Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-28T22:22:18.294Z Has data issue: false hasContentIssue false
  • English
  • Français

Relative dispersion with finite inertial ranges

Published online by Cambridge University Press:  09 December 2021

J.H. LaCasce Open the ORCID record for J.H. LaCasce [Opens in a new window]  and
Thomas Meunier Open the ORCID record for Thomas Meunier [Opens in a new window]
J.H. LaCasce*
Affiliation:
Department of Geosciences, University of Oslo, 0315 Oslo, Norway
Thomas Meunier
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA
*
†Email address for correspondence: j.h.lacasce@geo.uio.no
Get access Rights & Permissions [Opens in a new window]

Abstract

Relative dispersion experiments are often analysed using theoretical predictions from two- and three-dimensional turbulence. These apply to infinite inertial ranges, assuming the same dispersive behaviour over all scales. With finite inertial ranges, the metrics are less conclusive. We examine this using pair separation probability density functions (PDFs), obtained by integrating a Fokker–Planck equation with different diffusivity profiles. We consider time-based metrics, such as the relative dispersion, and separation-based metrics, such as the finite scale Lyapunov exponent (FSLE). As the latter cannot be calculated from a PDF, we introduce a new measure, the cumulative inverse separation time (CIST), which can. This behaves like the FSLE, but advantageously has analytical solutions in the inertial ranges. This allows the establishment of consistency between the time- and space-based metrics, something which has been lacking previously. We focus on three dispersion regimes: non-local spreading (as in a two-dimensional enstrophy inertial range), Richardson dispersion (as in an energy inertial range) and diffusion (for uncorrelated pair motion). The time-based metrics are more successful with non-local dispersion, as the corresponding PDF applies from the initial time. Richardson dispersion is barely observed, because the self-similar PDF applies only asymptotically in time. In contrast, the separation-based CIST correctly captures the dependencies, even with a short (one decade) inertial range, and is superior to the traditional FSLE at large scales. Nevertheless, it is advantageous to use all measures together, to seek consistent indications of the dispersion.

JFM classification

Geophysical and Geological Flows: Geostrophic turbulence Mass Transport: Dispersion
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 932 , 10 February 2022 , A39
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Artale, V., Boffetta, G., Celani, A., Cencini, M. & Vulpiani, A. 1997 Dispersion of passive tracers in closed basins: beyond the diffusion coefficient. Phys. Fluids 9, 3162–3171.CrossRefGoogle Scholar
Aurell, E., Boffetta, G., Crisianti, A., Paladin, G. & Vulpiani, A. 1997 Predictability in the large: an extension of the concept of Lyapunov exponent. J. Phys. A 30, 1–26.CrossRefGoogle Scholar
Babiano, A., Basdevant, C., LeRoy, P. & Sadourny, R. 1990 Relative dispersion in two-dimensional turbulence. J. Fluid Mech. 214, 535–557.CrossRefGoogle Scholar
Balwada, D., LaCasce, J.H. & Speer, K.G. 2016 Scale dependent distribution of kinetic energy in the gulf of Mexico. Geophys. Res. Let. 43 (20), 10856–10863.CrossRefGoogle Scholar
Balwada, D., LaCasce, J.H., Speer, K.G. & Ferrari, R. 2021 Relative dispersion in the Antarctic circumpolar current. J. Phys. Oceanogr. 51, 553–574.CrossRefGoogle Scholar
Batchelor, G.K. 1952 Diffusion in a field of homogeneous turbulence. II. The relative motion of particles. Proc. Camb. Phil. Soc. 48, 345–362.CrossRefGoogle Scholar
Batchelor, G.K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Bennett, A.F. 2006 Lagrangian Fluid Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Beron-Vera, F.J. & LaCasce, J.H. 2016 Statistics of simulated and observed pair separations in the Gulf of Mexico. J. Phys. Oceanogr. 46, 2183–2199.CrossRefGoogle Scholar
Berti, S. & Lapeyre, G. 2021 Lagrangian pair dispersion in upper-ocean turbulence in the presence of mixed-layer instabilities. Phys. Fluids 33, 036603.CrossRefGoogle Scholar
Boffetta, G. & Sokolov, I.M. 2002 Statistics of two-particle dispersion in two-dimensional turbulence. Phys. Fluids 14 (9), 3224–3232.CrossRefGoogle Scholar
Bracco, A., Choi, J., Joshi, K., Luo, H. & McWilliams, J.C. 2016 Submesoscale currents in the northern Gulf of Mexico: deep phenomena and dispersion over the continental slope. Ocean Model. 101, 43–58.CrossRefGoogle Scholar
Cencini, M. & Vulpiani, A. 2013 Finite size Lyapunov exponent: review on applications. J. Phys. A 46, 254019.CrossRefGoogle Scholar
Corrado, R., Lacorata, G., Palatella, L., Santoleri, R. & Zambianchi, E. 2017 General characteristics of relative dispersion in the ocean. Sci. Rep. 7, 1–11.CrossRefGoogle ScholarPubMed
Dräger-Dietel, J., Jochumsen, K., Griesel, A. & Badin, G. 2018 Relative dispersion of surface drifters in the Benguela upwelling region. J. Phys. Oceanogr. 48, 2325–2341.CrossRefGoogle Scholar
Er-El, J. & Peskin, R. 1981 Relative diffusion of constant-level balloons in the Southern Hemisphere. J. Atmos. Sci. 38, 2264–2274.2.0.CO;2>CrossRefGoogle Scholar
Essink, S., Hormann, V., Centurioni, L.R. & Mahadevan, A. 2019 Can we detect submesoscale motions in drifter pair dispersion? J. Phys. Oceanogr. 49, 2237–2254.CrossRefGoogle Scholar
Flierl, G.R., Malanotte-Rizzoli, P. & Nabusky, N.J. 1987 Nonlinear waves and coherent vortex structures in barotropic $\beta$-plane jets. J. Phys. Oceanogr. 17, 1408–1438.2.0.CO;2>CrossRefGoogle Scholar
Foussard, A., Berti, S., Perrot, X. & Lapeyre, G. 2017 Relative dispersion in generalized two-dimensional turbulence. J. Fluid Mech. 821, 358–383.CrossRefGoogle Scholar
Graff, L.S., Guttu, S. & LaCasce, J.H. 2015 Relative dispersion in the atmosphere from reanalysis winds. J. Atmos. Sci. 72, 2769–2785.CrossRefGoogle Scholar
Haza, A.C., Poje, A.C., Özgökmen, T.M. & Martin, P. 2008 Relative dispersion from a high-resolution coastal model of the Adriatic Sea. Ocean Model. 22, 48–65.CrossRefGoogle Scholar
Koszalka, I., LaCasce, J.H. & Orvik, K.A. 2009 Relative dispersion in the Nordic Seas. J. Mar. Res. 67 (4), 411–433.CrossRefGoogle Scholar
Kraichnan, R.H. 1966 Dispersion of particle pairs in homogeneous turbulence. Phys. Fluids 9, 1937–1943.CrossRefGoogle Scholar
Kraichnan, R.H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417–1423.CrossRefGoogle Scholar
LaCasce, J.H. 2000 Floats and f/H. J. Mar. Res. 58, 61–95.CrossRefGoogle Scholar
LaCasce, J.H. 2008 Statistics from Lagrangian observations. Prog. Oceanogr. 77, 1–29.CrossRefGoogle Scholar
LaCasce, J.H. 2010 Relative displacement probability distribution functions from balloons and drifters. J. Mar. Res. 68, 433–457.CrossRefGoogle Scholar
LaCasce, J.H. 2016 Estimating Eulerian energy spectra from drifters. Fluids 1 (4), 33.CrossRefGoogle Scholar
LaCasce, J.H. & Bower, A. 2000 Relative dispersion at the surface in the subsurface North Atlantic. J. Mar. Res. 58, 863–894.CrossRefGoogle Scholar
LaCasce, J.H., Ferrari, R., Marshall, J., Tulloch, R., Balwada, D. & Speer, K. 2014 Float-derived isopycnal diffusivities in the DIMES experiment. J. Phys. Oceanogr. 44, 764–780.CrossRefGoogle Scholar
LaCasce, J.H. & Ohlmann, C. 2003 Relative dispersion at the surface of the Gulf of Mexico. J. Mar. Res. 61, 285–312.CrossRefGoogle Scholar
Lacorata, G., Aurell, E., Legras, B. & Vulpiani, A. 2004 Evidence for a $\kappa ^-5/3$ spectrum from the EOLE Lagrangian balloons in the low stratosphere. J. Atmos. Sci. 61, 2936–2942.CrossRefGoogle Scholar
Lacorata, G., Aurell, E. & Vulpiani, A. 2001 Drifter dispersion in the Adriatic Sea: Lagrangian data and chaotic model. Ann. Geophys. 19, 121–129.CrossRefGoogle Scholar
Lin, J.-T. 1972 Relative dispersion in the enstrophy-cascading inertial range of homogeneous two-dimensional turbulence. J. Atmos. Sci. 29, 394–395.2.0.CO;2>CrossRefGoogle Scholar
Lindborg, E. 2015 A Helmholtz decomposition of structure functions and spectra calculated from aircraft data. J. Fluid Mech. 762, R4.CrossRefGoogle Scholar
Lumpkin, R. & Ellipot, S. 2010 Surface drifter pair spreading in the North Atlantic. J. Geophys. Res. 115, C12017.CrossRefGoogle Scholar
Lumpkin, R., Özgökmen, T. & Centurioni, L. 2017 Advances in the application of surface drifters. Annu. Rev. Mar. Sci. 9, 59–81.CrossRefGoogle ScholarPubMed
Lumpkin, R. & Pazos, M. 2007 Measuring surface currents with Surface Velocity Program drifters: the instrument, its data, and some recent results. In Lagrangian Analysis and Prediction of Coastal and Ocean Dynamics (ed. Teresa S. Hawley & Robert G. Hawley), p. 67. Cambridge University Press.Google Scholar
Lundgren, T.S. 1981 Turbulent pair dispersion and scalar diffusion. J. Fluid Mech. 111, 27–57.CrossRefGoogle Scholar
Mantovanelli, A., Heron, M.L., Heron, S.F. & Steinberg, C.R. 2012 Relative dispersion of surface drifters in a barrier reef region. J. Geophys. Res. 117, C11016.Google Scholar
Meunier, T. & LaCasce, J.H. 2021 Finite size Lyapunov exponent and finite amplitude growth rate. Fluids 6 (10), 348.CrossRefGoogle Scholar
Morel, P. & Larcheveque, M. 1974 Relative dispersion of constant-level balloons in the 200 mb general circulation. J. Atmos. Sci. 31, 2189–2196.2.0.CO;2>CrossRefGoogle Scholar
Nastrom, G.D. & Gage, K.S. 1985 A climatology of atmospheric wavenumber spectra of wind and temperature observed by commerical aircraft. J. Atmos. Sci. 42, 959–960.2.0.CO;2>CrossRefGoogle Scholar
Obhukov, A.M. 1941 Energy distribution in the spectrum of turbulent flow. Izv. Akad. Nauk SSSR Geogr. Geofiz. 5 (8), 453–466.Google Scholar
Ohlmann, J.C., LaCasce, J.H., Washburn, L., Mariano, A.J. & Emery, B. 2012 Relative dispersion observations and trajectory modeling in the Santa Barbara Channel. J. Geophys. Res. 117, C05040.Google Scholar
Ohlmann, J.C., Molemaker, M.J., Baschek, B., Holt, B., Marmorino, G. & Smith, G. 2017 Drifter observations of submesoscale flow kinematics in the coastal ocean. Geophys. Res. Let. 44, 330–337.CrossRefGoogle Scholar
Ohlmann, J.C., White, P.F., Sybrandy, A.L. & Niiler, P.P. 2005 GPS-cellular drifter technology for coastal ocean observing systems. J. Atmos. Ocean. Technol. 22, 1381–1388.CrossRefGoogle Scholar
Okubo, A. 1971 Oceanic diffusion diagrams. Deep-Sea Res. 18 (8), 789–802.Google Scholar
Ollitrault, M., Gabillet, C. & de Verdiere, A.C. 2005 Open ocean regimes of relative dispersion. J. Fluid Mech. 533, 381–407.CrossRefGoogle Scholar
Pearson, J., Fox-Kemper, B., Barkan, R., Choi, J., Bracco, A. & McWilliams, J.C. 2019 Impacts of convergence on structure functions from surface drifters in the Gulf of Mexico. J. Phys. Oceanogr. 49, 675–690.CrossRefGoogle Scholar
Poje, A.C., et al. 2014 Submesoscale dispersion in the vicinity of the Deepwater Horizon spill. Proc. Natl Acad. Sci. USA 111 (35), 12693–12698.CrossRefGoogle ScholarPubMed
Richardson, L.F. 1926 Atmospheric diffusion on a distance-neighbour graph. Proc. R. Soc. Lond. A 110, 709–737.Google Scholar
Richardson, L.F. & Stommel, H. 1948 Note on eddy diffusion in the sea. J. Meteorol. 5 (5), 238–240.2.0.CO;2>CrossRefGoogle Scholar
Salazar, J.P.L.C. & Collins, L.R. 2009 Two particle dispersion in isotropic turbulent flows. Annu. Rev. Fluid Mech. 41, 405–432.CrossRefGoogle Scholar
Sansón, L.Z., Pérez-Brunius, P. & Sheinbaum, J. 2017 Surface relative dispersion in the southwestern Gulf of Mexico. J. Phys. Oceanogr. 47, 387–403.CrossRefGoogle Scholar
Sawford, B. 2001 Turbulent relative dispersion. Annu. Rev. Fluid Mech. 33, 289–317.CrossRefGoogle Scholar
Schroeder, K., et al. 2012 Targeted lagrangian sampling of submesoscale dispersion at a coastal frontal zone. Geophys. Res. Lett. 39, 289–317.CrossRefGoogle Scholar
Shcherbina, A.Y., et al. 2015 The LatMix summer campaign: submesoscale stirring in the upper ocean. Bull. Am. Meteorol. Soc. 96, 1257–1279.CrossRefGoogle Scholar
Spydell, M.S., Feddersen, F. & MacMahan, J. 2021 Relative dispersion on the inner shelf: evidence of a Batchelor regime. J. Phys. Oceanogr. 51, 519–536.CrossRefGoogle Scholar
Thomas, L.N., Tandon, A. & Mahadevan, A. 2008 Submesoscale processes and dynamics. In Ocean Modeling in an Eddying Regime (ed. M.W. Hecht & H. Hasumi), vol. 177, pp. 17–38. John Wiley and Sons.CrossRefGoogle Scholar