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Title: 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 1024 3 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.

Authors:
; ORCiD logo
Publication Date:
Research Org.:
Univ. of Rochester, NY (United States). Lab. for Laser Energetics
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24); USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1514738
Alternate Identifier(s):
OSTI ID: 1531342
Grant/Contract Number:  
SC0014318; SC0019329; NA0003856
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 AG
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. doi:10.3390/fluids4020092.
Lees, Aarne, and Aluie, Hussein. Sat . "Baropycnal Work: A Mechanism for Energy Transfer across Scales". Switzerland. doi: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 1024 3 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}
}

Journal Article:
Free Publicly Available Full Text
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DOI: 10.3390/fluids4020092

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Works referenced in this record:

Multi-scale gradient expansion of the turbulent stress tensor
journal, February 2006


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
  • DOI: 10.1007/s00220-017-3078-4

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
  • DOI: 10.1063/1.3266883

Imprint of Large-Scale Flows on Turbulence
journal, December 2005


Further space-time correlations of velocity in a turbulent boundary layer
journal, January 1958


Energy transfer in compressible magnetohydrodynamic turbulence
journal, September 2017

  • Grete, Philipp; O'Shea, Brian W.; Beckwith, Kris
  • Physics of Plasmas, Vol. 24, Issue 9
  • DOI: 10.1063/1.4990613

Exact Results on Scaling Exponents in the 2D Enstrophy Cascade
journal, May 1995


Energy and Enstrophy Transfer in Decaying Two-Dimensional Turbulence
journal, March 2003


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
  • DOI: 10.1063/1.857956

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
  • DOI: 10.1063/1.3657086

Cascades and Dissipative Anomalies in Compressible Fluid Turbulence
journal, February 2018


Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements
journal, April 2002


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
  • DOI: 10.1063/1.4819351

Cascades and transitions in turbulent flows
journal, November 2018


Scale Locality of Magnetohydrodynamic Turbulence
journal, February 2010


High-Reynolds number Rayleigh–Taylor turbulence
journal, January 2009


Statistics of turbulence subgrid‐scale stresses: Necessary conditions and experimental tests
journal, February 1994


Supersonic Combustion in Air-Breathing Propulsion Systems for Hypersonic Flight
journal, January 2018


Compressible Turbulence: The Cascade and its Locality
journal, April 2011


Satellite Observations of Imprint of Oceanic Current on Wind Stress by Air-Sea Coupling
journal, December 2017


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
  • DOI: 10.1017/jfm.2015.754

Large-scale flow effects, energy transfer, and self-similarity on turbulence
journal, July 2006


Scale decomposition in compressible turbulence
journal, March 2013


Comparing the statistics of interstellar turbulence in simulations and observations: Solenoidal versus compressive turbulence forcing
journal, March 2010


Conservative Cascade of Kinetic Energy in Compressible Turbulence
journal, May 2012


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
  • DOI: 10.1086/595280

Dissipative anomalies in singular Euler flows
journal, August 2008


An Air-Sea Interaction Theory for Tropical Cyclones. Part I: Steady-State Maintenance
journal, March 1986


Self-Similar Multimode Bubble-Front Evolution of the Ablative Rayleigh-Taylor Instability in Two and Three Dimensions
journal, October 2018


A hybrid numerical simulation of isotropic compressible turbulence
journal, July 2010


Joint downscale fluxes of energy and potential enstrophy in rotating stratified Boussinesq flows
journal, November 2011


The Statistics of Supersonic Isothermal Turbulence
journal, August 2007

  • Kritsuk, Alexei G.; Norman, Michael L.; Padoan, Paolo
  • The Astrophysical Journal, Vol. 665, Issue 1
  • DOI: 10.1086/519443

Supernova Driving. ii. Compressive Ratio in Molecular-Cloud Turbulence
journal, June 2016


Inviscid criterion for decomposing scales
journal, May 2018


The pirouette effect in turbulent flows
journal, June 2011

  • Xu, Haitao; Pumir, Alain; Bodenschatz, Eberhard
  • Nature Physics, Vol. 7, Issue 9
  • DOI: 10.1038/nphys2010

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
  • DOI: 10.1063/1.4873579

Scale-Invariance and Turbulence Models for Large-Eddy Simulation
journal, January 2000


Locality of turbulent cascades
journal, July 2005


Equilibrium statistical mechanics of compressible isotropic turbulence
journal, June 1997


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
  • DOI: 10.1017/jfm.2014.62

The analysis and modelling of dilatational terms in compressible turbulence
journal, June 1991


An overview of Rayleigh-Taylor instability
journal, July 1984


Long-range ordering of turbulent stresses in two-dimensional flow
journal, June 2015


Realizability conditions for the turbulent stress tensor in large-eddy simulation
journal, November 1994


Air entrainment and bubble statistics in breaking waves
journal, July 2016

  • Deike, Luc; Melville, W. Kendall; Popinet, Stéphane
  • Journal of Fluid Mechanics, Vol. 801
  • DOI: 10.1017/jfm.2016.372

On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet
journal, September 1994


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


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
  • DOI: 10.1063/1.3266948

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
  • DOI: 10.1175/JPO-D-17-0100.1

Energy transfer in Rayleigh-Taylor instability
journal, August 2002


Advection and the Efficiency of Spectral Energy Transfer in Two-Dimensional Turbulence
journal, August 2016


On the role of anisotropic turbomachinery flow structures in inter-scale turbulence energy flux as deduced from SPIV measurements
journal, November 2013


Influence of orientation on the evolution of small perturbations in compressible shear layers with inflection points
journal, March 2017


Energy transfer in turbulence under rotation
journal, March 2018


Nonlinear excitation of the ablative Rayleigh-Taylor instability for all wave numbers
journal, January 2018


Coarse-grained incompressible magnetohydrodynamics: analyzing the turbulent cascades
journal, February 2017


Energy and spectral dynamics in forced compressible turbulence
journal, June 1990

  • Kida, Shigeo; Orszag, Steven A.
  • Journal of Scientific Computing, Vol. 5, Issue 2
  • DOI: 10.1007/BF01065580

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
  • DOI: 10.1063/1.1990206

Cascade of Kinetic Energy in Three-Dimensional Compressible Turbulence
journal, May 2013


Turbulence: the filtering approach
journal, May 1992


Local energy flux and subgrid-scale statistics in three-dimensional turbulence
journal, July 1998


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
  • DOI: 10.1063/1.4940917

Forcing for statistically stationary compressible isotropic turbulence
journal, November 2010

  • Petersen, Mark R.; Livescu, Daniel
  • Physics of Fluids, Vol. 22, Issue 11
  • DOI: 10.1063/1.3488793

Local energy flux and the refined similarity hypothesis
journal, January 1995

  • Eyink, Gregory L.
  • Journal of Statistical Physics, Vol. 78, Issue 1-2
  • DOI: 10.1007/BF02183352

An examination of forcing in direct numerical simulations of turbulence
journal, January 1988


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
  • DOI: 10.1063/1.2001689

Scale interactions of turbulence subjected to a straining–relaxation–destraining cycle
journal, August 2006


Compressibility Effects on Turbulence
journal, January 1994


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
  • DOI: 10.1017/jfm.2013.342

Physical Mechanism of the Two-Dimensional Enstrophy Cascade
journal, November 2003


Simulating liquid droplets: A quantitative assessment of lattice Boltzmann and Volume of Fluid methods
journal, April 2018


Extracting the spectrum of a flow by spatial filtering
journal, December 2018


Cascade of circulations in fluid turbulence
journal, December 2006