  We propose an aerodynamic force model associated with a Galerkin model for
the unforced fluidic pinball, the two-dimensional flow around three equal
cylinders with one radius distance to each other. The starting point is a
Galerkin model of a bluff-body flow. The force on this body is derived as a
constant-linear-quadratic function of the mode amplitudes from first principles
following the pioneering work of Noca (1997, 1999) and Liang & Dong (2014). The
force model is simplified for the mean-field model of the unforced fluidic
pinball (Deng et al. 2020) using symmetry properties and sparse calibration.
The model is successfully applied to transient and post-transient dynamics in
different Reynolds number regimes: the periodic vortex shedding after the
Hopf-bifurcation and the asymmetric vortex shedding after the pitchfork
bifurcation comprising six different Navier-Stokes solutions. We foresee many
applications of the Galerkin force model for other bluff bodies and flow
control.
