Reduced descriptions of hydrodynamic turbulence

Navier-Stokes turbulence at ordinarily large Reynolds numbers can involve excitation of perhaps 1018 Fourier modes. A variety of proposals for reduced description have been offered, both to gain physical insight and to make computation feasible. The present brief and idiosyncratic survey discusses Galerkin approximations, Liapunov bases, Karhunen-Loeve decompositions, and statistically based decimation techniques