A spin-off from mathematical research of fluid-dynamics may one day help provide more accurate mid-term weather forecasts for Hong Kong.
The research, at The Chinese University of Hong Kong, uses nonlinear partial differential equations to study the characteristics of air or gas

Prof Xin with some of his students.

Immediate benefits are solutions to help designers of materials used in high speed flight. Using the same nonlinear partial differential equations, notably the Navier-Stokes equation first evolved in the 18th century, Principal Investigator Prof Zhou-ping Xin is also looking at how topography of the sea bed affects air circulation and therefore the weather.
“It’s possible that we can use the calculations to help predict with some accuracy trends in the weather for the mid-term, from four weeks to several months. That would be very useful for Hong Kong.”
Prof Xin added: “Many phenomena in the physical world are governed by nonlinear partial differential equations which enable us to describe the phenomena mathematically.
“Doing this means we can assimilate many situations, across many fields of physical science, some of which may be impossible to assimilate or be too expensive to mimic experimentally.”
In aerodynamics, the researchers have added to analysis and understanding of shock waves caused when air or gases flow at supersonic speeds.
Specifically, they have verified design criteria for jet engine nozzles where gases are converted from subsonic to supersonic speeds. They have also come up with new understandings in aerodynamics.
Previously it was thought that the shock wave, forming from supersonic flow past a sharp body was unstable. “Our theory suggests, in fact, that the shock wave is globally stable,” said Prof Xin.
Calculations that assimilate the behaviour of “space shapes” in flight far greater than the speed of sound can be easily made, without the expense of wind tunnel experiments, he added.
“The numerical code resulting from the research is so reliable that it can form the basis of the initial design of space shapes.”
The mathematical methods developed by the researchers can be used to solve other multi-dimensional problems.
Another possible application, said Prof Xin, could be predicting trends for the Hong Kong stock market.
“The mathematical model would be similar to one for weather prediction.” Prof Xin said: “The research was about achieving a better theoretical understanding of the subject, so the uses of these models go beyond event-specific aerodynamics and military applications.
“It’s an important analysis that bridges engineering and pure mathematics, and can equally be applied to population dynamics or meteorology.
“We hope that our theories can provide valuable insights and guidelines for engineers for their future work.” The research, said Prof Xin, is an example of how international Hong Kong is becoming academically.
Last year, the International Congress of Mathematicians invited Prof Xin to make a presentation on his work. Addressing the congress, which meets only once every four years, is considered prestigious.
“The fact that Hong Kong is sponsoring research of this nature also shows its international outlook,” said Prof Xin.

Principal Investigator
Prof Zhou-ping Xin : zpxin@ims.cuhk.hk