  We introduce a closure model for coarse-grained kinetic theories of polar
active fluids. Based on a quasi-equilibrium approximation of the particle
distribution function, the model closely captures important analytical
properties of the kinetic theory, including its linear stability and the
balance of entropy production and dissipation. Nonlinear simulations show the
model reproduces the qualitative behavior and nonequilibrium statistics of the
kinetic theory, unlike commonly used closure models. We use the closure model
to simulate highly turbulent suspensions in both two and three dimensions in
which we observe complex multiscale dynamics, including large concentration
fluctuations and a proliferation of polar and nematic defects.
