  The combined effectiveness of model reduction and the quasilinear
approximation for the reproduction of the low-order statistics of oceanic
surface boundary-layer turbulence is investigated. Idealized horizontally
homogeneous problems of surface-forced thermal convection and Langmuir
turbulence are studied in detail. Model reduction is achieved with a Galerkin
projection of the governing equations onto an subset of modes determined by
proper orthogonal decomposition. For less than 0.2% of the modes retained, the
reduced quasilinear model is able to reproduce vertical profiles of horizontal
mean fields as well as certain energetically important second-order turbulent
transport statistics and energies to within 30% error. For intermediate sizes
of the basis truncation some statistics approach those found in the fully
nonlinear simulations. Thus basis reduction can actually improve upon the
accuracy of quasilinear dynamics. A test model with a small total number of
modes demonstrates the non-monotonic convergence toward the correct statistics
as the size of the basis is increased.
