We present an analytical theory of turbulence based upon the procedure of successive elimination of small-scale modes that leads to gradual coarsening of the flow field and accumulation of eddy viscosity. The Reynolds number based upon the eddy viscosity remains O(1). The main results of the theory are analytical expressions for eddy viscosity and kinetic energy spectrum. Partial scale elimination yields a subgrid-scale representation for large eddy simulations while the elimination of all fluctuating scales is analogous to the Reynolds averaging.