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Transition from shear-dominated to Rayleigh–Taylor turbulence

Published online by Cambridge University Press:  05 August 2021

Stefano Brizzolara*
Affiliation:
Institute of Environmental Engineering, ETH Zurich, CH-8039 Zurich, Switzerland Swiss Federal Institute of Forest, Snow and Landscape Research WSL, 8903 Birmensdorf, Switzerland
Jean-Paul Mollicone
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK Division of Fluid Dynamics, Department of Mechanics and Maritime Sciences, Chalmers University of Technology, SE-41296 Gothenburg, Sweden
Maarten van Reeuwijk
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK
Andrea Mazzino
Affiliation:
DICCA, University of Genova and INFN, Genova Section, Via Montallegro, 1, 16145 Genova, Italy
Markus Holzner
Affiliation:
Swiss Federal Institute of Forest, Snow and Landscape Research WSL, 8903 Birmensdorf, Switzerland Swiss Federal Institute of Aquatic Science and Technology Eawag, 8600 Dübendorf, Switzerland
*
Email address for correspondence: brizzolara@ifu.baug.ethz.ch

Abstract

Turbulent mixing layers in nature are often characterised by the presence of a mean shear and an unstable buoyancy gradient between two streams of different velocities. Depending on the relative strength of shear versus buoyancy, either the former or the latter may dominate the turbulence and mixing between the two streams. In this paper, we present a phenomenological theory that leads to the identification of two distinct turbulent regimes: an early regime, dominated by mean shear, and a later regime dominated by buoyancy. The main theoretical result consists of the identification of a cross-over timescale that distinguishes between the shear- and the buoyancy-dominated turbulence. This cross-over time depends on three large-scale constants of the flow, namely, the buoyancy difference, the velocity difference between the two streams and the gravitational acceleration. We validate our theory against direct numerical simulations of a temporal turbulent mixing layer compounded with an unstable stratification. We observe that the cross-over time correctly predicts the transition from shear- to buoyancy-driven turbulence, in terms of turbulent kinetic energy production, energy spectra scaling and mixing layer thickness.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Akula, B., Andrews, M.J. & Ranjan, D. 2013 Effect of shear on Rayleigh–Taylor mixing at small Atwood number. Phys. Rev. E 87 (3), 033013.CrossRefGoogle Scholar
Akula, B., Suchandra, P., Mikhaeil, M. & Ranjan, D. 2017 Dynamics of unstably stratified free shear flows: an experimental investigation of coupled Kelvin–Helmholtz and Rayleigh–Taylor instability. J. Fluid Mech. 816, 619660.CrossRefGoogle Scholar
Atzeni, S. & Meyer-ter Vehn, J. 2004 The Physics of Inertial Fusion: Beam Plasma Interaction, Hydrodynamics, Hot Dense Matter. Oxford University Press.CrossRefGoogle Scholar
Bell, J.H. & Mehta, R.D. 1990 Development of a two-stream mixing layer from tripped and untripped boundary layers. AIAA J. 28 (12), 20342042.CrossRefGoogle Scholar
Bernal, L.P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499525.CrossRefGoogle Scholar
Boffetta, G., De Lillo, F., Mazzino, A. & Vozella, L. 2012 The ultimate state of thermal convection in Rayleigh–Taylor turbulence. Physica D 241 (3), 137140.CrossRefGoogle Scholar
Boffetta, G. & Mazzino, A. 2017 Incompressible Rayleigh–Taylor turbulence. Annu. Rev. Fluid Mech. 49, 119143.CrossRefGoogle Scholar
Breidenthal, R. 1981 Structure in turbulent mixing layers and wakes using a chemical reaction. J. Fluid Mech. 109, 124.CrossRefGoogle Scholar
Celani, A., Mazzino, A., Muratore-Ginanneschi, P. & Vozella, L. 2009 Phase-field model for the Rayleigh–Taylor instability of immiscible fluids. J. Fluid Mech. 622, 115134.CrossRefGoogle Scholar
Chertkov, M. 2003 Phenomenology of Rayleigh–Taylor turbulence. Phys. Rev. Lett. 91 (11), 115001.CrossRefGoogle ScholarPubMed
Craske, J. & van Reeuwijk, M. 2015 Energy dispersion in turbulent jets. Part 1. Direct simulation of steady and unsteady jets. J. Fluid Mech. 763, 500537.CrossRefGoogle Scholar
Finn, J.M. 1993 Nonlinear interaction of Rayleigh–Taylor and shear instabilities. Phys. Fluids B: Plasma Phys. 5 (2), 415432.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. C. R. Acad. Sci. URSS 30, 301305.Google Scholar
Kolmogorov, A.N. 1962 A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13 (1), 8285.CrossRefGoogle Scholar
Koochesfahani, M.M. & Dimotakis, P.E. 1986 Mixing and chemical reactions in a turbulent liquid mixing layer. J. Fluid Mech. 170, 83112.CrossRefGoogle Scholar
Kraichnan, R.H. 1962 Turbulent thermal convection at arbitrary Prandtl number. Phys. Fluids 5 (11), 13741389.CrossRefGoogle Scholar
Lohse, D. & Toschi, F. 2003 Ultimate state of thermal convection. Phys. Rev. Lett. 90 (3), 034502.CrossRefGoogle ScholarPubMed
Morgan, B.E., Schilling, O. & Hartland, T.A. 2018 Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing. Phys. Rev. E 97 (1), 013104.CrossRefGoogle ScholarPubMed
Nagata, K. & Komori, S. 2000 The effects of unstable stratification and mean shear on the chemical reaction in grid turbulence. J. Fluid Mech. 408, 3952.CrossRefGoogle Scholar
Obukhov, A.M. 1941 a On the distribution of energy in the spectrum of turbulent flow. Bull. Acad. Sci. USSR Geog. Geophys. 5, 453466.Google Scholar
Obukhov, A. 1941 b Spectral energy distribution in a turbulent flow. Izv. Akad. Nauk. SSSR. Ser. Geogr. i. Geofiz 5, 453466.Google Scholar
Obukhov, A.M. 1962 Some specific features of atmospheric turbulence. J. Geophys. Res. 67 (8), 30113014.CrossRefGoogle Scholar
Olson, B.J., Larsson, J., Lele, S.K. & Cook, A.W. 2011 Nonlinear effects in the combined Rayleigh–Taylor/Kelvin-Helmholtz instability. Phys. Fluids 23 (11), 114107.CrossRefGoogle Scholar
Pope, S.B. 2001 Turbulent Flows. Cambridge University Press.Google Scholar
Rogers, M.M. & Moser, R.D. 1994 Direct simulation of a self-similar turbulent mixing layer. Phys. Fluids 6 (2), 903923.CrossRefGoogle Scholar
Satyanarayana, P., Guzdar, P.N., Huba, J.D. & Ossakow, S.L. 1984 Rayleigh–Taylor instability in the presence of a stratified shear layer. J. Geophys. Res. 89 (A5), 29452954.CrossRefGoogle Scholar
Shumlak, U. & Roderick, N.F. 1998 Mitigation of the Rayleigh–Taylor instability by sheared axial flows. Phys. Plasmas 5 (6), 23842389.CrossRefGoogle Scholar
Snider, D.M. & Andrews, M.J. 1994 Rayleigh–Taylor and shear driven mixing with an unstable thermal stratification. Phys. Fluids 6 (10), 33243334.CrossRefGoogle Scholar
Turner, J.S. 1979 Buoyancy Effects in Fluids. Cambridge University Press.Google Scholar
Verstappen, R.W.C.P. & Veldman, A.E.P. 2003 Symmetry-preserving discretization of turbulent flow. J. Comput. Phys. 187 (1), 343368.CrossRefGoogle Scholar
Vladimirova, N. & Chertkov, M. 2009 Self-similarity and universality in Rayleigh–Taylor, Boussinesq turbulence. Phys. Fluids 21 (1), 015102.CrossRefGoogle Scholar
Waddell, J.T., Niederhaus, C.E. & Jacobs, J.W. 2001 Experimental study of Rayleigh–Taylor instability: low Atwood number liquid systems with single-mode initial perturbations. Phys. Fluids 13 (5), 12631273.CrossRefGoogle Scholar

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