Abstract We present the first in situ observations of the full turbulence tensor of free convection under lake ice, obtained using an original method based on a set of two synchronized acoustic Doppler profilers to measure all six turbulent stress components. Convection revealed strong anisotropy, with prevailing horizontal transport components. Convective energy closely followed buoyancy flux scaling modified for spatially distributed buoyancy production by solar radiation under ice. The scaling coefficients, however, differ from those known in atmospheric convection driven by surface buoyancy flux, indicating stronger horizontal fluctuations. Local non‐stationarity due to diurnal variations in solar radiation contributed about 10% of the total energy budget. Direct quantification of convective energy components and shear transport in free convection provides a framework for estimating ice–water heat exchange in lakes and for testing convection models with applications to a wide range of geo‐ and astrophysical flows.