Estimation of the ratio between the Lagrangian and Eulerian time scales in an atmospheric boundary layer generated by large eddy simulation

The estimation of the ratio β=TL/TE between Lagrangian and Eulerian time scales is an important problem, both in basic turbulence theory and in atmospheric pollution dispersion studies. The present paper aims at contributing to this research field by examining planetary boundary layer (PBL) turbulence data generated by an LES model in strongly convective, buoyancy-dominated and neutral stability conditions, respectively. Standard deviations of wind velocity, integral time scales, autocorrelation functions and spectra, for the three wind components, both in the Lagrangian and Eulerian frames, have been calculated. The Hay and Pasquill hypothesis which says that, at a first approximation, Eulerian and Lagrangian autocorrelation functions and spectra are identical after rescaling of the time axis by a factor β, was verified for the lower time lags of autocorrelation functions, and for frequencies describing the energy-containing eddies. Also. the usual assumption that β is inversely proportional to the turbulence intensity i, i.e. β=γ/i, was verified. Other four relationships, all relating β and i were tested, finding that all could be confidently used in practical applications. It was found that γ is a function of the different turbulent regimes, being greater in the strongly convective PBL, than in the neutral one. Values found are in agreement with previous experimental results and theoretical evaluations.