Microbes play a primary role in aquatic ecosystems and biogeochemical cycles. Spatial patchiness is a critical factor underlying these activities, influencing biological productivity, nutrient cycling and dynamics across trophic levels. Incorporating spatial dynamics into microbial models is a long-standing challenge, particularly where small-scale turbulence is involved. Here, we combine a fully 3D direct numerical simulation of convective mixed layer turbulence, with an individual-based microbial model to test the key hypothesis that the coupling of gyrotactic motility and turbulence drives intense microscale patchiness. The fluid model simulates turbulent convection caused by heat loss through the fluid surface, for example during the night, during autumnal or winter cooling or during a cold-air outbreak. We find that under such conditions, turbulence-driven patchiness is depth-structured and requires high motility: Near the fluid surface, intense convective turbulence overpowers motility, homogenising motile and non-motile microbes approximately equally. At greater depth, in conditions analogous to a thermocline, highly motile microbes can be over twice as patch-concentrated as non-motile microbes, and can substantially amplify their swimming velocity by efficiently exploiting fast-moving packets of fluid. Our results substantiate the predictions of earlier studies, and demonstrate that turbulence-driven patchiness is not a ubiquitous consequence of motility but rather a delicate balance of motility and turbulent intensity.