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Abstract:

The large-scale structures in the ocean and the atmosphere are in geostrophic balance, and a conduit must be found to channel the energy to the small scales where it can be dissipated. In turbulence, this takes the form of an energy cascade, whereas a possible mechanism in a balanced flow is through the formation of fronts, a common occurrence in geophysics. We show that an iconic configuration in laboratory and numerical experiments for the study of turbulence, the so-called Taylor-Green or von Kármán swirling flow, can be suitably adapted to domains with large aspect ratios, leading to the creation of an imposed large-scale vertical shear. To this effect, we use direct numerical simulations of the Boussinesq equations without net rotation and with no small-scale modeling. Various grid spacings are used, up to 20482 × 256 spatial points. The grids are always isotropic, with box aspect ratios of either 1:4 or 1:8. We find that when shear and stratification are comparable, the imposed shear layer resulting from the forcing leads to the formation of fronts and filaments which destabilize and evolve into a turbulent flow in the bulk, with a sizable amount of dissipation and mixing, following a cycle of front creation, instability, and development of turbulence. The results depend on the vertical length scales of shear and stratification. © 2018 Author(s).

Registro:

Documento: Artículo
Título:Generation of turbulence through frontogenesis in sheared stratified flows
Autor:Sujovolsky, N.E.; Mininni, P.D.; Pouquet, A.
Filiación:Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, IFIBA, CONICET, Buenos Aires, 1428, Argentina
NCAR, P.O. Box 3000, Boulder, CO 80307-3000, United States
Laboratory for Atmospheric and Space Physics, CU, Boulder, CO 80309-256, United States
Palabras clave:Aspect ratio; Turbulence; Boussinesq equations; Geostrophic balance; Large aspect ratio; Large scale structures; Numerical experiments; Possible mechanisms; Small-scale modeling; Stratified flows; Shear flow
Año:2018
Volumen:30
Número:8
DOI: http://dx.doi.org/10.1063/1.5043293
Título revista:Physics of Fluids
Título revista abreviado:Phys. Fluids
ISSN:10706631
CODEN:PHFLE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10706631_v30_n8_p_Sujovolsky

Referencias:

  • Charney, J., Geostrophic turbulence (1971) J. Atmos. Sci., 28, p. 1087
  • Munro, R., Foster, M., Davies, P., Instabilities in the spin-up of a rotating, stratified fluid (2010) Phys. Fluids, 22
  • Waite, M.L., Stratified turbulence at the buoyancy scale (2011) Phys. Fluids, 23
  • Liang, Y., Zareei, A., Reza Alam, M., Inherently unstable internal gravity waves due to resonant harmonic generation (2016) J. Fluid Mech., 811, p. 400
  • Kartashova, E., Nazarenko, S., Rudenko, O., Resonant interactions of nonlinear water waves in a finite basin (2008) Phys. Rev. e, 78
  • Brouzet, C., Ermanyuk, E., Joubaud, S., Pillet, G., Dauxois, T., Internal wave attractors: Different scenatios of instability (2017) J. Fluid Mech., 811, p. 544
  • Kafiabad, H., Bartello, P., Balance dynamics in rotating stratified turbulence (2016) J. Fluid Mech., 795, p. 914
  • Deusebio, E., Vallgren, A., Lindborg, E., The route to dissipation in strongly stratified and rotating flows (2013) J. Fluid Mech., 720, p. 66
  • Deusebio, E., Augier, P., Lindborg, E., Third-order structure functions in rotating and stratified turbulence: A comparison between numerical, analytical and observational results (2014) J. Fluid Mech., 755, p. 294
  • King, G.P., Vogelzang, J., Stoffelen, A., Upscale and downscale energy transfer over the tropical Pacific revealed by scatterometer winds (2015) J. Geophys. Res., 120, p. 346. , https://doi.org/10.1002/2014jc009993
  • Pouquet, A., Rosenberg, D., Marino, R., Herbert, C., Scaling laws for mixing and dissipation in unforced rotating stratified turbulence (2018) J. Fluid Mech., 844, p. 519
  • McWilliams, J., Yavneh, I., Cullen, M., Gent, P., The breakdown of large-scale flows in rotating, stratified fluids (1998) Phys. Fluids, 10, p. 3178
  • Davis, A., Yan, X.-H., Hurricane forcing on chlorophyll-a concentration off the northeast coast of the U.S (2004) Geophys. Res. Lett., 31, p. L17304. , https://doi.org/10.1029/2004gl020668
  • Rossi, V., López, C., Hernández-Garciá, E., Sudre, J., Garçon, V., Morel, Y., Surface mixing and biological activity in the four eastern boundary upwelling systems (2009) Nonlinear Processes Geophys., 16, p. 557
  • Gruber, N., Lachkar, Z., Frenzel, H., Marchesiello, P., Münnich, M., McWilliams, J.C., Nagai, T., Plattner, G.-K., Eddy-induced reduction of biological production in eastern boundary upwelling systems (2011) Nat. Geosci., 4, p. 787
  • Shulman, I., Penta, B., Richman, J., Jacobs, G., Anderson, S., Sakalaukus, P., Impact of submesoscale processes on dynamics of phytoplankton filaments (2015) J. Geophys. Res., 120, p. 2050. , https://doi.org/10.1002/2014jc010326
  • Smith, K., Hamlington, P., Fox-Kemper, B., Effects of submesoscale turbulence on ocean tracers (2016) J. Geophys. Res., 121, p. 908. , https://doi.org/10.1002/2015jc011089
  • Papenberg, C., Klaeschen, D., Krahmann, G., Hobbs, R.W., Ocean temperature and salinity inverted from combined hydrographic and seismic data (2010) Geophys. Res. Lett., 37, p. L04601. , https://doi.org/10.1029/2009gl042115
  • McWilliams, J., Submesoscale currents in the ocean (2016) Proc. R. Soc. A, 472
  • Celani, A., Cencini, M., Mazzino, A., Vergassola, M., Active and passive fields face to face (2004) New J. Phys., 6, p. 72
  • Ishihara, T., Gotoh, T., Kaneda, Y., Study of high Reynolds number isotropic turbulence by direct numerical simulation (2009) Annu. Rev. Fluid Mech., 41, p. 165
  • Oieroset, M., Phan, T., Eastwood, J.P., Fujimoto, M., Daughton, W., Shay, M.A., Angelopoulos, V., Larson, D.E., Direct evidence for a three-dimensional magnetic flux rope flanked by two active magnetic reconnection X lines at Earth's magnetopause (2011) Phys. Rev. Lett., 107
  • Mininni, P., Pouquet, A., Montgomery, D., Small-scale structures in three-dimensional magnetohydrodynamic turbulence (2006) Phys. Rev. Lett., 97
  • Hoskins, B., The mathematical theory of frontogenesis (1982) Annu. Rev. Fluid Mech., 14, p. 131
  • Grabowski, W., Wang, L.-P., Growth of cloud droplets in a turbulent environment (2013) Annu. Rev. Fluid Mech., 45, p. 293
  • Rorai, C., Mininni, P., Pouquet, A., Turbulence comes in bursts in stably stratified flows (2014) Phys. Rev. e, 89
  • Maffioli, A., Davidson, P., Dalziel, S., Swaminathan, N., The evolution of a stratified turbulent cloud (2014) J. Fluid Mech., 739, p. 229
  • Métais, O., Herring, J., Numerical simulations of freely evolving turbulence in stably stratified fluids (1989) J. Fluid Mech., 202, p. 117
  • Métais, O., Riley, J., Lesieur, M., Numerical simulations of stably stratified rotating turbulence (1994) Stably-Stratified Flows: Flow and Dispersion over Topography, pp. 139-151. , edited by I. P. Castro and N. J. Roskliff (Clarendon Press, Oxford)
  • Lilly, D., Stratified turbulence and the meso-scale variability of the atmosphere (1983) J. Atmos. Sci., 40, p. 749
  • Cambon, C., Godeferd, F.S., Nicolleau, F., Vassilicos, J.C., Turbulent diffusion in rapidly rotating flows with and without stable stratification (2004) J. Fluid Mech., 499, p. 231
  • Lindborg, E., The effect of rotation on the mesoscale energy cascade in the free atmosphere (2005) Geophys. Res. Lett., 32, p. L01809. , https://doi.org/10.1029/2004gl021319
  • Lindborg, E., The energy cascade in a strongly stratified fluid (2006) J. Fluid Mech., 550, p. 207
  • Waite, M., Snyder, C., The mesoscale kinetic energy spectrum of a baroclinic life cycle (2009) J. Atmos. Sci., 66, p. 883
  • Rorai, C., Mininni, P., Pouquet, A., Stably stratified turbulence in the presence of large-scale forcing (2015) Phys. Rev. e, 92
  • Maffioli, A., Davidson, P., Dynamics of stratified turbulence decaying from a high buoyancy Reynolds number (2016) J. Fluid Mech., 786, p. 210
  • Augier, P., Chomaz, J.-M., Billant, P., Spectral analysis of the transition to turbulence from a dipole in stratified fluid (2012) J. Fluid Mech., 713, p. 86
  • Billant, P., Chomaz, J.-M., Self-similarity of strongly stratified inviscid flows (2001) Phys. Fluids, 13, p. 1645
  • Mininni, P., Rosenberg, D., Pouquet, A., Isotropization at small scales of rotating helically driven turbulence (2012) J. Fluid Mech., 699, p. 263
  • Brethouwer, G., Billant, P., Lindborg, E., Chomaz, J.-M., Scaling analysis and simulation of strongly stratified turbulent flows (2007) J. Fluid Mech., 585, p. 343
  • Ivey, G., Winters, K., Koseff, J., Density stratification, turbulence but how much mixing? (2008) Annu. Rev. Fluid Mech., 40, p. 169
  • Winters, K., Lombard, P., Riley, J., D'Asaro, E., Available potential energy and mixing in density-stratified fluids (1995) J. Fluid Mech., 289, p. 115
  • Venayagamoorthy, S., Koseff, J., On the flux Richardson number in stably stratified turbulence (2016) J. Fluid Mech., 798, p. R1
  • Venaille, A., Gostiaux, L., Sommeria, J., A statistical mechanics approach to mixing in stratified fluids (2017) J. Fluid Mech., 810, p. 554
  • Maffioli, A., Brethouwer, G., Lindborg, E., Mixing efficiency in stratified turbulence (2016) J. Fluid Mech., 794, p. R3
  • Marino, R., Pouquet, A., Rosenberg, D., Resolving the paradox of oceanic large-scale balance and small-scale mixing (2015) Phys. Rev. Lett., 114
  • Pouquet, A., Marino, R., Mininni, P.D., Rosenberg, D., Dual constant-flux energy cascades to both large scales and small scales (2017) Phys. Fluids, 29
  • Klymak, J., Pinkel, R., Rainville, L., Direct breaking of the internal tide near topography: Kaena Ridge, Hawaii (2008) J. Phys. Oceanogr., 38, p. 380
  • Van Haren, H., Gostiaux, L., Convective mixing by internal waves in the Puerto Rico Trench (2016) J. Mar. Res., 74, p. 161
  • Clément, L., Thurnherr, A.M., Laurent, L.C.S., Turbulent mixing in a deep fracture zone on the mid-Atlantic ridge (2017) J. Phys. Oceanogr., 47, p. 1873
  • David, T.W., Marshall, D.P., Zanna, L., The statistical nature of turbulent barotropic ocean jets (2017) Ocean Modell., 113, p. 34
  • Smyth, W., Moum, J., Anisotropy of turbulence in stably stratified mixing layers (2000) Phys. Fluids, 12, p. 1343
  • Taylor, G., Green, A., Mechanism of the production of small eddies from large ones (1937) Proc. R. Soc. London, Ser. A, 158, p. 499
  • Brachet, M., Meiron, D., Orszag, S., Nickel, B., Morf, R., Frisch, U., Small-scale structure of the Taylor-Green vortex (1983) J. Fluid Mech., 130, p. 411
  • Cichowlas, C., Bonaïti, P., Debbasch, F., Brachet, M., Effective dissipation and turbulence in spectrally truncated Euler flows (2005) Phys. Rev. Lett., 95
  • Brachet, M., Bustamante, M., Krstulovic, G., Mininni, P., Pouquet, A., Rosenberg, D., Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries (2013) Phys. Rev. e, 87
  • Nore, C., Brachet, M.E., Politano, H., Pouquet, A., Dynamo action in a Taylor-Green vortex near threshold (1997) Phys. Plasmas, 4, p. 1
  • Ponty, Y., Mininni, P.D., Montgomery, D., Pinton, J.-F., Politano, H., Pouquet, A., Numerical study of dynamo action at low magnetic Prandtl numbers (2005) Phys. Rev. Lett., 94
  • Riley, J., De Bruyn Kops, S., Dynamics of turbulence strongly influenced by buoyancy (2003) Phys. Fluids, 15, p. 2047
  • Douady, S., Couder, Y., Brachet, M.-E., Direct observation of the intermittency of intense vorticity filaments in turbulence (1991) Phys. Rev. Lett., 67, p. 983
  • Odier, P., Pinton, J.-F., Fauve, S., Advection of a magnetic field by a turbulent swirling flow (1998) Phys. Rev. e, 58, p. 7397
  • Lee, E., Brachet, M., Pouquet, A., Mininni, P., Rosenberg, D., Lack of universality in decaying magnetohydrodynamic turbulence (2010) Phys. Rev. e, 81
  • Davidson, P., (2013) Turbulence in Rotating, Stratified and Electrically Conducting Fluids, , (Cambridge University Press)
  • Komori, S., Nagata, K., Effects of molecular diffusivities on counter-gradient scalar and momentum transfer in strongly stable stratification (1996) J. Fluid Mech., 326, pp. 205-237
  • Forster, D., Nelson, D., Stephen, M., Long-time tails and the large-eddy behavior of a randomly stirred fluid (1976) Phys. Rev. Lett., 36, p. 867
  • Salehipour, H., Peltier, W., Diapycnal diffusivity, turbulent Prandtl number and mixing efficiency in Boussinesq stratified turbulence (2015) J. Fluid Mech., 775, p. 464
  • Rosenberg, D., Pouquet, A., Marino, R., Mininni, P., Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations (2015) Phys. Fluids, 27
  • Gómez, D.O., Mininni, P.D., Dmitruk, P., Parallel simulations in turbulent MHD (2005) Phys. Scr., T116, p. 123
  • Mininni, P., Rosenberg, D., Reddy, R., Pouquet, A., A hybrid MPI-OpenMP scheme for scalable parallel pseudospectral computations for fluid turbulence (2011) Parallel Comput., 37, p. 316
  • Clark Di Leoni, P., Mininni, P.D., Brachet, M.E., Helicity, topology, and Kelvin waves in reconnecting quantum knots (2016) Phys. Rev. A, 94
  • Waite, M., Bartello, P., Stratified turbulence dominated by vortical motion (2004) J. Fluid Mech., 517, p. 281
  • Smith, L.M., Waleffe, F., Generation of slow large scales in forced rotating stratified turbulence (2002) J. Fluid Mech., 451, p. 145
  • Marino, R., Mininni, P., Rosenberg, D., Pouquet, A., Inverse cascades in rotating stratified turbulence: Fast growth of large scales (2013) Europhys. Lett., 102, p. 44006
  • Marino, R., Rosenberg, D., Herbert, C., Pouquet, A., Interplay of waves and eddies in rotating stratified turbulence and the link with kinetic-potential energy partition (2015) Europhys. Lett., 112, p. 49001
  • Celani, A., Musacchio, S., Vincenzi, D., Turbulence in more than two and less than three dimensions (2010) Phys. Rev. Lett., 104
  • Deusebio, E., Boffetta, G., Lindborg, E., Musacchio, S., Dimensional transition in rotating turbulence (2014) Phys. Rev. e, 90
  • Sozza, A., Boffetta, G., Muratore-Ginanneschi, P., Musacchio, S., Dimensional transition of energy cascades in stably stratified forced thin fluid layers (2015) Phys. Fluids, 27
  • Babin, A., Mahalov, A., Nicolaenko, B., On the asymptotic regimes and the strongly stratified limit of rotating Boussinesq equations (1997) Theor. Comput. Fluid Dyn., 9, p. 223
  • D'Asaro, E., Lee, C., Rainville, L., Harcourt, R., Thomas, L., Enhanced turbulence and energy dissipation at ocean fronts (2011) Science, 332, p. 318
  • Zuo, J.-C., Zhang, M., Xu, Q., Mu, L., Li, J., Chen, M.-X., Seasonal and interannual variabilities of mean velocity of Kuroshio based on satellite data (2012) Water Sci. Eng., 5, p. 428
  • Hoskins, B., Bretherton, F., Atmospheric frontogenesis models: Mathematical formulation and solution (1972) J. Atmos. Sci., 29, p. 11
  • Molemaker, M., McWilliams, J., Capet, X., Balanced and unbalanced routes to dissipation in an equilibrated Eady flow (2010) J. Fluid Mech., 654, p. 35
  • Kimura, Y., Herring, J.R., Energy spectra of stably stratified turbulence (2012) J. Fluid Mech., 698, p. 19
  • De Bruyn Kops, S., Classical scaling and intermittency in strongly stratified Boussinesq turbulence (2015) J. Fluid Mech., 775, p. 436
  • Clyne, J., Mininni, P., Norton, A., Rast, M., Interactive desktop analysis of high resolution simulations: Application to turbulent plume dynamics and current sheet formation (2007) New J. Phys., 9, p. 301
  • Clark Di Leoni, P., Cobelli, P., Mininni, P.D., The full title is: The spatio-temporal spectrum of turbulent flows (2017) Eur. Phys. J. e, 38, p. 136
  • Brachet, M., Meneguzzi, M., Vincent, A., Politano, H., Sulem, P., Numerical evidence of smooth self-similar dynamics and possibility of subsequent collapse for three-dimensional ideal flows (1992) Phys. Fluids A, 4, p. 2845
  • Lapeyre, G., Klein, P., Hua, B.L., Oceanic restratification forced by surface frontogenesis (2006) J. Phys. Oceanogr., 36, p. 1577
  • Rosenberg, D., Marino, R., Herbert, C., Pouquet, A., Variations of characteristic time scales in rotating stratified turbulence using a large parametric numerical study (2016) Eur. Phys. J. e, 39, p. 8
  • Rosenberg, D., Marino, R., Herbert, C., Pouquet, A., Correction to: Variations of characteristic time scales in rotating stratified turbulence using a large parametric numerical study (2017) Eur. Phys. J. e, 40, p. 87
  • Bartello, P., Geostrophic adjustment and inverse cascades in rotating stratified turbulence (1995) J. Atmos. Sci., 52, p. 4410
  • Kurien, S., Smith, L.M., Effect of rotation and domain aspect-ratio on layer formation in strongly stratified Boussinesq flows (2014) J. Turbul., 15, p. 241
  • Teitelbaum, T., Mininni, P., Effect of helicity and rotation on the free decay of turbulent flows (2009) Phys. Rev. Lett., 103
  • Rorai, C., Rosenberg, D., Pouquet, A., Mininni, P., Helicity dynamics in stratified turbulence in the absence of forcing (2013) Phys. Rev. e, 87
  • Koprov, B., Koprov, V., Ponomarev, V., Chkhetiani, O., Experimental studies of turbulent helicity and its spectrum in the atmospheric boundary layer (2005) Dokl. Phys., 50, p. 419

Citas:

---------- APA ----------
Sujovolsky, N.E., Mininni, P.D. & Pouquet, A. (2018) . Generation of turbulence through frontogenesis in sheared stratified flows. Physics of Fluids, 30(8).
http://dx.doi.org/10.1063/1.5043293
---------- CHICAGO ----------
Sujovolsky, N.E., Mininni, P.D., Pouquet, A. "Generation of turbulence through frontogenesis in sheared stratified flows" . Physics of Fluids 30, no. 8 (2018).
http://dx.doi.org/10.1063/1.5043293
---------- MLA ----------
Sujovolsky, N.E., Mininni, P.D., Pouquet, A. "Generation of turbulence through frontogenesis in sheared stratified flows" . Physics of Fluids, vol. 30, no. 8, 2018.
http://dx.doi.org/10.1063/1.5043293
---------- VANCOUVER ----------
Sujovolsky, N.E., Mininni, P.D., Pouquet, A. Generation of turbulence through frontogenesis in sheared stratified flows. Phys. Fluids. 2018;30(8).
http://dx.doi.org/10.1063/1.5043293