  A stochastic model is derived to predict the turbulent torque produced by a
swirling flow. It is a simple Langevin process, with a colored noise. Using the
unified colored noise approximation, we derive analytically the PDF of the
fluctuations of injected power in two forcing regimes: constant angular
velocity or constant applied torque. In the limit of small velocity
fluctuations and vanishing inertia, we predict that the injected power
fluctuates twice less in the case of constant torque than in the case of
constant angular velocity forcing. The model is further tested against
experimental data in a von Karman device filled with water. It is shown to
allow for a parameter-free prediction of the PDF of power fluctuations in the
case where the forcing is made at constant torque. A physical interpretation of
our model is finally given, using a quasi-linear model of turbulence.
