Mixing, Chaotic Advection, and Turbulence

The establishment of a paradigm for mixing of fluids can substantially affect the development of various branches of physical sciences and technology. Mixing is intimately connected with turbulence, Earth and natural sciences, and various branches of engineering. However, in spite of its universality, there have been surprisingly few attempts to construct a general framework for analysis. An examination of any library index reveals that there are almost no works textbooks or monographs focusing on the fluid mechanics of mixing from a global perspective. In fact, there have been few articles published in these pages devoted exclusively to mixing since the first issue in 1969 one possible exception is Hill’s Homogeneous Turbulent Mixing With Chemical Reaction (1976), which is largely based on statistical theory. However, mixing has been an important component in various other articles; a few of them are Mixing-Controlled Supersonic Combustion (Ferri 1973), and Mixing in Stably Stratified Waters (Sherman et al. 1978), Eddies, Waves, Circulation, and Mixing: Statistical Geofluid Mechanics (Holloway 1986), and Ocean Turbulence (Gargett 1989). It is apparent that mixing appears in both industry and nature and the problems span an enormous range of time and length scales; the Reynolds number in problems where mixing is important varies by 40 orders of magnitude (see Figure 1). Virtually everyone agrees that mixing is complicated. However, there is no agreement as to the source of the complications; to a rhcologist, the constitutive equation is of paramount importance; to someone in turbu-