Turbulence, raindrops and thel1/2number density law
New Journal of Physics
Using a unique data set of three dimensional drop positions and masses (the HYDROP experiment), we show that the distribution of liquid water in rain displays a sharp transition between large scales which follow a passive scalar like Corrsin-Obukhov (k -5/3 ) spectrum and a small scale white noise regime. We argue that the transition occurs at the critical scale l c where the Stokes number (= drop inertial time/turbulent eddy time) St l is unity. For five storms, we found l c 3/7/08 2
... 3/7/08 2 determined by the strongly scale dependent turbulent velocity whereas the time scale for the transfer of the number variance flux ψ is determined by the weakly scale dependent drop coalescence speed. We argue that the l 1/2 law may also hold (although in a slightly different form) for cloud drops. The combination of number and mass density laws can be used to develop stochastic compound multifractal Poisson processes which are useful new tools for studying and modeling rain. We discuss the implications of this for the rain rate statistics including a simplified model which can explain the observed rain rate spectra. In contrast to many other studies, which have concentrated on the cloud microscale dynamics, we concentrate on the inertial scales showing that it leads to important constraints on the liquid water mass density distribution and on the number density distribution. It is therefore complementary to microphysical considerations.