Baropycnal Work: A Mechanism for Energy Transfer across Scales
Abstract
The role of baroclinicity, which arises from the misalignment of pressure and density gradients, is well-known in the vorticity equation, yet its role in the kinetic energy budget has never been obvious. Here, we show that baroclinicity appears naturally in the kinetic energy budget after carrying out the appropriate scale decomposition. Strain generation by pressure and density gradients, both barotropic and baroclinic, also results from our analysis. These two processes underlie the recently identified mechanism of “baropycnal work”, which can transfer energy across scales in variable density flows. As such, baropycnal work is markedly distinct from pressure-dilatation into which the former is implicitly lumped in Large Eddy Simulations. We provide numerical evidence from 10243 direct numerical simulations of compressible turbulence. The data shows excellent pointwise agreement between baropycnal work and the nonlinear model we derive, supporting our interpretation of how it operates.
- Publication Date:
- Research Org.:
- Univ. of Rochester, NY (United States). Lab. for Laser Energetics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES); USDOE National Nuclear Security Administration (NNSA); National Aeronautics and Space Administration (NASA)
- OSTI Identifier:
- 1514738
- Alternate Identifier(s):
- OSTI ID: 1531342; OSTI ID: 1658632
- Grant/Contract Number:
- SC0014318; SC0019329; NA0003856; AC02-05CH11231; 80NSSC18K0772
- Resource Type:
- Published Article
- Journal Name:
- Fluids
- Additional Journal Information:
- Journal Name: Fluids Journal Volume: 4 Journal Issue: 2; Journal ID: ISSN 2311-5521
- Publisher:
- MDPI
- Country of Publication:
- Switzerland
- Language:
- English
- Subject:
- 42 ENGINEERING; multiscale; energy transfer; cascade; turbulence; variable density flow; baroclinic vortex generation
Citation Formats
Lees, Aarne, and Aluie, Hussein. Baropycnal Work: A Mechanism for Energy Transfer across Scales. Switzerland: N. p., 2019.
Web. doi:10.3390/fluids4020092.
Lees, Aarne, & Aluie, Hussein. Baropycnal Work: A Mechanism for Energy Transfer across Scales. Switzerland. https://doi.org/10.3390/fluids4020092
Lees, Aarne, and Aluie, Hussein. Sat .
"Baropycnal Work: A Mechanism for Energy Transfer across Scales". Switzerland. https://doi.org/10.3390/fluids4020092.
@article{osti_1514738,
title = {Baropycnal Work: A Mechanism for Energy Transfer across Scales},
author = {Lees, Aarne and Aluie, Hussein},
abstractNote = {The role of baroclinicity, which arises from the misalignment of pressure and density gradients, is well-known in the vorticity equation, yet its role in the kinetic energy budget has never been obvious. Here, we show that baroclinicity appears naturally in the kinetic energy budget after carrying out the appropriate scale decomposition. Strain generation by pressure and density gradients, both barotropic and baroclinic, also results from our analysis. These two processes underlie the recently identified mechanism of “baropycnal work”, which can transfer energy across scales in variable density flows. As such, baropycnal work is markedly distinct from pressure-dilatation into which the former is implicitly lumped in Large Eddy Simulations. We provide numerical evidence from 10243 direct numerical simulations of compressible turbulence. The data shows excellent pointwise agreement between baropycnal work and the nonlinear model we derive, supporting our interpretation of how it operates.},
doi = {10.3390/fluids4020092},
journal = {Fluids},
number = 2,
volume = 4,
place = {Switzerland},
year = {2019},
month = {5}
}
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.3390/fluids4020092
https://doi.org/10.3390/fluids4020092
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Multi-scale gradient expansion of the turbulent stress tensor
journal, February 2006
- Eyink, Gregory L.
- Journal of Fluid Mechanics, Vol. 549, Issue -1
An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations
journal, December 2017
- Drivas, Theodore D.; Eyink, Gregory L.
- Communications in Mathematical Physics, Vol. 359, Issue 2
Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining
journal, November 2009
- Eyink, Gregory L.; Aluie, Hussein
- Physics of Fluids, Vol. 21, Issue 11
Imprint of Large-Scale Flows on Turbulence
journal, December 2005
- Alexakis, A.; Mininni, P. D.; Pouquet, A.
- Physical Review Letters, Vol. 95, Issue 26
Further space-time correlations of velocity in a turbulent boundary layer
journal, January 1958
- Favre, A. J.; Gaviglio, J. J.; Dumas, R. J.
- Journal of Fluid Mechanics, Vol. 3, Issue 4
Energy transfer in compressible magnetohydrodynamic turbulence
journal, September 2017
- Grete, Philipp; O'Shea, Brian W.; Beckwith, Kris
- Physics of Plasmas, Vol. 24, Issue 9
Exact Results on Scaling Exponents in the 2D Enstrophy Cascade
journal, May 1995
- Eyink, Gregory L.
- Physical Review Letters, Vol. 74, Issue 19
Energy and Enstrophy Transfer in Decaying Two-Dimensional Turbulence
journal, March 2003
- Rivera, M. K.; Daniel, W. B.; Chen, S. Y.
- Physical Review Letters, Vol. 90, Issue 10
Subgrid‐scale backscatter in turbulent and transitional flows
journal, July 1991
- Piomelli, Ugo; Cabot, William H.; Moin, Parviz
- Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 7
Spatiotemporal persistence of spectral fluxes in two-dimensional weak turbulence
journal, November 2011
- Kelley, Douglas H.; Ouellette, Nicholas T.
- Physics of Fluids, Vol. 23, Issue 11
Cascades and Dissipative Anomalies in Compressible Fluid Turbulence
journal, February 2018
- Eyink, Gregory L.; Drivas, Theodore D.
- Physical Review X, Vol. 8, Issue 1
Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements
journal, April 2002
- Tao, Bo; Katz, Joseph; Meneveau, Charles
- Journal of Fluid Mechanics, Vol. 457
Experimental study of spectral energy fluxes in turbulence generated by a fractal, tree-like object
journal, November 2013
- Bai, Kunlun; Meneveau, Charles; Katz, Joseph
- Physics of Fluids, Vol. 25, Issue 11
Cascades and transitions in turbulent flows
journal, November 2018
- Alexakis, A.; Biferale, L.
- Physics Reports, Vol. 767-769
Scale Locality of Magnetohydrodynamic Turbulence
journal, February 2010
- Aluie, Hussein; Eyink, Gregory L.
- Physical Review Letters, Vol. 104, Issue 8
High-Reynolds number Rayleigh–Taylor turbulence
journal, January 2009
- Livescu, D.; Ristorcelli, J. R.; Gore, R. A.
- Journal of Turbulence, Vol. 10
Statistics of turbulence subgrid‐scale stresses: Necessary conditions and experimental tests
journal, February 1994
- Meneveau, Charles
- Physics of Fluids, Vol. 6, Issue 2
Supersonic Combustion in Air-Breathing Propulsion Systems for Hypersonic Flight
journal, January 2018
- Urzay, Javier
- Annual Review of Fluid Mechanics, Vol. 50, Issue 1
Compressible Turbulence: The Cascade and its Locality
journal, April 2011
- Aluie, Hussein
- Physical Review Letters, Vol. 106, Issue 17
Satellite Observations of Imprint of Oceanic Current on Wind Stress by Air-Sea Coupling
journal, December 2017
- Renault, Lionel; McWilliams, James C.; Masson, Sebastien
- Scientific Reports, Vol. 7, Issue 1
Reynolds and Mach number scaling in solenoidally-forced compressible turbulence using high-resolution direct numerical simulations
journal, January 2016
- Jagannathan, Shriram; Donzis, Diego A.
- Journal of Fluid Mechanics, Vol. 789
Large-scale flow effects, energy transfer, and self-similarity on turbulence
journal, July 2006
- Mininni, P. D.; Alexakis, A.; Pouquet, A.
- Physical Review E, Vol. 74, Issue 1
Study of ultrahigh Atwood-number Rayleigh–Taylor mixing dynamics using the nonlinear large-eddy simulation method
journal, April 2011
- Burton, Gregory C.
- Physics of Fluids, Vol. 23, Issue 4
Scale decomposition in compressible turbulence
journal, March 2013
- Aluie, Hussein
- Physica D: Nonlinear Phenomena, Vol. 247, Issue 1
Comparing the statistics of interstellar turbulence in simulations and observations: Solenoidal versus compressive turbulence forcing
journal, March 2010
- Federrath, C.; Roman-Duval, J.; Klessen, R. S.
- Astronomy and Astrophysics, Vol. 512
Conservative Cascade of Kinetic Energy in Compressible Turbulence
journal, May 2012
- Aluie, Hussein; Li, Shengtai; Li, Hui
- The Astrophysical Journal, Vol. 751, Issue 2
The Density Probability Distribution in Compressible Isothermal Turbulence: Solenoidal versus Compressive Forcing
journal, October 2008
- Federrath, Christoph; Klessen, Ralf S.; Schmidt, Wolfram
- The Astrophysical Journal, Vol. 688, Issue 2
Dissipative anomalies in singular Euler flows
journal, August 2008
- Eyink, Gregory L.
- Physica D: Nonlinear Phenomena, Vol. 237, Issue 14-17
An Air-Sea Interaction Theory for Tropical Cyclones. Part I: Steady-State Maintenance
journal, March 1986
- Emanuel, Kerry A.
- Journal of the Atmospheric Sciences, Vol. 43, Issue 6
Self-Similar Multimode Bubble-Front Evolution of the Ablative Rayleigh-Taylor Instability in Two and Three Dimensions
journal, October 2018
- Zhang, H.; Betti, R.; Yan, R.
- Physical Review Letters, Vol. 121, Issue 18
A hybrid numerical simulation of isotropic compressible turbulence
journal, July 2010
- Wang, J.; Wang, L. -P.; Xiao, Z.
- Journal of Computational Physics, Vol. 229, Issue 13
Joint downscale fluxes of energy and potential enstrophy in rotating stratified Boussinesq flows
journal, November 2011
- Aluie, H.; Kurien, S.
- EPL (Europhysics Letters), Vol. 96, Issue 4
The Statistics of Supersonic Isothermal Turbulence
journal, August 2007
- Kritsuk, Alexei G.; Norman, Michael L.; Padoan, Paolo
- The Astrophysical Journal, Vol. 665, Issue 1
Supernova Driving. ii. Compressive Ratio in Molecular-Cloud Turbulence
journal, June 2016
- Pan, Liubin; Padoan, Paolo; Haugbølle, Troels
- The Astrophysical Journal, Vol. 825, Issue 1
Inviscid criterion for decomposing scales
journal, May 2018
- Zhao, Dongxiao; Aluie, Hussein
- Physical Review Fluids, Vol. 3, Issue 5
The pirouette effect in turbulent flows
journal, June 2011
- Xu, Haitao; Pumir, Alain; Bodenschatz, Eberhard
- Nature Physics, Vol. 7, Issue 9
The direct enstrophy cascade of two-dimensional soap film flows
journal, May 2014
- Rivera, M. K.; Aluie, H.; Ecke, R. E.
- Physics of Fluids, Vol. 26, Issue 5
Scale-Invariance and Turbulence Models for Large-Eddy Simulation
journal, January 2000
- Meneveau, Charles; Katz, Joseph
- Annual Review of Fluid Mechanics, Vol. 32, Issue 1
Locality of turbulent cascades
journal, July 2005
- Eyink, Gregory L.
- Physica D: Nonlinear Phenomena, Vol. 207, Issue 1-2
Equilibrium statistical mechanics of compressible isotropic turbulence
journal, June 1997
- Shivamoggi, B. K.
- Europhysics Letters (EPL), Vol. 38, Issue 9
Subgrid-scale backscatter in reacting and inert supersonic hydrogen–air turbulent mixing layers
journal, March 2014
- O’Brien, J.; Urzay, J.; Ihme, M.
- Journal of Fluid Mechanics, Vol. 743
The analysis and modelling of dilatational terms in compressible turbulence
journal, June 1991
- Sarkar, S.; Erlebacher, G.; Hussaini, M. Y.
- Journal of Fluid Mechanics, Vol. 227
An overview of Rayleigh-Taylor instability
journal, July 1984
- Sharp, D. H.
- Physica D: Nonlinear Phenomena, Vol. 12, Issue 1-3
Long-range ordering of turbulent stresses in two-dimensional flow
journal, June 2015
- Liao, Yang; Ouellette, Nicholas T.
- Physical Review E, Vol. 91, Issue 6
Realizability conditions for the turbulent stress tensor in large-eddy simulation
journal, November 1994
- Vreman, Bert; Geurts, Bernard; Kuerten, Hans
- Journal of Fluid Mechanics, Vol. 278
Air entrainment and bubble statistics in breaking waves
journal, July 2016
- Deike, Luc; Melville, W. Kendall; Popinet, Stéphane
- Journal of Fluid Mechanics, Vol. 801
On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet
journal, September 1994
- Liu, Shewen; Meneveau, Charles; Katz, Joseph
- Journal of Fluid Mechanics, Vol. 275
Incipient thermal choking and stable shock-train formation in the heat-release region of a scramjet combustor. Part II: Large eddy simulations
journal, April 2015
- Larsson, Johan; Laurence, Stuart; Bermejo-Moreno, Iván
- Combustion and Flame, Vol. 162, Issue 4
Localness of energy cascade in hydrodynamic turbulence. II. Sharp spectral filter
journal, November 2009
- Aluie, Hussein; Eyink, Gregory L.
- Physics of Fluids, Vol. 21, Issue 11
Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-Graining Approach
journal, February 2018
- Aluie, Hussein; Hecht, Matthew; Vallis, Geoffrey K.
- Journal of Physical Oceanography, Vol. 48, Issue 2
Energy transfer in Rayleigh-Taylor instability
journal, August 2002
- Cook, Andrew W.; Zhou, Ye
- Physical Review E, Vol. 66, Issue 2
Advection and the Efficiency of Spectral Energy Transfer in Two-Dimensional Turbulence
journal, August 2016
- Fang, Lei; Ouellette, Nicholas T.
- Physical Review Letters, Vol. 117, Issue 10
On the role of anisotropic turbomachinery flow structures in inter-scale turbulence energy flux as deduced from SPIV measurements
journal, November 2013
- Akbari, Ghasem; Montazerin, Nader
- Journal of Turbulence, Vol. 14, Issue 11
Influence of orientation on the evolution of small perturbations in compressible shear layers with inflection points
journal, March 2017
- Karimi, Mona; Girimaji, Sharath S.
- Physical Review E, Vol. 95, Issue 3
Energy transfer in turbulence under rotation
journal, March 2018
- Buzzicotti, Michele; Aluie, Hussein; Biferale, Luca
- Physical Review Fluids, Vol. 3, Issue 3
Nonlinear excitation of the ablative Rayleigh-Taylor instability for all wave numbers
journal, January 2018
- Zhang, H.; Betti, R.; Gopalaswamy, V.
- Physical Review E, Vol. 97, Issue 1
Coarse-grained incompressible magnetohydrodynamics: analyzing the turbulent cascades
journal, February 2017
- Aluie, Hussein
- New Journal of Physics, Vol. 19, Issue 2
Energy and spectral dynamics in forced compressible turbulence
journal, June 1990
- Kida, Shigeo; Orszag, Steven A.
- Journal of Scientific Computing, Vol. 5, Issue 2
Effect of filter type on the statistics of energy transfer between resolved and subfilter scales from a-priori analysis of direct numerical simulations of isotropic turbulence
journal, November 2017
- Buzzicotti, M.; Linkmann, M.; Aluie, H.
- Journal of Turbulence, Vol. 19, Issue 2
Decomposition of the spatially filtered and ensemble averaged kinetic energy, the associated fluxes and scaling trends in a rotor wake
journal, August 2005
- Chow, Yi-Chih; Uzol, Oguz; Katz, Joseph
- Physics of Fluids, Vol. 17, Issue 8
Cascade of Kinetic Energy in Three-Dimensional Compressible Turbulence
journal, May 2013
- Wang, Jianchun; Yang, Yantao; Shi, Yipeng
- Physical Review Letters, Vol. 110, Issue 21
Turbulence: the filtering approach
journal, May 1992
- Germano, M.
- Journal of Fluid Mechanics, Vol. 238
Local energy flux and subgrid-scale statistics in three-dimensional turbulence
journal, July 1998
- Borue, Vadim; Orszag, Steven A.
- Journal of Fluid Mechanics, Vol. 366
Three-dimensional single-mode nonlinear ablative Rayleigh-Taylor instability
journal, February 2016
- Yan, R.; Betti, R.; Sanz, J.
- Physics of Plasmas, Vol. 23, Issue 2
Forcing for statistically stationary compressible isotropic turbulence
journal, November 2010
- Petersen, Mark R.; Livescu, Daniel
- Physics of Fluids, Vol. 22, Issue 11
Local energy flux and the refined similarity hypothesis
journal, January 1995
- Eyink, Gregory L.
- Journal of Statistical Physics, Vol. 78, Issue 1-2
An examination of forcing in direct numerical simulations of turbulence
journal, January 1988
- Eswaran, V.; Pope, S. B.
- Computers & Fluids, Vol. 16, Issue 3
On using large-eddy simulation for the prediction of noise from cold and heated turbulent jets
journal, August 2005
- Bodony, Daniel J.; Lele, Sanjiva K.
- Physics of Fluids, Vol. 17, Issue 8
Scale interactions of turbulence subjected to a straining–relaxation–destraining cycle
journal, August 2006
- Chen, Jun; Meneveau, Charles; Katz, Joseph
- Journal of Fluid Mechanics, Vol. 562
Compressibility Effects on Turbulence
journal, January 1994
- Lele, Sanjiva K.
- Annual Review of Fluid Mechanics, Vol. 26, Issue 1
Energy cascade and scaling in supersonic isothermal turbulence
journal, July 2013
- Kritsuk, Alexei G.; Wagner, Rick; Norman, Michael L.
- Journal of Fluid Mechanics, Vol. 729
Physical Mechanism of the Two-Dimensional Enstrophy Cascade
journal, November 2003
- Chen, Shiyi; Ecke, Robert E.; Eyink, Gregory L.
- Physical Review Letters, Vol. 91, Issue 21
Simulating liquid droplets: A quantitative assessment of lattice Boltzmann and Volume of Fluid methods
journal, April 2018
- Mukherjee, Siddhartha; Zarghami, Ahad; Haringa, Cees
- International Journal of Heat and Fluid Flow, Vol. 70
Extracting the spectrum of a flow by spatial filtering
journal, December 2018
- Sadek, Mahmoud; Aluie, Hussein
- Physical Review Fluids, Vol. 3, Issue 12
Cascade of circulations in fluid turbulence
journal, December 2006
- Eyink, Gregory L.
- Physical Review E, Vol. 74, Issue 6
Works referencing / citing this record:
Editorial for Special Issue “Multiscale Turbulent Transport”
journal, October 2019
- Martins Afonso, Marco; Gama, Sílvio M. A.
- Fluids, Vol. 4, Issue 4