Dynamics of unstably stratified free shear flows: an experimental investigation of coupled Kelvin–Helmholtz and Rayleigh–Taylor instability
Abstract
The dynamics of the coupled Kelvin–Helmholtz (KH) and Rayleigh–Taylor (RT) instability (referred to as KHRT instability or KHRTI) is studied using statistically steady experiments performed in a multi-layer gas tunnel. Experiments are performed at four density ratios ranging in Atwood number$$A_{t}$$from 0.035 to 0.159, with varying amounts of shear and$$\unicode[STIX]{x0394}U/U$$ranging from 0 to 0.48, where$$\unicode[STIX]{x0394}U$$is the speed difference between the two flow streams being investigated and$$U$$is the mean velocity of these two streams. Three types of diagnostics – back-lit visualization, hot-wire anemometry and particle image velocimetry (PIV) – are employed to obtain the mixing widths, velocity field and density field. The flow is found to be governed by KH dynamics at early times and RT dynamics at late times. This transition from KH-instability-like to RT-instability-like behaviour is quantified using the Richardson number. Transitional Richardson number magnitudes obtained for the present KHRT flows are found to be in the range 0.17–0.56 similar to the critical Richardson numbers for stably stratified free shear flows. Comparing the evolution of density and velocity mixing widths, the density mixing layer is found to be approximately two times as thick as the velocity mixing layer. Scaling of velocity fluctuations is attempted using combinations of KH andmore »
- Authors:
- Publication Date:
- Research Org.:
- Georgia Inst. of Technology, Atlanta, GA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1534392
- DOE Contract Number:
- NA0002575
- Resource Type:
- Journal Article
- Journal Name:
- Journal of Fluid Mechanics
- Additional Journal Information:
- Journal Volume: 816; Journal ID: ISSN 0022-1120
- Publisher:
- Cambridge University Press
- Country of Publication:
- United States
- Language:
- English
- Subject:
- Mechanics; Physics
Citation Formats
Akula, Bhanesh, Suchandra, Prasoon, Mikhaeil, Mark, and Ranjan, Devesh. Dynamics of unstably stratified free shear flows: an experimental investigation of coupled Kelvin–Helmholtz and Rayleigh–Taylor instability. United States: N. p., 2017.
Web. doi:10.1017/jfm.2017.95.
Akula, Bhanesh, Suchandra, Prasoon, Mikhaeil, Mark, & Ranjan, Devesh. Dynamics of unstably stratified free shear flows: an experimental investigation of coupled Kelvin–Helmholtz and Rayleigh–Taylor instability. United States. https://doi.org/10.1017/jfm.2017.95
Akula, Bhanesh, Suchandra, Prasoon, Mikhaeil, Mark, and Ranjan, Devesh. Wed .
"Dynamics of unstably stratified free shear flows: an experimental investigation of coupled Kelvin–Helmholtz and Rayleigh–Taylor instability". United States. https://doi.org/10.1017/jfm.2017.95.
@article{osti_1534392,
title = {Dynamics of unstably stratified free shear flows: an experimental investigation of coupled Kelvin–Helmholtz and Rayleigh–Taylor instability},
author = {Akula, Bhanesh and Suchandra, Prasoon and Mikhaeil, Mark and Ranjan, Devesh},
abstractNote = {The dynamics of the coupled Kelvin–Helmholtz (KH) and Rayleigh–Taylor (RT) instability (referred to as KHRT instability or KHRTI) is studied using statistically steady experiments performed in a multi-layer gas tunnel. Experiments are performed at four density ratios ranging in Atwood number$A_{t}$from 0.035 to 0.159, with varying amounts of shear and$\unicode[STIX]{x0394}U/U$ranging from 0 to 0.48, where$\unicode[STIX]{x0394}U$is the speed difference between the two flow streams being investigated and$U$is the mean velocity of these two streams. Three types of diagnostics – back-lit visualization, hot-wire anemometry and particle image velocimetry (PIV) – are employed to obtain the mixing widths, velocity field and density field. The flow is found to be governed by KH dynamics at early times and RT dynamics at late times. This transition from KH-instability-like to RT-instability-like behaviour is quantified using the Richardson number. Transitional Richardson number magnitudes obtained for the present KHRT flows are found to be in the range 0.17–0.56 similar to the critical Richardson numbers for stably stratified free shear flows. Comparing the evolution of density and velocity mixing widths, the density mixing layer is found to be approximately two times as thick as the velocity mixing layer. Scaling of velocity fluctuations is attempted using combinations of KH and RT scales. It is found that the proposed KHRT velocity scale, obtained using the combined mixing-layer growth equation, is appropriate for intermediate stages of the flow when both KH and RT dynamics are comparable. Probability density functions (p.d.f.s) for different fluctuating quantities are presented. Multiple peaks in p.d.f.s are qualitatively explained from the development of coherent KH roll-ups and their subsequent transition into turbulent pockets. The evolution of energy spectra indicates that density fluctuations start to show an inertial subrange from earlier times compared to velocity fluctuations. The spectra exhibit a slightly steeper slope than the Kolmogorov–Obukhov five-thirds law.},
doi = {10.1017/jfm.2017.95},
url = {https://www.osti.gov/biblio/1534392},
journal = {Journal of Fluid Mechanics},
issn = {0022-1120},
number = ,
volume = 816,
place = {United States},
year = {2017},
month = {3}
}
Works referenced in this record:
The Structure of Shear Driven Mixing With an Unstable Thermal Stratification
journal, March 1996
- Snider, D. M.; Andrews, M. J.
- Journal of Fluids Engineering, Vol. 118, Issue 1
The effects of unstable stratification and mean shear on the chemical reaction in grid turbulence
journal, April 2000
- Nagata, Kouji; Komori, Satoru
- Journal of Fluid Mechanics, Vol. 408
On the two-dimensional mixing region
journal, March 1976
- Champagne, F. H.; Pao, Y. H.; Wygnanski, I. J.
- Journal of Fluid Mechanics, Vol. 74, Issue 2
Reynolds number effects on Rayleigh–Taylor instability with possible implications for type Ia supernovae
journal, July 2006
- Cabot, William H.; Cook, Andrew W.
- Nature Physics, Vol. 2, Issue 8
A scaling analysis of turbulent flows driven by Rayleigh–Taylor and Richtmyer–Meshkov instabilities
journal, February 2001
- Zhou, Ye
- Physics of Fluids, Vol. 13, Issue 2
Laboratory observations of shear-layer instability in a stratified fluid
journal, April 1973
- Browand, F. K.; Winant, C. D.
- Boundary-Layer Meteorology, Vol. 5, Issue 1-2
Stratified shear turbulence: Evolution and statistics
journal, February 1999
- Werne, Joseph; Fritts, David C.
- Geophysical Research Letters, Vol. 26, Issue 4
On hot-wire diagnostics in Rayleigh–Taylor mixing layers
journal, March 2009
- Kraft, Wayne N.; Banerjee, Arindam; Andrews, Malcolm J.
- Experiments in Fluids, Vol. 47, Issue 1
Instability and turbulence in a stratified fluid with shear
journal, July 1979
- Koop, C. G.; Browand, F. K.
- Journal of Fluid Mechanics, Vol. 93, Issue 1
Persistence of a Kelvin-Helmholtz instability complex in the upper troposphere: KELVIN-HELMHOLTZ INSTABILITY IN THE TROPOSPHERE
journal, July 2005
- Kelley, M. C.; Chen, C. Y.; Beland, R. R.
- Journal of Geophysical Research: Atmospheres, Vol. 110, Issue D14
Comparing measures of sample skewness and kurtosis
journal, March 1998
- Joanes, D. N.; Gill, C. A.
- Journal of the Royal Statistical Society: Series D (The Statistician), Vol. 47, Issue 1
Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories
journal, February 2000
- Dimonte, Guy; Schneider, Marilyn
- Physics of Fluids, Vol. 12, Issue 2
Numerical simulation of turbulent mixing by Rayleigh-Taylor instability
journal, July 1984
- Youngs, David L.
- Physica D: Nonlinear Phenomena, Vol. 12, Issue 1-3
Experimental investigation of RayleighTaylor mixing at small Atwood numbers
journal, January 1999
- Ramaprabhu, P.; Andrews, M. J.
- Journal of Fluid Mechanics, Vol. 502
Nonlinear effects in the combined Rayleigh-Taylor/Kelvin-Helmholtz instability
journal, November 2011
- Olson, Britton J.; Larsson, Johan; Lele, Sanjiva K.
- Physics of Fluids, Vol. 23, Issue 11
Testing of a hot- and cold-wire probe to measure simultaneously the speed and temperature in supercritical CO2 flow
journal, July 2005
- Vukoslavčević, Petar V.; Radulović, Ivana M.; Wallace, James M.
- Experiments in Fluids, Vol. 39, Issue 4
Rayleigh-Taylor Turbulence is Nothing Like Kolmogorov Turbulence in the Self-Similar Regime
journal, November 2006
- Poujade, Olivier
- Physical Review Letters, Vol. 97, Issue 18
Development of a two-stream mixing layer from tripped and untripped boundary layers
journal, December 1990
- Bell, James H.; Mehta, Rabindra D.
- AIAA Journal, Vol. 28, Issue 12
A Viscosity Equation for Gas Mixtures
journal, April 1950
- Wilke, C. R.
- The Journal of Chemical Physics, Vol. 18, Issue 4
The Simulation of Mixing Layers Driven by Compound Buoyancy and Shear
journal, June 1996
- Snider, D. M.; Andrews, M. J.
- Journal of Fluids Engineering, Vol. 118, Issue 2
Scale-to-scale energy and enstrophy transport in two-dimensional Rayleigh–Taylor turbulence
journal, December 2015
- Zhou, Quan; Huang, Yong-Xiang; Lu, Zhi-Ming
- Journal of Fluid Mechanics, Vol. 786
Measuring Skewness and Kurtosis
journal, December 1984
- Groeneveld, Richard A.; Meeden, Glen
- The Statistician, Vol. 33, Issue 4
Inertial-confinement fusion with lasers
journal, May 2016
- Betti, R.; Hurricane, O. A.
- Nature Physics, Vol. 12, Issue 5
A method of producing a shear flow in a stratified fluid
journal, June 1968
- Thorpe, S. A.
- Journal of Fluid Mechanics, Vol. 32, Issue 4
Mitigation of the Rayleigh–Taylor instability by sheared axial flows
journal, June 1998
- Shumlak, U.; Roderick, N. F.
- Physics of Plasmas, Vol. 5, Issue 6
Turbulence reduction by screens
journal, December 1988
- Groth, Johan; Johansson, Arne V.
- Journal of Fluid Mechanics, Vol. 197
The two-dimensional mixing region
journal, April 1970
- Wygnanski, I.; Fiedler, H. E.
- Journal of Fluid Mechanics, Vol. 41, Issue 2
Simple model for the turbulent mixing width at an ablating surface
journal, February 1996
- Cherfils, Catherine; Mikaelian, Karnig O.
- Physics of Fluids, Vol. 8, Issue 2
The Critical Richardson Number and Its Implications for Forecast Problems
journal, April 1964
- Lyons, Richard; Panofsky, H. A.; Wollaston, Sarah
- Journal of Applied Meteorology, Vol. 3, Issue 2
An overview of Rayleigh-Taylor instability
journal, July 1984
- Sharp, D. H.
- Physica D: Nonlinear Phenomena, Vol. 12, Issue 1-3
Statistically steady measurements of Rayleigh-Taylor mixing in a gas channel
journal, March 2006
- Banerjee, Arindam; Andrews, Malcolm J.
- Physics of Fluids, Vol. 18, Issue 3
On fundamentals of Rayleigh-Taylor turbulent mixing
journal, August 2010
- Abarzhi, S. I.
- EPL (Europhysics Letters), Vol. 91, Issue 3
Small-Scale Properties of Turbulent Rayleigh-Bénard Convection
journal, January 2010
- Lohse, Detlef; Xia, Ke-Qing
- Annual Review of Fluid Mechanics, Vol. 42, Issue 1
A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number
journal, May 1962
- Kolmogorov, A. N.
- Journal of Fluid Mechanics, Vol. 13, Issue 1
Turbulent spectra in a stably stratified atmosphere
journal, December 1959
- Bolgiano, R.
- Journal of Geophysical Research, Vol. 64, Issue 12
Computation of the Energy Spectrum in Homogeneous Two-Dimensional Turbulence
journal, January 1969
- Batchelor, G. K.
- Physics of Fluids, Vol. 12, Issue 12
Transition stages of Rayleigh–Taylor instability between miscible fluids
journal, September 2001
- Cook, Andrew W.; Dimotakis, Paul E.
- Journal of Fluid Mechanics, Vol. 443
Study of hydrodynamic instabilities with a multiphase lattice Boltzmann model
journal, October 2015
- Velasco, Ali Mauricio; Muñoz, José Daniel
- Comptes Rendus Mécanique, Vol. 343, Issue 10-11
Detailed measurements of a statistically steady Rayleigh–Taylor mixing layer from small to high Atwood numbers
journal, August 2010
- Banerjee, Arindam; Kraft, Wayne N.; Andrews, Malcolm J.
- Journal of Fluid Mechanics, Vol. 659
The Spectrum of Turbulence
journal, February 1938
- Taylor, G. I.
- Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, Vol. 164, Issue 919
Effect of the Prandtl number on a stratified turbulent wake
journal, September 2010
- de Stadler, Matthew B.; Sarkar, Sutanu; Brucker, Kyle A.
- Physics of Fluids, Vol. 22, Issue 9
The Kelvin-Helmholtz instability in National Ignition Facility hohlraums as a source of gold-gas mixing
journal, May 2016
- Vandenboomgaerde, M.; Bonnefille, M.; Gauthier, P.
- Physics of Plasmas, Vol. 23, Issue 5
Turbulence in stably stratified fluids: A review of laboratory experiments
journal, April 1973
- Thorpe, S. A.
- Boundary-Layer Meteorology, Vol. 5, Issue 1-2
Experiments on the instability of stratified shear flows: miscible fluids
journal, March 1971
- Thorpe, S. A.
- Journal of Fluid Mechanics, Vol. 46, Issue 2
Rayleigh–Taylor turbulence: self-similar analysis and direct numerical simulations
journal, May 2004
- Ristorcelli, J. R.; Clark, T. T.
- Journal of Fluid Mechanics, Vol. 507
Dynamics of buoyancy-driven flows at moderately high Atwood numbers
journal, April 2016
- Akula, Bhanesh; Ranjan, Devesh
- Journal of Fluid Mechanics, Vol. 795
The mixing transition in RayleighTaylor instability
journal, January 1999
- Cook, Andrew W.; Cabot, William; Miller, Paul L.
- Journal of Fluid Mechanics, Vol. 511
The structure of isotropic turbulence at very high Reynolds numbers
journal, May 1959
- Kraichnan, Robert H.
- Journal of Fluid Mechanics, Vol. 5, Issue 04
Vortex pairing : the mechanism of turbulent mixing-layer growth at moderate Reynolds number
journal, April 1974
- Winant, C. D.; Browand, F. K.
- Journal of Fluid Mechanics, Vol. 63, Issue 02
Simultaneous Measurements of Velocity and Temperature in Nonisothermal Flows
journal, May 1978
- Hishida, M.; Nagano, Y.
- Journal of Heat Transfer, Vol. 100, Issue 2
Rayleigh–Taylor and shear driven mixing with an unstable thermal stratification
journal, October 1994
- Snider, Dale M.; Andrews, Malcolm J.
- Physics of Fluids, Vol. 6, Issue 10
On density effects and large structure in turbulent mixing layers
journal, July 1974
- Brown, Garry L.; Roshko, Anatol
- Journal of Fluid Mechanics, Vol. 64, Issue 4
Incompressible Rayleigh–Taylor Turbulence
journal, January 2017
- Boffetta, Guido; Mazzino, Andrea
- Annual Review of Fluid Mechanics, Vol. 49, Issue 1
Experimental characterization of initial conditions and spatio-temporal evolution of a small-Atwood-number Rayleigh–Taylor mixing layer
journal, October 2006
- Mueschke, Nicholas J.; Andrews, Malcolm J.; Schilling, Oleg
- Journal of Fluid Mechanics, Vol. 567
Experiments on instability and turbulence in a stratified shear flow
journal, December 1973
- Thorpe, S. A.
- Journal of Fluid Mechanics, Vol. 61, Issue 4
Effect of Variation in Density on the Stability of Superposed Streams of Fluid
journal, August 1931
- Taylor, G. I.
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 132, Issue 820
Some specific features of atmospheric turbulence
journal, July 1962
- Obukhov, A. M.
- Journal of Geophysical Research, Vol. 67, Issue 8
The stability of a sheared density interface
journal, October 1991
- Lawrence, G. A.; Browand, F. K.; Redekopp, L. G.
- Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 10