  Self-sustained turbulent structures have been observed in a wide range of
living fluids, yet no quantitative theory exists to explain their properties.
We report experiments on active turbulence in highly concentrated 3D
suspensions of Bacillus subtilis and compare them with a minimal fourth-order
vector-field theory for incompressible bacterial dynamics. Velocimetry of
bacteria and surrounding fluid, determined by imaging cells and tracking
colloidal tracers, yields consistent results for velocity statistics and
correlations over two orders of magnitude in kinetic energy, revealing a
decrease of fluid memory with increasing swimming activity and linear scaling
between energy and enstrophy. The best-fit model parameters allow for
quantitative agreement with experimental data.
