| Abstrakt: |
We consider the time dependence of a hierarchy of scaled L2m-norms Dm,ω and Dm,θ of the vorticity ω = ∇ x u and the density gradient ∇θ, where θ = log(ρ*/ρ*0), in a buoyancy-driven turbulent flow as simulated by Livescu & Ristorcelli (J. Fluid Mech., vol. 591, 2007, pp. 43-71). Here, ρ* (x, t) is the composition density of a mixture of two incompressible miscible fluids with fluid densities ρ*2 > ρ*1, and ρ*0 is a reference normalization density. Using data from the publicly available Johns Hopkins turbulence database, we present evidence that the L²-spatial average of the density gradient ∇θ can reach extremely large values at intermediate times, even in flows with low Atwood number At = (ρ*2 - ρ*1)/(ρ*2 + ρ*1) = 0.05, implying that very strong mixing of the density field at small scales can arise in buoyancy-driven turbulence. This large growth raises the possibility that the density gradient ∇θ might blow up in a finite time. [ABSTRACT FROM AUTHOR] |
