Lagrangian renormalized approximation of turbulence

A review is made of a two-point closure approximation called Lagrangian renormalized approximation (LRA), which is derived by a simple truncation of systematic Lagrangian renormalized expansions and is free from any ad hoc adjusting parameters or quantities. Emphasis is given to three key ideas: (i) representative, (ii) mapping and (iii) renormalized expansion underlying the LRA. The nature of the method of the expansion is explained by simple models, and general properties of the expansion as well as the truncated approximation are discussed in a general framework. A brief survey of the consequences of the LRA applied to three- and two-dimensional turbulences and passive scalar fields convected by turbulence is also presented.