Statistics of active and passive scalars in one-dimensional compressible turbulence.
Statistics of the active temperature and passive concentration advected by the one-dimensional stationary compressible turbulence at Re_{λ}=2.56×10^{6} and M_{t}=1.0 is investigated by using direct numerical simulation with all-scale forcing. It is observed that the signal of velocity, as well as the two scalars, is full of small-scale sawtooth structures. The temperature spectrum corresponds to G(k)∝k^{-5/3}, whereas the concentration spectrum acts as a double power law of H(k)∝k^{-5/3} and H(k)∝k^{-7/3}. The probability distribution functions (PDFs) for the two scalar increments show that both δT and δC are strongly intermittent at small separation distance r and gradually approach the Gaussian distribution as r increases. Simultaneously, the exponent values of the PDF tails for the large negative scalar gradients are q_{θ}=-4.0 and q_{ζ}=-3.0, respectively. A single power-law region of finite width is identified in the structure function (SF) of δT; however, in the SF of δC, there are two regions with the exponents taken as a local minimum and a local maximum. As for the scalings of the two SFs, they are close to the Burgers and Obukhov-Corrsin scalings, respectively. Moreover, the negative filtered flux at large scales and the time-increasing total variance give evidences to the existence of an inverse cascade of the passive concentration, which is induced by the implosive collapse in the Lagrangian trajectories.
State Key Laboratory of Turbulence and Complex Systems, Center for Applied Physics and Technology, and Key Laboratory of High Energy Density Physics Simulation, Ministry of Education, College of Engineering, Peking University, 100871 Beijing, People's Republic of China. niql.pku@gmail.com
Qionglin
Q
Ni
Shiyi
S
Chen