Nonlinear effects in buoyancy-driven variable-density turbulence. (25th November 2016)

• Record Type: Journal Article
• Authors: Rao, P.; Caulfield, C. P.; Gibbon, J. D.
• Is Part Of: Journal of fluid mechanics. Volume 810(2017)
• Page Start: 362
• Page End: 377
• Publication Date: 2016-11-25
• Subjects: buoyancy-driven instability, -- mathematical foundations, -- Navier–Stokes equations; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2016.719
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : We consider the time dependence of a hierarchy of scaled $L^{2m}$ -norms $D_{m, \unicode[STIX]{x1D714}}$ and $D_{m, \unicode[STIX]{x1D703}}$ of the vorticity $\unicode[STIX]{x1D74E}=\unicode[STIX]{x1D735}\times \boldsymbol{u}$ and the density gradient $\unicode[STIX]{x1D735}\unicode[STIX]{x1D703}$, where $\unicode[STIX]{x1D703}=\log (\unicode[STIX]{x1D70C}^{\ast }/\unicode[STIX]{x1D70C}_{0}^{\ast })$, in a buoyancy-driven turbulent flow as simulated by Livescu & Ristorcelli ( J. Fluid Mech., vol. 591, 2007, pp. 43–71). Here, $\unicode[STIX]{x1D70C}^{\ast }(\boldsymbol{x}, t)$ is the composition density of a mixture of two incompressible miscible fluids with fluid densities $\unicode[STIX]{x1D70C}_{2}^{\ast }>\unicode[STIX]{x1D70C}_{1}^{\ast }$, and $\unicode[STIX]{x1D70C}_{0}^{\ast }$ 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 $\unicode[STIX]{x1D735}\unicode[STIX]{x1D703}$ can reach extremely large values at intermediate times, even in flows with low Atwood number $At=(\unicode[STIX]{x1D70C}_{2}^{\ast }-\unicode[STIX]{x1D70C}_{1}^{\ast })/(\unicode[STIX]{x1D70C}_{2}^{\ast }+\unicode[STIX]{x1D70C}_{1}^{\ast })=0.05$, 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 $\unicode[STIX]{x1D735}\unicode[STIX]{x1D703}$ might blow up in a finite time.