Hard State of the Urban Canopy Layer Turbulence and Its Self-Similar Multiplicative Cascade Models

The atmospheric turbulence is usually more complex than that in laboratory. There will be large temperature gradient in the atmospheric boundary layer, especially in the urban canopy layer with buildings and canyons, the so-called ‘hard turbulence’ with high Rayleigh number (Ra ~109 ) will appear. In this paper, we use the high frequency (100 Hz) turbulent fluctuation data to analyze the temperature structure function. The data were obtained with an advanced R3A type sonic anemometer at 47m platform on the 325 m meteorological tower in Beijing city of China. It is found that under the thermal convection condition, the temperature fluctuation in the urban canopy layer does have the characteristics of hard turbulence, and the temperature difference between two points (using Taylor's freezing hypothesis) has the exponential probability density function distribution. At the same time, the turbulent energy dissipation rate fits the log-normal distribution, and is in accord with the hypothesis proposed by Kolmogorov in 1962 and lots of reported experimental results. We proposed a new scaling formula of hard state temperature n order structure function by the self-similar multiplicative cascade models, that is , where is intermittent exponent. This new formula can fit the experimental results up to order 8 exponents. In addition, a numerical simulation based on a shell model is carried out to verify this formula. Numerical result also agrees well with our scaling exponents of orders n = 1 to 8. Both experiment and numerical simulation show that our new scaling formula is better than that given by K41 theory, log-normal model and β model.