Bulletin Spring‧Summer 2001

turbulence can be gaine d by studying the properties of a contaminant or pollutant that is carried by a turbulent flow. They found that one conditional average of the f o r m s t u d i e d e x t e n s i v e ly i n P r o f . Ch i n g 's f r amewo r k plays a c r u c i a l r o l e . Th is generated even greater interest i n Prof . Ching's work, and led, in particular, to the research collaboration between her and Dr . Robert H. Kraichnan. Dr. Kraichnan is a world-renowned physicist who has studied turbulence for more than 40 years and been awarded various awards and prizes. The duo were able to obtain exact results for some c ond i t i ona l averages d i r e c t l y f r om the equations of fluid motion i n certain turbulent flows 3 . Prof. Ching has further proposed that the i n t e rmi t t en t nature o f the po l l u t an t concentration i n one particular model is the sole result of the variations of the pollutant's local dissipation rate. Using this hypothesis, she obtained some quantitative results 4 . Present and Future Research P r o f . Ch i n g ' s f i r s t p r o j e ct at the University was completed i n early 1998. It answered some questions but raised even more. In August 1998, she was awarded funding from the RGC to embark on a second and ongoing project. The objective of this project is to test her hypothesis on the i n t e r m i t t e nt na t u re o f the p o l l u t a n t concentration, and to study the intermittency p r ob l em o f temperature fluctuations in thermal convection. The physical essence o f the hypothesis receives support from the numerica l data obtained from simulation of the model but the exact mathematical form proposed turns out to be invalid. I n thermal convection, a temperature difference is applied across a closed box of fluid. Hot fluid rises and cold fluid falls. As a result, the fluid is driven into m o t i o n by the a p p l i e d t emp e r a t u r e difference. Thus, temperature i n thermal convection is known as an active scalar, in contrast to a pollutant that is just carried by the flaw. The problem o f active scalar is richer and thus more interesting . Prof. Ching's results indicate that the temperature fluctuations i n thermal convectio n have different statistical properties under different regimes 5 ( F i gu re 7). I n N o v e m b e r 2 0 0 0, P r o f . C h i ng launched a third project, again with funding from the RGC. The focus this time is to study the relation between the velocity and the t emp e r a t u r e f l u c t u a t i o n s i n t h e r ma l convection. Currently, there is no consensus among scientists on the interplay between velocity and temperature, and it is expected that this project can help to resolve th e situation. Prof. Ching said, ‘Turbulence is a huge challenge. But I believe light w i l l be t h r own on this i n t r i g u i n g phenomenon slowly through hard work.' References 1. Emily S.C. Ching, Phys. Rev. Lett., 70, 283 (1993); S.B. Pope and Emily S.C. Ching, Phys. Fluids, A 5 , 1529 (1993). 2. Emily S.C. Ching, Phys. Rev., E53, 5899 (1996). 3. Emily S.C. Ching and Robert H. Kraichnan, J. Stat Phys., 93, 787 (1998). 4. Emily S.C. Ching, Phys. Rev. Lett., 79,3644 (1997). 5. Emily S.C. Ching, Phys. Rev., E61, R33 (2000). Figure 1 The black line represents the statistical properties of the temperature fluctuations in thermal convection under a buoyancy-dominated regime, while the red line represents that under an inertia- dominated regime. Chinese University Bulletin Spring • Summer 2001 36