ASYMPTOTIC GROWTH RATES AND STRONG BENDING OF TURBULENT FLAME SPEEDS OF G-EQUATION IN STEADY TWO-DIMENSIONAL INCOMPRESSIBLE PERIODIC FLOWS

作者：Xin Jack^*; Yu Yifeng

来源：SIAM Journal on Mathematical Analysis, 2014, 46(4): 2444-2467.

DOI：10.1137/130929990

• G-equation
• optimal control
• cat's-eye flow
• turbulent flame speed
• front speed
• bending effect
• large flow
• invariant measure
• periodic orbit
• rotation vector
• travel time of flow intensity

The study of turbulent flame speeds (the large time front speeds) is a fundamental problem in turbulent combustion theory. A significant project is to understand how the turbulent flame speed (s(T)) depends on the flow intensity (A). The G-equation is a very popular level set flame propagation model in the turbulent combustion community. The main purpose of this paper is to study properties of lim(A ->+infinity) sT/A and lim(A ->+infinity) s(T) (if finite, or strong bending) in the G-equation model for two-dimensional (2D) divergence-free periodic flows. Our analysis is based on the invariant measures and rotation vectors of the 2D flows and the travel times of the associated flow trajectories under control. Optimal linear/sublinear growth and strong bending conditions are precisely given in terms of rotation vectors and periodic orbits. A strong bending formula of s(T) in the cat's-eye flow is discovered by averaging the controlled characteristics of the G-equation. The growth rate of sT and that of the related front speeds of reaction-diffusion-advection equations (with Kolmogorov-Petrovsky-Piskunov nonlinearity) are shown to be zero or nonzero simultaneously in 2D flows, yet they differ in the three-dimensional (3D) Roberts cell flows that depend on two spatial variables. A future program will be to extend our analysis to more complex fluid flows, such as unsteady 2D flows and 3D flows with chaotic structures.

• 出版日期2014