed so that complex geometries can be accurately approximated, and implicit time stepping allows to use large time steps. Numerical results are presented in various test cases, in which comparisons between different turbulence models are provided.