Nonlinear effects in buoyancy-driven variable-density turbulence. Rao, P., Caulfield, C., P., & Gibbon, J., D. Journal of Fluid Mechanics, 810:362-377, Cambridge University Press, 4, 2017. ![Nonlinear effects in buoyancy-driven variable-density turbulence [link]](https://bibbase.org/img/filetypes/link.svg "link")
Website doi abstract bibtex 2 downloads 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.
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title = {Nonlinear effects in buoyancy-driven variable-density turbulence},
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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.},
bibtype = {article},
author = {Rao, P and Caulfield, C P and Gibbon, J D},
doi = {10.1017/jfm.2016.719},
journal = {Journal of Fluid Mechanics}
}
Downloads: 2
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