Basic Properties of Turbulent Flows

Basic properties observed in turbulent flows, such as turbulence is chaotic and random; turbulence is vortical; turbulence is dissipative; turbulence is three dimensional, unsteady, and diffusive, are collected and analyzed. A working definition of turbulence is deduced from previous attempts and the list of these basic properties. The turbulent attractor is defined and elementary properties of its asymptotic state are discussed. Asymptotic properties and the number of degrees of freedom in maintained turbulence are analyzed.