I will start discussing briefly the fundamental results of d-dimensional (dD) ideal flows, where d can be non-integer and can be greater than 3. Then, I will talk about 2D and 3D passive scalars from the point of view of cylindrical reduction from dD flows. The differences between 2D helical passive scalar and active scalar will be emphasized. If time permits, I will present the study of the possibility of extending the Taylor-Proudman theorem to 4D.
Dr. Jian-Zhou Zhu completed his undergraduate study majoring in ship building. Since graduating from Harbin Engineering University in 2000, he turned to study and work on super- and hyper-sonic shock/boundary layer interaction problems for his master degree in the Graduate School of Chinese Academy of Sciences, and to fundamental turbulence theory, during his PhD period 2000-2003 in the State Key Laboratory of Turbulence and Complex System at the Beijing University. He then solved the problems relevant to (partial) thermalization of fluid and plasma turbulence (both hydrodynamic and kinetic), relevant to controlled fusion and space/astro-physics in Los Alamos, Princeton and other institutes. At present, he is the director of Su-Cheng Centre for Fundamental and Interdisciplinary Sciences (SCCFIS) at Gaochun, Nanjing. His recent interests are on the dynamo theory of SCCFIS and other chirality relevant physical and life sciences, including the helicity effects and their control in plasmas and quantum fluids, as well as the aerodynamic or even the aero-thermo-dynamic issues, such as in wall-bounded turbulence.