On Turbulent Fluid Motion

The following report considers certain aspects of the statistical problems presented by turbulence. Attention has been given in the first place to correlations as defining a structure in the field and to their importance in the phenomenon of diffusion. In attempting to describe the structure of the field by resolving it into simple components, we are faced with the coupling between the components as expressed by the nonlinear form of the hydrodynamic equations of motion. A number of basic effects of nonlinearity in a dissipative system can be studied with the aid of a simplified mathematical model. This model enables us to investigate various problems closely analogous to cases of turbulent fluid motion and presents similar questions referring to spectral resolution. Finally, some aspects of the current statistical theory of isotropic turbulence have been compared with results deduced from the model.