This study is concerned with turbulence in the ocean, and in particular how the turbulence generated by a manoeuvering self-propelled body is affected by the different background environments found at various depths, well below and adjacent to the ocean surface. We are interested in both fundamental and practical issues. Examples of the former include the manner in which stable background stratification (the situation that exists when the fluid density increases with depth) alters the evolution of the wake, and the underlying physics of the process by which (for strong enough stratification) the small-scale three-dimensional wake turbulence is converted into a single large, persistent (essentially two-dimensional) dipolar vortex . The practical applications include remote detection of submerged bodies via the signature they leave in the ocean surface. The work is also relevant to a broad range of other engineering and geophysical problems, including the behaviour and environmental impact of wakes created by aircraft, yachts, supertankers, and wind and tidal turbines. Results are obtained from large-scale simulations on the national High Performance Computer (HPC) facilities (HECToR): Numerical experiments of turbulent wakes in a virtual ocean are performed using Direct Numerical Simulation (DNS) to produce high-fidelity solutions of the equations that govern the unsteady dynamics of the turbulence (the Navier-Stokes equations). Since these DNS solutions (which involve no approximations or phenomenological models) faithfully capture the details of the turbulence at each point in the flow field, they can be used to provide unambiguous answers to the fundamental and practical questions with which we are concerned.