Fluid turbulence

The swirling motion of fluids that occurs irregularly in space and time is called turbulence. However, this randomness, apparent from a casual observa tion, is ndt without some order. Turbulent flows are as abundant in nature as life itself, and are pervasive in technology. They are a paradigm for sp atially extended nonlinear dissipative systems in which many length scales are excited simultaneously and coupled strongly. The phenomenon has been st udied extensively in engineering and in diverse fields such as astrophysics , oceanography, and meteorology. A few aspects of turbulence research in th is century are briefly reviewed, and a partial assessment is made of the pr esent directions. [S0034-6861(99)03202-X].