Nonlinear effects in buoyancy-driven variable-density turbulence. (25th November 2016) - Rao, P.; Caulfield, C. P.; Gibbon, J. D.
Abstract : We consider the time dependence of a hierarchy of scaled L^2m -norms D_m, [STIX]x1D714 and D_m, [STIX]x1D703 of the vorticity [STIX]x1D74E=[STIX]x1D735× u and the density gradient [STIX]x1D735[STIX]x1D703, where [STIX]x1D703=([STIX]x1D70C^* /[STIX]x1D70C_0^* ), in a buoyancy-driven turbulent flow as simulated by Livescu & Ristorcelli ( J. Fluid Mech., vol. 591, 2007, pp. 43–71). Here, [STIX]x1D70C^* (x, t) is the composition density of a mixture of two incompressible miscible fluids with fluid densities [STIX]x1D70C_2^* >[STIX]x1D70C_1^* , and [STIX]x1D70C_0^* is a reference normalization density. Using data from the publicly available Johns Hopkins turbulence database, we present evidence that the L^2 -spatial average of the density gradient [STIX]x1D735[STIX]x1D703 can reach extremely large values at intermediate times, even in flows with low Atwood number At=([STIX]x1D70C_2^* -[STIX]x1D70C_1^* )/([STIX]x1D70C_2^* +[STIX]x1D70C_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 [STIX]x1D735[STIX]x1D703 might blow up in a finite time.