An investigation of turbulent transport in the extreme lower atmosphere - Sadeh, Willy Z., author; Koper, Chester A., Jr., author; Fluid Dynamics and Diffusion Laboratory, Department of Civil Engineering, Colorado State University, publisher (Colorado State University. Libraries, 1975)
A model in which the Lagrangian turbulent velocity autocorrelation is expressed by a domain integral over a set of usual Eulerian autocorrelations was put forth. The Lagrangian autocorrelation can be readily computed provided that the Eulerian autocorrelations are obtained concurrently at all points within the flow field of interest, i.e., within a selected turbulence "box". A method for ascertaining the statistical stationarity of turbulent velocity by creating an equivalent ensemble which approximates the real ensemble of turbulent velocity realizations was developed. An experimental investigation of the flow in the extreme lower atmospheric layer, i.e., the layer up to about 5 m depth, was conducted for the purpose of verifying the model put forth for computing Lagrangian autocorrelation and its application to predicting turbulent diffusion. This flow was both dynamically and thermally simulated satisfactorily using the wake flow generated by a 3.04 m diameter fan installed at a field site located on flat grassland. Simultaneous measurements of turbulent velocity at five stations on a turbulence "line" along the wake axis were carried out under calm wind, dry and stable conditions utilizing a longitudinal array of five hot-wire anemometers remotely operated. The stationarity test revealed that the turbulent velocity can be approximately considered a realization of a weakly self-stationary random process. The streamwise changing properties of turbulence were deduced from a set of five Eulerian autocorrelations. A first integral time scale, based solely on the positive autocorrelation, was introduced as a characteristic large time scale. The micro and first integral time and length scales exhibited a consistent streamwise increase. This behavior testified to the nonhomogeneity of the turbulence and to a continuous accumulation of turbulent energy at large scales. The turbulence structure was dominated by relatively large-scale eddies since the first integral time and length scales were consistently about tenfold greater than their micro scale counterparts. Continuous time and spatial variations of the Eulerian autocorrelations along the turbulence line were secured by advancing Eulerian referencepoint autocorrelations and Eulerian autocorrelation envelopes. The longitudinal Lagrangian autocorrelation was estimated by means of a line integral over all the Eulerian autocorrelation envelopes for the turbulence line. Large diffusion times predominated since the Lagrangian first diffusion time scale was about ten times larger than the short diffusion time scale. Ratios of the Lagrangian to Eulerian time scales smaller than unity were found. Both short and long diffusion time scales were constrained within their Eulerian counterparts. The turbulent momentum exchange coefficient and the dispersion coefficient were computed employing the calculated Lagrangian autocorrelation. Concentration of diffusing material along the turbulence line was predicted utilizing this dispersion coefficient. Corroboration of the computed concentration distribution along the turbulence line was accomplished by a gas diffusion experiment utilizing sulfur hexaflouride. A remarkable similar streamwise variation of both predicted and measured concentrations within a difference ranging from 4 to 13%, at the most, was found.
CER74-75CAK-WZS34.
Prepared for Aerospace Environment Division, George C. Marshall Space Flight Center, National Aeronautics and Space Administration contract no. NAS 8-28590.
February 1975.
Keywords: Turbulent diffusion (Meteorology) -- Mathematical models; Atmospheric turbulence -- Mathematical models; Atmospheric turbulence -- Measurement