Large-scale anisotropy in stably stratified rotating flows
Abstract
We present results from direct numerical simulations of the Boussinesq equations in the presence of rotation and/or stratification, both in the vertical direction. The runs are forced isotropically and randomly at small scales and have spatial resolutions of up to $1024^3$ grid points and Reynolds numbers of $$\approx 1000$$. We first show that solutions with negative energy flux and inverse cascades develop in rotating turbulence, whether or not stratification is present. However, the purely stratified case is characterized instead by an early-time, highly anisotropic transfer to large scales with almost zero net isotropic energy flux. This is consistent with previous studies that observed the development of vertically sheared horizontal winds, although only at substantially later times. However, and unlike previous works, when sufficient scale separation is allowed between the forcing scale and the domain size, the total energy displays a perpendicular (horizontal) spectrum with power law behavior compatible with $$\sim k_\perp^{-5/3}$$, including in the absence of rotation. In this latter purely stratified case, such a spectrum is the result of a direct cascade of the energy contained in the large-scale horizontal wind, as is evidenced by a strong positive flux of energy in the parallel direction at all scales including the largest resolved scales.
- Authors:
-
- National Center for Atmospheric Research, Boulder, CO (United States); Inst. for Chemical-Physical Processes, Rende (Italy); Univ. of California, Berkeley, CA (United States). Space Sciences Lab.
- Univ. of Buenos Aires (Argentina)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). National Center for Computational Sciences,
- Univ. of Colorado, Boulder, CO (United States). Laboratory for Atmospheric and Space Physics
- Publication Date:
- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1159997
- Grant/Contract Number:
- AC05-00OR22725; 20020110200359
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
- Additional Journal Information:
- Journal Volume: 90; Journal Issue: 2; Journal ID: ISSN 1539-3755
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 17 WIND ENERGY
Citation Formats
Marino, R., Mininni, P. D., Rosenberg, D. L., and Pouquet, A. Large-scale anisotropy in stably stratified rotating flows. United States: N. p., 2014.
Web. doi:10.1103/PhysRevE.90.023018.
Marino, R., Mininni, P. D., Rosenberg, D. L., & Pouquet, A. Large-scale anisotropy in stably stratified rotating flows. United States. https://doi.org/10.1103/PhysRevE.90.023018
Marino, R., Mininni, P. D., Rosenberg, D. L., and Pouquet, A. Thu .
"Large-scale anisotropy in stably stratified rotating flows". United States. https://doi.org/10.1103/PhysRevE.90.023018. https://www.osti.gov/servlets/purl/1159997.
@article{osti_1159997,
title = {Large-scale anisotropy in stably stratified rotating flows},
author = {Marino, R. and Mininni, P. D. and Rosenberg, D. L. and Pouquet, A.},
abstractNote = {We present results from direct numerical simulations of the Boussinesq equations in the presence of rotation and/or stratification, both in the vertical direction. The runs are forced isotropically and randomly at small scales and have spatial resolutions of up to $1024^3$ grid points and Reynolds numbers of $\approx 1000$. We first show that solutions with negative energy flux and inverse cascades develop in rotating turbulence, whether or not stratification is present. However, the purely stratified case is characterized instead by an early-time, highly anisotropic transfer to large scales with almost zero net isotropic energy flux. This is consistent with previous studies that observed the development of vertically sheared horizontal winds, although only at substantially later times. However, and unlike previous works, when sufficient scale separation is allowed between the forcing scale and the domain size, the total energy displays a perpendicular (horizontal) spectrum with power law behavior compatible with $\sim k_\perp^{-5/3}$, including in the absence of rotation. In this latter purely stratified case, such a spectrum is the result of a direct cascade of the energy contained in the large-scale horizontal wind, as is evidenced by a strong positive flux of energy in the parallel direction at all scales including the largest resolved scales.},
doi = {10.1103/PhysRevE.90.023018},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics},
number = 2,
volume = 90,
place = {United States},
year = {Thu Aug 28 00:00:00 EDT 2014},
month = {Thu Aug 28 00:00:00 EDT 2014}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 37 works
Citation information provided by
Web of Science
Web of Science
Figures / Tables:
TABLE I: Parameters used in the simulations: np is the linear grid resolution, kF the forcing wavenumber, Ro the Rossby number, Fr the Froude number, kZ the Zeman scale, and kO the Ozmidov scale (see text for definitions). The Reynolds number in all the runs is ≈ 1000.
All figures and tables
(8 total)
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:
Forced stratified turbulence: Successive transitions with Reynolds number
journal, September 2003
- Laval, J. -P.; McWilliams, J. C.; Dubrulle, B.
- Physical Review E, Vol. 68, Issue 3
Scale-Dependent Models for Atmospheric Flows
journal, January 2010
- Klein, Rupert
- Annual Review of Fluid Mechanics, Vol. 42, Issue 1
Geophysical Turbulence and the Duality of the Energy Flow Across Scales
journal, December 2013
- Pouquet, A.; Marino, R.
- Physical Review Letters, Vol. 111, Issue 23
Turbulence and diapycnal mixing over the East Pacific Rise crest near 10°N: TURBULENCE AND MIXING ON THE EPR CREST
journal, August 2011
- Thurnherr, A. M.; St. Laurent, L. C.
- Geophysical Research Letters, Vol. 38, Issue 15
Two-Dimensional Turbulence
journal, January 2012
- Boffetta, Guido; Ecke, Robert E.
- Annual Review of Fluid Mechanics, Vol. 44, Issue 1
The k −3 and k −5/3 Energy Spectrum of Atmospheric Turbulence: Quasigeostrophic Two-Level Model Simulation
journal, March 2003
- Tung, Ka Kit; Orlando, Wendell Welch
- Journal of the Atmospheric Sciences, Vol. 60, Issue 6
Experimental evidence of a triadic resonance of plane inertial waves in a rotating fluid
journal, January 2012
- Bordes, Guilhem; Moisy, Frédéric; Dauxois, Thierry
- Physics of Fluids, Vol. 24, Issue 1
Routes to energy dissipation for geostrophic flows in the Southern Ocean
journal, December 2012
- Nikurashin, Maxim; Vallis, Geoffrey K.; Adcroft, Alistair
- Nature Geoscience, Vol. 6, Issue 1
Geostrophic Adjustment and Inverse Cascades in Rotating Stratified Turbulence
journal, December 1995
- Bartello, Peter
- Journal of the Atmospheric Sciences, Vol. 52, Issue 24
Stratified turbulence dominated by vortical motion
journal, January 1999
- Waite, Michael L.; Bartello, Peter
- Journal of Fluid Mechanics, Vol. 517
A New Large Scale Instability in Rotating Stratified Fluids Driven by Small Scale Forces
journal, January 2013
- Tur, Anatoly; Chabane, Malik; Yanovsky, Vladimir
- Open Journal of Fluid Dynamics, Vol. 03, Issue 04
Low Rossby limiting dynamics for stably stratified flow with finite Froude number
journal, April 2011
- Wingate, Beth A.; Embid, Pedro; Holmes-Cerfon, Miranda
- Journal of Fluid Mechanics, Vol. 676
The route to dissipation in strongly stratified and rotating flows
journal, February 2013
- Deusebio, Enrico; Vallgren, A.; Lindborg, E.
- Journal of Fluid Mechanics, Vol. 720
A hybrid MPI–OpenMP scheme for scalable parallel pseudospectral computations for fluid turbulence
journal, June 2011
- Mininni, Pablo D.; Rosenberg, Duane; Reddy, Raghu
- Parallel Computing, Vol. 37, Issue 6-7
Wave turbulence and intermittency
journal, May 2001
- Newell, Alan C.; Nazarenko, Sergey; Biven, Laura
- Physica D: Nonlinear Phenomena, Vol. 152-153
Fluid Motions in the Presence of Strong Stable Stratification
journal, January 2000
- Riley, James J.; Lelong, Marie-Pascale
- Annual Review of Fluid Mechanics, Vol. 32, Issue 1
Large-scale flow driven by the anisotropic kinetic alpha effect
journal, October 1987
- Frisch, U.; She, Z. S.; Sulem, P. L.
- Physica D: Nonlinear Phenomena, Vol. 28, Issue 3
Sensitivity of stratified turbulence to the buoyancy Reynolds number
journal, May 2013
- Bartello, P.; Tobias, S. M.
- Journal of Fluid Mechanics, Vol. 725
Quasi-monochromatic inertia-gravity waves in the lower stratosphere from MST radar observations
journal, January 2006
- Nastrom, G. D.; Eaton, F. D.
- Journal of Geophysical Research, Vol. 111, Issue D19
Anisotropy and nonuniversality in scaling laws of the large-scale energy spectrum in rotating turbulence
journal, September 2012
- Sen, Amrik; Mininni, Pablo D.; Rosenberg, Duane
- Physical Review E, Vol. 86, Issue 3
Turbulence and vortex structures in rotating and stratified flows
journal, July 2001
- Cambon, Claude
- European Journal of Mechanics - B/Fluids, Vol. 20, Issue 4
Low Froude number limiting dynamics for stably stratified flow with small or finite Rossby numbers
journal, March 1998
- Embid, Pedro F.; Majda, Andrew J.
- Geophysical & Astrophysical Fluid Dynamics, Vol. 87, Issue 1-2
Scaling analysis and simulation of strongly stratified turbulent flows
journal, August 2007
- Brethouwer, G.; Billant, P.; Lindborg, E.
- Journal of Fluid Mechanics, Vol. 585
Crossover from Two- to Three-Dimensional Turbulence
journal, September 1996
- Smith, Leslie M.; Chasnov, Jeffrey R.; Waleffe, Fabian
- Physical Review Letters, Vol. 77, Issue 12
The transition from geostrophic to stratified turbulence
journal, November 2006
- Waite, Michael L.; Bartello, Peter
- Journal of Fluid Mechanics, Vol. 568
Heating the Solar Wind by a Magnetohydrodynamic Turbulent Energy Cascade
journal, March 2008
- Marino, R.; Sorriso-Valvo, L.; Carbone, V.
- The Astrophysical Journal, Vol. 677, Issue 1
On the Occurrence of the Third-Order Scaling in high Latitude Solar wind
journal, April 2012
- Marino, R.; Sorriso-Valvo, L.; D’Amicis, R.
- The Astrophysical Journal, Vol. 750, Issue 1
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 generation and quantitative visualization of breaking internal waves
journal, March 2005
- Troy, C. D.; Koseff, J. R.
- Experiments in Fluids, Vol. 38, Issue 5
Kinetic energy dynamics in forced, homogeneous, and axisymmetric stably stratified turbulence
journal, January 2012
- Almalkie, Saba; de Bruyn Kops, Stephen M.
- Journal of Turbulence, Vol. 13
Two-dimensional turbulence
journal, May 1980
- Kraichnan, R. H.; Montgomery, D.
- Reports on Progress in Physics, Vol. 43, Issue 5
I NTERNAL G RAVITY W AVES : From Instabilities to Turbulence
journal, January 2002
- Staquet, C.; Sommeria, J.
- Annual Review of Fluid Mechanics, Vol. 34, Issue 1
Inverse cascade in stably stratified rotating turbulence
journal, January 1996
- Métais, O.; Bartello, P.; Garnier, E.
- Dynamics of Atmospheres and Oceans, Vol. 23, Issue 1-4
Thermalization and free decay in surface quasigeostrophic flows
journal, July 2012
- Teitelbaum, Tomas; Mininni, Pablo D.
- Physical Review E, Vol. 86, Issue 1
Sources of gravity waves in the lower stratosphere above South Pole
journal, January 2009
- Li, Z.; Robinson, W.; Liu, A. Z.
- Journal of Geophysical Research, Vol. 114, Issue D14
Inverse Energy Cascade in Three-Dimensional Isotropic Turbulence
journal, April 2012
- Biferale, Luca; Musacchio, Stefano; Toschi, Federico
- Physical Review Letters, Vol. 108, Issue 16
Nusselt number and friction factor in thermally stratified turbulent channel flow under Non-Oberbeck–Boussinesq conditions
journal, December 2013
- Zonta, Francesco
- International Journal of Heat and Fluid Flow, Vol. 44
Emergence of helicity in rotating stratified turbulence
journal, March 2013
- Marino, Raffaele; Mininni, Pablo D.; Rosenberg, Duane
- Physical Review E, Vol. 87, Issue 3
Non Linear Vortex Structures in Stratified Fluid Driven by Small-Scale Helical Force
journal, January 2013
- Tur, Anatoly; Yanovsky, Vladimir
- Open Journal of Fluid Dynamics, Vol. 03, Issue 02
Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence?
journal, June 1999
- Lindborg, Erik
- Journal of Fluid Mechanics, Vol. 388
The magnetohydrodynamic turbulent cascade in the ecliptic solar wind: Study of Ulysses data
journal, May 2011
- Marino, Raffaele; Sorriso-Valvo, Luca; Carbone, Vincenzo
- Planetary and Space Science, Vol. 59, Issue 7
Energy spectra of stably stratified turbulence
journal, March 2012
- Kimura, Y.; Herring, J. R.
- Journal of Fluid Mechanics, Vol. 698
Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence
journal, June 1999
- Smith, Leslie M.; Waleffe, Fabian
- Physics of Fluids, Vol. 11, Issue 6
A theory for the atmospheric energy spectrum: Depth-limited temperature anomalies at the tropopause
journal, September 2006
- Tulloch, R.; Smith, K. S.
- Proceedings of the National Academy of Sciences, Vol. 103, Issue 40
Isotropization at small scales of rotating helically driven turbulence
journal, April 2012
- Mininni, P. D.; Rosenberg, D.; Pouquet, A.
- Journal of Fluid Mechanics, Vol. 699
MHD simulations and astrophysical applications
journal, January 2005
- Gómez, Daniel O.; Mininni, Pablo D.; Dmitruk, Pablo
- Advances in Space Research, Vol. 35, Issue 5
Experiments on rapidly rotating turbulent flows
journal, September 2009
- van Bokhoven, L. J. A.; Clercx, H. J. H.; van Heijst, G. J. F.
- Physics of Fluids, Vol. 21, Issue 9
Power laws and inverse motion modelling: application to turbulence measurements from satellite images
journal, December 2011
- Héas, Patrick; Mémin, Etienne; Heitz, Dominique
- Tellus A: Dynamic Meteorology and Oceanography, Vol. 64, Issue 1
Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 2. Large-scale and small-scale anisotropy
journal, June 2003
- Godeferd, F. S.; Staquet, C.
- Journal of Fluid Mechanics, Vol. 486
Inertial Ranges in Two-Dimensional Turbulence
journal, January 1967
- Kraichnan, Robert H.
- Physics of Fluids, Vol. 10, Issue 7
Stratified Turbulence: A Possible Interpretation of Some Geophysical Turbulence Measurements
journal, July 2008
- Riley, James J.; Lindborg, Erik
- Journal of the Atmospheric Sciences, Vol. 65, Issue 7
Scaling in three-dimensional and quasi-two-dimensional rotating turbulent flows
journal, August 2003
- Baroud, Charles N.; Plapp, Brendan B.; Swinney, Harry L.
- Physics of Fluids, Vol. 15, Issue 8
Turbulence and internal waves in stably-stratified channel flow with temperature-dependent fluid properties
journal, March 2012
- Zonta, Francesco; Onorato, Miguel; Soldati, Alfredo
- Journal of Fluid Mechanics, Vol. 697
Decaying grid turbulence in a rotating stratified fluid
journal, January 2006
- Praud, Olivier; Sommeria, Joel; Fincham, Adam M.
- Journal of Fluid Mechanics, Vol. 547, Issue -1
Generation of slow large scales in forced rotating stratified turbulence
journal, January 2002
- Smith, Leslie M.; Waleffe, Fabian
- Journal of Fluid Mechanics, Vol. 451
Numerical experiments in forced stably stratified turbulence
journal, May 1989
- Herring, Jackson R.; Métais, Olivier
- Journal of Fluid Mechanics, Vol. 202
Generalized quasi-geostrophy for spatially anisotropic rotationally constrained flows
journal, May 2006
- Julien, Keith; Knobloch, Edgar; Milliff, Ralph
- Journal of Fluid Mechanics, Vol. 555
Inverse cascades in rotating stratified turbulence: Fast growth of large scales
journal, May 2013
- Marino, R.; Mininni, P. D.; Rosenberg, D.
- EPL (Europhysics Letters), Vol. 102, Issue 4
Stratified turbulence at the buoyancy scale
journal, June 2011
- Waite, Michael L.
- Physics of Fluids, Vol. 23, Issue 6
Overturning circulation driven by breaking internal waves in the deep ocean: MOC DRIVEN BY BREAKING INTERNAL WAVES
journal, June 2013
- Nikurashin, Maxim; Ferrari, Raffaele
- Geophysical Research Letters, Vol. 40, Issue 12
Inertial transfers in the helical decomposition
journal, March 1993
- Waleffe, Fabian
- Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 3
Inverse cascades in turbulence and the case of rotating flows
journal, July 2013
- Pouquet, A.; Sen, A.; Rosenberg, D.
- Physica Scripta, Vol. T155
Anisotropic constraints on energy distribution in rotating and stratified turbulence
journal, October 2008
- Kurien, S.; Wingate, B.; Taylor, M. A.
- EPL (Europhysics Letters), Vol. 84, Issue 2
Kinetic energy spectrum of large-and mesoscale atmospheric processes
journal, July 1984
- Nastrom, G. D.; Gage, K. S.; Jasperson, W. H.
- Nature, Vol. 310, Issue 5972
Modulation of turbulence in forced convection by temperature-dependent viscosity
journal, March 2012
- Zonta, Francesco; Marchioli, Cristian; Soldati, Alfredo
- Journal of Fluid Mechanics, Vol. 697
Scale Interactions in Magnetohydrodynamic Turbulence
journal, January 2011
- Mininni, Pablo D.
- Annual Review of Fluid Mechanics, Vol. 43, Issue 1
Effect of Temperature Dependent Fluid Properties on Heat Transfer in Turbulent Mixed Convection
journal, November 2013
- Zonta, Francesco; Soldati, Alfredo
- Journal of Heat Transfer, Vol. 136, Issue 2
Nonlinear formation of structures in rotating stratified turbulence
journal, January 2005
- Liechtenstein, L.; Godeferd, F. S.; Cambon, C.
- Journal of Turbulence, Vol. 6
Turbulence comes in bursts in stably stratified flows
journal, April 2014
- Rorai, C.; Mininni, P. D.; Pouquet, A.
- Physical Review E, Vol. 89, Issue 4
Experimental quantification of inverse energy cascade in deep rotating turbulence
journal, August 2013
- Yarom, Ehud; Vardi, Yuval; Sharon, Eran
- Physics of Fluids, Vol. 25, Issue 8
Works referencing / citing this record:
Observing Mesospheric Turbulence With Specular Meteor Radars: A Novel Method for Estimating Second‐Order Statistics of Wind Velocity
journal, July 2019
- Vierinen, J.; Chau, J. L.; Charuvil, H.
- Earth and Space Science, Vol. 6, Issue 7
Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations
journal, May 2015
- Rosenberg, D.; Pouquet, A.; Marino, R.
- Physics of Fluids, Vol. 27, Issue 5
Dual constant-flux energy cascades to both large scales and small scales
journal, November 2017
- Pouquet, A.; Marino, R.; Mininni, P. D.
- Physics of Fluids, Vol. 29, Issue 11
Single-particle dispersion in stably stratified turbulence
journal, March 2018
- Sujovolsky, N. E.; Mininni, P. D.; Rast, M. P.
- Physical Review Fluids, Vol. 3, Issue 3
Vertical dispersion of Lagrangian tracers in fully developed stably stratified turbulence
journal, January 2019
- Sujovolsky, N. E.; Mininni, P. D.
- Physical Review Fluids, Vol. 4, Issue 1
Inverse and Direct Energy Cascades in Three-Dimensional Magnetohydrodynamic Turbulence at Low Magnetic Reynolds Number
journal, June 2018
- Baker, Nathaniel T.; Pothérat, Alban; Davoust, Laurent
- Physical Review Letters, Vol. 120, Issue 22
Turbulence-Driven Ion Beams in the Magnetospheric Kelvin-Helmholtz Instability
journal, January 2019
- Sorriso-Valvo, Luca; Catapano, Filomena; Retinò, Alessandro
- Physical Review Letters, Vol. 122, Issue 3
Vertical dispersion of Lagrangian tracers in fully developed stably stratified turbulence
text, January 2018
- Sujovolsky, Nicolas E.; Mininni, Pablo D.
- arXiv
Figures / Tables found in this record:
Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.