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Fluid Mechanics has parked increasing research areas of interest to mathematicians, physicists, applied mechanician, oceanographers, atmospheric scientists, etc. because of its importance recognized in both fundamental research and practical application. The current research areas in the Program of Fluid Mechanics include fundamentals, modeling and large-eddy simulation (LES) of turbulent flows, structure ensemble dynamics (SED) theory, environmental and geophysical thermal convections, laminar-turbulent transition, flow control, Lagrangian studies and multi-scale geometric analysis of turbulence, fundamental combustion theory and flame dynamics of hydrocarbon fuels.
Impacts: Over the past five years, more than 40 scientific and engineering research projects have been finished, including several projects supported by the Foundation for Innovative Research Groups, the State Key Program, and the Major Research plan of the National Natural Science Foundation of China, a project supported by National Basic Research Program (973 Program) of China, and a project supported by the Ministry of Industry and Information Technology of China. Significant and substantial progress has been achieved in different research areas. Over 120 peer-reviewed articles have been published on international journals, including Journal of Fluid Mechanics, Physical Review Letters, Physics of Fluids, Journal of Turbulence, Physical Review E, Combustion and Flame, Journal of Computational Physics, etc. A one-week "International Symposium on Turbulence" was held at Peking University on September 21-25, 2009. Prof. Shiyi Chen gave the opening presentation as the initial Chinese presenter at the 23rd International Congress of Theoretical and Applied Mechanics (ICTAM2012).
Listed below are selected research achievements in the Program of Fluid Mechanics. 
a)      Direct numerical simulation and fundamental theory of compressible turbulence
A hybrid compact finite difference-weighted weighted essentially non-oscillatory method has been developed for numerical simulation of high Mach- and Reynolds-number compressible turbulence. Helmholtz decomposition technique is used to study the multi-scale and multi-process dynamics of compressible turbulence. Particular focus has been on the understanding of how small-scale motion is related to large-scale motion, with the specific purpose of developing improved turbulence models and how fluid particles are accelerated in compressible turbulent flow.
Figure 1 Instantaneous rendering of shocklets (dark brown sheetlike surface) and vortices (light gray tubelike surface) with typical tracer trajectories (Yang et al., Phys. Rev. Lett. 110(6): 064503, 2013).
b)      Development of the constrained large-eddy Simulation (CLES) method
A Reynolds (stress and heat flux) constrained Large-eddy Simulation method has been proposed for simulation of wall-bounded turbulent flows. Such a technique makes the pure LES of wall-bounded turbulent flows feasible on moderate grid and has been successfully applied to simulating many turbulent flows with complex geometries, e.g., the flow past a commercial aircraft.
Figure 2 Instantaneous flow structures obtained in CLES of flow around a commercial aircraft (Chen et al., Sci. China-Phys. Mech. Astron. 56 : 270-276, 2013).
c)      Development of structure ensemble dynamics (SED) theory
A structure ensemble dynamics (SED) theory has been developed, which emphasizes the Lie-group symmetry of the problem with a set of new concepts (order functions, multi-layer structures, etc.), and has achieved accurate descriptions for a series of mean profiles (velocity, kinetic energy, temperature etc.) in canonical wall-bounded flows (channel, pipe, turbulent boundary layer, and Rayleigh-Bernard convection). The theory has also been extended to study flows with compressibility, pressure gradient, roughness effects, and yielded significantly improved predictions for engineering CFD models, such as k-ω model.
Figure 3 Global Mach number invariance of density viscosity rescaled Prandtl’s mixing length (Zhang et al., Phys. Rev. Lett. 109(5): 054502, 2012).
d)    Ignition and flame propagation theory considering transport and reaction of radical
The dynamics of flame kernel development has been studied and a general theory on ignition and flame propagation has been developed which considers transport and reaction of radical chain-branching kinetics of intermediate species. The theory can successfully describe all the flame regions such as stationary flame balls, self-extinction flames, and traveling flames.
Figure 4 Left: Spherical flame initiation and propagation considering; Right: spherical flame propagation speed as a function of flame radius at different fuel Lewis numbers (Zhang and Chen, Combustion and Flame158:1520-1531, 2011).
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