14.2 Introduction

Virtually every interaction between organisms and their environment involves the transport or exchange of either mass or energy. Transport processes of particular emphasis in this series of modules include heat transfer and the mass fluxes of water vapor, carbon dioxide and other trace contaminants. For example, Stevenson (1979a) (see also Monteith 1973) has shown that by use of the concept of conservation of energy, which follows from the First Law of Thermodynamics, one can quantitatively describe the balance of energy inputs, outputs and production (e.g., metabolism) which is necessary to understand temperature dependent biological processes. Since many mass fluxes of interest are directly related to energy production or consumption (e.g., oxygen and respiration, carbon dioxide and photosynthesis, water vapor and the latent heat of vaporization), they too should be included in an energy balance description.

The next step in the development of a quantitative understanding of organism-environment interactions is the development of explicit expressions for each of the terms in the energy balance. Several of the terms in such a balance represent the flux of a quantity through a fluid, which for our purposes is usually water or air. Consequently, the transport will be highly dependent upon fluid motion and this is the rub. The flow of real fluids tends to be quite complicated, that is, turbulent. As a matter of fact, most flows occurring in nature are turbulent. Tennekes and Lumley (1972) present a representative listing of such flows. Included are ocean currents, river flow, combustion processes, the photosphere of the sun, the solar “wind,” flow around birds’ wings, a fish’s wake, and the earth’s atmosphere–especially trophospheric jet streams and wind fields near the earth’s surface. As a result of the ubiquitous nature of turbulent flows, it is necessary to come to some sort of understanding about their behavior, in order to be able at last to accomplish that which we started out to do: quantify organism-environment interactions.

It is interesting to note in the modules of this series concerned with such interactions that while heat transfer by radiation (e.g., Gates and Stevenson 1979 and Roseman 1979) and conduction (e.g., Simpson 1979a) can be expressed in exact analytic forms, the remaining major terms of the energy budget, convection and evaporation are treated empirically. For example, Stevenson (1979a) gives evaporation as a function of air temperature only because “water loss is a complex process,” while Gates (1979a) and Hatheway (1979) give expressions for convective heat transfer that include various complex empirical functions of wind speed, In fact, if one were to inspect any one of a number of texts dealing with transport processes (e.g., Tanner 1968, Monteith 1973 and 1975, Campbell 1977), a variety of ways would be found to quantify convection and evaporation, all of which are empirical. In practice, then, the attempt to solve problems involving turbulent flow exactly is often discarded in favor of the more expedient and, hopefully, useful empirical formulas.

In describing the energy and mass exchanges relevant to biological systems, an empirical description of turbulence is not only useful but usually essential. The practical question remaining for the physiologist or ecologist is how much and what sort of empirical scheme best suits a particular problem. A sound answer requires at least a modicum of understanding of the basic physical process involved: turbulence. This module introduces some of the basic terminology and concepts of turbulence theory, along with relevant examples. These concepts are used to develop the basic form of the most widely used semi-empirical flux relationships, the so-called K-theory.