Classical Measures of Turbulence

In an experimental effort, measurements of turbulent flame speeds in gaseous reactants in a classic cylindrical Taylor-Couette burner were made by Ralph Aldredge at the University of California at Davis (Chapter 15). The study established sensitivity of the turbulent flame speed to turbulence intensity, and provided some influence of flame front wrinkling on flame propagation. 

The result that the diapycnal diffusivity in the pycnocline is of order O.lcm s confirms estimates based on internal wave dynamics and on measurements of turbulent dissipation rates. Some analyses of the penetration of transient tracers into the deep pycnocline also have implied diffusivities on the order of 0.1cm s . Values of diffusivity of lcm s were inferred by Munk s classic abyssal recipes analysis, but this was for depths between 1000 and 4000 m and included boundary processes as well as interior processes. It is now clear that lcm s is an overestimate for the interior pycnocline. 

Wu, Ruff and Faeth12491 studied the breakup of liquid jets with holography. Their measurements showed that the liquid volume fraction on the spray centerline starts to decrease from unit atZ/<70=150 for non-turbulent flows, whereas the decrease starts at aboutZ/<70=10 for fully developed turbulent flows. Their measurements of the primary breakup also showed that the classical linear wave growth theories were not effective, plausibly due to the non-linear nature of liquid breakup processes. 

Traditional turbulence-diffusion models (based on the boundary layer adjoining a solid wall) imply that n = 2/3, but a value n = 1/2 is appropriate for a boundary layer adjoining a free surface (Jahne and Haussecker 1998). The appropriate value of n depends on the wind stress and the surfactant loading of the surface. Soloviev and Schluessel (1994) have described a procedure for estimating gas transfer velocities from measurements of heat transport, assuming that transport is adequately described by the classical (Danckwerts) surface renewal model. The key relationship can be written in the form ... 

Film Theory. Many theories have been put forth to explain and correlate experimentally measured mass transfer coefficients. The classical model has been the film theory (13,26) that proposes to approximate the real situation at the interface by hypothetical "effective" gas and Hquid films. The fluid is assumed to be essentially stagnant within these effective films making a sharp change to totally turbulent flow where the film is in contact with the bulk of the fluid. As a result, mass is transferred through the effective films only by steady-state molecular diffusion and it is possible to compute the concentration profile through the films by integrating Fick s law ... 

Hubbard and Lightfoot (HI la) earlier reported a Sc,/3 dependence on the basis of measurements in which the Schmidt number was varied over a very large range. The data did not exclude a lower Reynolds number exponent than 0.88, and reaffirmed the value of the classical Chilton-Colburn equation for practical purposes. Recent measurements on smooth transfer surfaces in turbulent channel flow by Dawson and Trass (D8) also firmly suggest a Sc13 dependence and no explicit dependence of k+ on the friction coefficient, with Sh thus depending on Re0,875. The extensive data of Landau... 

In order to get a more detailed picture of the processes occurring in flowing systems, several investigators have directly measured concentration fluctuations. The basic ideas were introduced by Taylor (Tl) in a classic paper, and are discussed in detail in books on turbulence such as those by Hinze (H9) and Pai (PI). 

A versatile and classical method for studying kinetic reactions and other kinetic phenomena on short time scales is the use of a stopped-flow apparatus (SFA) for fast reproducible mixing and then to apply, e.g., spectroscopic methods for detection. In this technique, the reactants are rapidly mixed in a mixing chamber, usually under full turbulent flow that ensures fast homogenization on length scales down to nanometers [99]. Provided that short, synchronized acquisitions can be made. X-ray or neutron scattering can be used to probe kinetic transitions and other processes directly by measuring the temporal evolution of the intensity of the (mixed) sample. 

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