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Microscale complexity in the ocean: turbulence, intermittency and plankton life. (English) Zbl 1337.76036

Summary: This contribution reviews the nonlinear stochastic properties of turbulent velocity and passive scalar intermittent fluctuations in Eulerian and Lagrangian turbulence. These properties are illustrated with original data sets of (i) velocity fluctuations collected in the field and in the laboratory, and (ii) temperature, salinity and in vivo fluorescence (a proxy of phytoplankton biomass, i.e. unicelled vegetals passively advected by turbulence) sampled from highly turbulent coastal waters. The strength of three of the most popular models describing intermittent fluctuations (the lognormal, log-Lévy and log-Poisson models) to fit the distribution of in vivo fluorescence has subsequently been critically assessed. A theoretical formulation for the stochastic properties of biologically active scalars is also provided and validated. Finally, the potential effect of the intermittent properties of turbulent velocity fluctuations on processes relevant to the life of plankton organisms are theoretically investigated. It is shown that the intermittent nature of microscale turbulence may result in (i) a decrease in the rate of nutrient fluxes towards non-motile phytoplankton cells (6-62 \(\%\)), (ii) a decrease in the physical coagulation of phytoplankton cells (25-48 \(\%\)) and in the subsequent phytoplankton aggregate volumes (22-41 \(\%\)), and (iii) a decrease of the turbulence contribution to predator-prey encounter rates (25-50 \(\%\)).

MSC:

76F25 Turbulent transport, mixing
76Z05 Physiological flows
92D25 Population dynamics (general)
86A05 Hydrology, hydrography, oceanography
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[2] M. A. Baker, C. H. Gibson. Sampling turbulence in the stratified ocean: statistical consequences of strong intermittency. J. Phys. Oceanogr., 17 (1987), 1817-1836.
[3] Gibson. Kolmogorov similarity hypotheses for scalar fields: sampling intermittent turbulent mixing in the ocean and galaxy. Proc. R. Soc. Lond. A, 434 (1991), 149-164. · Zbl 0726.76049
[4] M. Pascual, F. Ascioti, H. Caswell. Intermittency in the plankton: a multifractal analysis of zooplankton biomass variability. J. Plankton Res., 17 (1995), 1209-1232.
[5] L. Seuront, F. Schmitt, Y. Lagadeuc, D. Schertzer, S. Lovejoy, S. Frontier. Multifractal structure of phytoplankton biomass and temperature in the ocean. Geophys. Res. Lett., 23 (1996), 3591-3594
[6] L. Seuront, F. Schmitt, D. Schertzer, Y. Lagadeuc, S. Lovejoy. Multifractal intermittency of Eulerian and Lagrangian turbulence of ocean temperature and plankton fields. Nonlin. Proc. Geophys., 3 (1996), 236-246.
[7] L. Seuront, F. Schmitt, Y. Lagadeuc, D. Schertzer, S. Lovejoy. Multifractal analysis as a tool to characterize multiscale inhomogeneous patterns. Example of phytoplankton distribution in turbulent coastal waters. J. Plankton Res., 21 (1999), 877-922.
[8] L. Seuront, V. Gentilhomme, Y. Lagadeuc. Small-scale nutrient patches in tidally mixed coastal waters. Mar. Ecol. Prog. Ser., 232 (2002), 29-44.
[9] D. Jou. Intermittent turbulence: a short introduction. Sci. Mar., 61 (1997), 57-62.
[10] J. Jimanez. Intermittency and cascades. Sci. Mar., 409 (2000), 99-120. · Zbl 0963.76041
[11] S. Lovejoy, W. J. S. Currie, Y. Tessier, M. R. Claereboudt, M. R. Bourget, E. Roff, D. Schertzer. Universal multifractals and ocean patchiness: phytoplankton, physical fields and coastal heterogeneity. J. Plankton Res., 23 (2001), 117-141.
[12] L. Seuront. Hydrodynamical and tidal controls of small-scale phytoplankton patchiness. Mar. Ecol. Prog. Ser., 302 (2005), 93-101.
[13] L. Seuront, Y. Lagadeuc. Multiscale patchiness of the calanoid copepod Temora longicornis in a turbulent coastal sea. J. Plankton Res., 23 (2001), 1137-1145.
[14] L. Seuront, F. G. Schmitt, M. C. Brewer, J. R. Strickler, S. Souissi. From random walk to multifractal random walk in zooplankton swimming behavior. Zool. Stud., 43 (2004), 8-19.
[15] L. Seuront, S. C. Leterme. Increased zooplankton behavioural stress in response to short-term exposure to hydrocarbon contamination. The Open Oceanography Journal, 1 (2007), 1-7. 35 L. SeurontMicroscale complexity in the ocean
[16] L. Seuront, A. C. Duponchel, C. Chapperon. Heavy-tailed distributions in the intermittent motion behaviour of the intertidal gastropod Littorina littorea. Physica A, 385 (2007), 573582.
[17] A. M. Obukhov. Some specific features of atmospheric turbulence. J. Fluid Mech., 13 (1962), 77-81. · Zbl 0133.44303
[18] A. N. Kolmogorov. A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech., 13 (1962), 82-85. · Zbl 0112.42003
[19] B. B. Mandelbrot. Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J. Fluid Mech., 62 (1974), 305-330. · Zbl 0289.76031
[20] B. B. Mandelbrot. Intermittent turbulence and fractal dimension: kurtosis and the spectral exponent 5/3 + . In: R. Teman (ed.), Turbulence and Naviers Stokes equations. Lectures notes in Mathematics, vol. 55, 121-145. Springer, 1976. · Zbl 0372.76043
[21] H. Yamazaki. Breakage models: lognormality and intermittency. J. Fluid Mech., 79 (1990), 159-165. · Zbl 0709.76061
[22] U. Frisch. Turbulence. Cambridge University Press, 1995.
[23] L. Seuront, H. Yamazaki, F. Schmitt. Intermittency. In: H. Baumert, J. Sundermann, J. Simpson (eds.), Marine Turbulences: Theories, Observations and Models. Cambridge University Press, Cambridge, 2005, 66-78.
[24] G. K. Batchelor. Small-scale variation of convected quantities like temperature in turbulent fluid, Part I. General discussion and the case of small conductivity, J. Fluid Mech., 1959, No. 5, 113. · Zbl 0085.39701
[25] R. W. Stewart. Turbulence. Cambridge University Press, Cambridge, 1969.
[26] H. Baumert, J. Sndermann, J. Simpson (eds.). Marine Turbulences: Theories, Observations and Models. Cambridge University Press, Cambridge, 2005.
[27] S. Pond, G.L. Pickard. Introductory dynamical oceanography. Butterworth-Heineman, Oxford, 1983.
[28] C. P. Summerhayes, S. A. Thorpe. Oceanography. An illustrated guide. Manson Publishing, London, 1996.
[29] T. Bohr, M. H. Jensen, G. Paladin, A. Vulpiani. Dynamical systems approach to turbulence. Cambridge University Press, 1998. · Zbl 0933.76002
[30] L. H. Kantha, C. A. Clayson. Small scale processes in geophysical fluid flows. International geophysics series, Vol. 67, 888 p., 2000. 36 L. SeurontMicroscale complexity in the ocean · Zbl 0989.76002
[31] S. B. Pope. Turbulent Flows. Cambridge University Press, Cambridge, 2000. · Zbl 0966.76002
[32] J. Jimanez. Oceanic turbulence at millimeter scales. Sci. Mar., 61 (1997), 47-56.
[33] M. Bohle-Carbonel. Pitfalls in sampling, comments on reliability and suggestions for simulation. Cont. Shelf Res., 12 (1992), 3-24.
[34] L. Seuront, Y. Lagadeuc. Towards a terminological consensus in ecology: variability, inhomogeneity and heterogeneity. J. Biol. Syst., 9 (2001), 81-87.
[35] E. Haeckel. Plakton studien. J. Zeitschriftfuer Naturwis., 25 (1891), 232-336.
[36] A. C. Hardy. Observation of the uneven distribution of oceanic plankton. Discovery Report, 1936, No. 11, 511-538.
[37] R. M. Cassie. An experimental study of factors inducing aggregation in marine plankton. New Zealand J. Sci., 2 (1959), 339-365.
[38] D. H. Cushing. Patchiness. Rapp. Cons. Int. Explor. Mer, 153 (1962), 152-163.
[39] R. M. Cassie. Microdistribution in the plankton. Oceanogr. Mar. Biol. Ann. Rev., 1 (1963), 223-252.
[40] J. G.Mitchell, J. A. Furhman. Centimeter scale vertical heterogeneity in bacteria and chlorophyll a. Mar. Ecol. Prog. Ser., 54 (1989), 141-148.
[41] P. K. Bjrnsen, T. G.Nielsen. Decimeter scale heterogeneity in the plankton during a pycnocline bloom of Gyrodinuim aureolum, Mar. Ecol. Prog. Ser., 73 (1991), 263-267.
[42] L. Seuront, Y. Lagadeuc. Characterisation of space-time variability in stratified and mixed coastal waters (Baie des Chaleurs, Quebec, Canada): application of fractal theory. Mar. Ecol. Prog. Ser., 159 (1997), 81-95.
[43] L. Seuront, Y. Lagadeuc. Spatio-temporal structure of tidally mixed coastal waters: variability and heterogeneity. J. Plankton Res., 20 (1998), 1387-1401.
[44] R. L. Waters, J. G. Mitchell. Centimeter-scale spatial structure of estuarine in vivo fluorescence profiles. Mar. Ecol. Prog. Ser., 237 (2002), 51-63.
[45] R. L. Waters, J. G. Mitchell, J. R. Seymour. Geostatistical characterization of centimetre-scale spatial structure of in vivo fluorescence. Mar. Ecol. Prog. Ser., 251 (2003), 49-58.
[46] M. Estrada, E. Berdalet. Phytoplankton in a turbulent world. Sci. Mar., 61 (1997), 125-140.
[47] L. Seuront, F.G. Schmitt, Y. Lagadeuc. Turbulence intermittency, small-scale phytoplankton patchiness and encounter rates in plankton: where do we go from here? Deep-Sea Res. I, 48 (2001), 1199-1215. 37 L. SeurontMicroscale complexity in the ocean
[48] H. Svendsen. Physical oceanography and marine ecosystems: some illustrative examples. Sci. Mar., 61 (1997), 93-108.
[49] L. P. Sanford. Turbulent mixing in experimental ecosystem studies. Mar. Ecol. Prog. Ser., 161 (1997), 265-293.
[50] G. K. Batchelor, A. A. Towsend. The nature of turbulent motion at large wavenumbers. Proc. R. Soc. A, 199 (1949), 238-250.
[51] D. C. Wilcox. Turbulence modeling for CFD. DCW Industries, 1998.
[52] A. N. Kolmogorov. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR, 30 (1941), 299-303.
[53] A. S. Monin, A. M. Yaglom. Statistical Fluid Mechanics: Mechanics of Turbulence. MIT Press, 1975.
[54] A. M. Obukhov. Spectral energy distribution in a turbulent flow. Dokl. Akad. Nauk. SSSR, 32 (1941), 22-24.
[55] A. M. Obukhov. Structure of the temperature field in a turbulent flow. Izv. Akad. Nauk SSSR., Geogr. I Jeofiz., 1949, No. 13, 55.
[56] S. Corrsin. On the spectrum of isotropic temperature in an isotropic turbulence. J. Appl. Phys., 22 (1951), 469-473. · Zbl 0044.40601
[57] A. S. Gurvich. Experimental research on frequency spectra of atmospheric turbulence. Izv. Akad. Nauk SSSR, geofiz. ser., 1960, 1042-1055.
[58] H. Yamazaki, J.G. Mitchell, L. Seuront, F. Wolk, H. Li. Phytoplankton microsctructure in fully developed oceanic turbulence. Geophys. Res. Lett., 33 (2006), L01603, doi:10.1029/2005GL024103.
[59] W. J. S. Currie, J.C. Roff. Plankton are not passive tracers: plankton in a turbulent environment. J. Geophys. Res., 111 (2006), C05S07, doi:10.1029/2005JC002967.
[60] L. Seuront, F. G. Schmitt. Multiscaling statistical procedures for the exploration of biophysical couplings in intermittent turbulence. Part I. Theory. Deep-Sea Res. II, 52 (2005), 13081324.
[61] A. M. Yaglom. Local structure of the temperature field in a turbulent flow. Dokl. Akad. Nauk SSSR, 69 (1949), 743. · Zbl 0036.25701
[62] L. F. Richardson. Weather prediction by numerical processes. Cambridge University Press, Cambridge, 1922. · JFM 48.0629.07
[63] A. M. Yaglom. The influence of fluctuations in energy dissipation on the shape of turbulent characteristics in the inertial interval. Sov. Phys. Dokl., 11 (1966), 26-29. 38 L. SeurontMicroscale complexity in the ocean
[64] A. S. Gurvich, A. M. Yaglom. Breakdown of eddies and probability distributions for smallscale turbulence. Phys. Fluids, 10 (1967), 59-65. · Zbl 0153.29902
[65] G. Paladin, A. Vulpiani. Anomalous scaling laws in multifractal objects. Phys. Rep., 156 (1987), 147-225.
[66] C. Meneveau, K. R. Sreenivasan. Simple multifractal cascade model for fully developed turbulence. Phys. Rev. Lett., 59 (1991), 1424-1427.
[67] W. Feller. An introduction to probability theory and its applications, Vol. II. Wiley, 1971. · Zbl 0219.60003
[68] D. Schertzer, S. Lovejoy. Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes. J. Geophys. Res., 92 (1987), 96-99.
[69] S. Kida. Log-stable distribution and intermittency of turbulence. J. Phys. Soc. Japan, 60 (1991), 5-8.
[70] M.F. Shlesinger, G.M. Zaslavsky, U. Frish (Eds.), Lvy Flights and Related Topics in Physics, Springer, Berlin, 1996
[71] B. Dubrulle. Intermittency in fully developed turbulence: log-Poisson statistics and generalized scale covariance. Phys. Rev. Lett., 73 (1994), 959-962.
[72] Z. S. She, E. C. Waymire. Quantized energy cascade and log-Poisson statistics in fully developed turbulence. Phys. Rev. Lett., 74 (1995), 262-265.
[73] B. Castaing, B. Dubrulle. Fully developed turbulence: a unifying point of view. J. Phys. II France, (1995), No. 5, 895-899.
[74] B. Dubrulle. Anomalous scaling and generic structure function in turbulence. J. Phys. II France, 2006, No. 6, 1825-1840.
[75] P. J. S. Franks. Plankton patchiness, turbulent transport and spatial spectra. Mar. Ecol. Prog. Ser., 294 (2005), 295-309.
[76] M. B. Priestley. Spectral analysis and time series. Academic Press, 1983. · Zbl 0537.93066
[77] P. Bloomfield. Fourier analysis of time series: an introduction. Wiley Interscience, 2000. · Zbl 0994.62093
[78] C. Chatfield. The analysis of time series: an introduction. Chapman & Hall/CRC, 2003. · Zbl 1027.62068
[79] H. Kantz, T. Schreiber. Nonlinear time series analysis. Cambridge University Press, 2004. · Zbl 1050.62093
[80] W. S. Wei. Time series analysis: univariate and multivariate methods. Addison Wesley, 2005.
[81] A. Tsuda, H. Sugisaki, T. Ishimaru, T. Saino, T. Sato. White-noise-like distribution of the oceanic copepod Neocalanus cristatus in the subarctic North Pacific. Mar. Ecol. Prog. Ser., (97) 1993, 39-46. 39 L. SeurontMicroscale complexity in the ocean
[82] D. G. Mountain, M. H. Taylor. Fluorescence structure in the region of the tidal mixing front on the southern flank of Georges Bank. Deep-Sea Res II, 43 (1996), 1831-1853.
[83] P. H. Wiebe, D. G. Mountain, T. K. Stanton, C. H. Greene, G. Lough, S. Kaartvedt, J. Dawson, N. Copley. Acoustical study of the spatial distribution of plankton on Georges Bank and the relationship between volume backscattering strength and the taxonomic composition of the plankton. Deep-Sea Res II, 43 (1996), 1971-2001.
[84] A. J. Pershing, P. H. Wiebe, J. P. Manning, N. J. Copley. Evidence for vertical circulation cells in the well-mixed area of Georges Bank and their biological implications. Deep-Sea Res. II, 48 (2001), 283-310.
[85] P. J. S. Franks, J. S. Jaffe. Microscale variability in the distributions of large fluorescent particles observed in situ with a planar laser imaging fluorometer. J. Mar. Syst., 69 (2008), 254-270.
[86] S. Corrsin. The reactant concentration spectrum in turbulent mixing with a first-order reaction. J. Fluid Mech., 11 (1961), 407-416. · Zbl 0111.39205
[87] K. L. Denman, T. Platt. The variance spectrum of phytoplankton in a turbulent ocean. J. Mar. Res., 34 (1976), 593-601.
[88] K. L. Denman, A. Okubo, T. Platt. The chlorophyll fluctuation spectrum in the sea. Limnol. Oceanogr., 22 (1977), 1033-1038.
[89] G. I. Taylor. The spectrum of turbulence. Proc. R. Soc. London Ser. A, 164 (1938), 476-490. · JFM 64.1454.02
[90] L. Seuront, F.G. Schmitt. Eulerian and Lagrangian properties of biophysical intermittency in the ocean. Geophysical Research Letters, 31 (2004), L03306, doi:10.1029/2003GL018185.
[91] H. Yamazaki, D. Mackas, K. Denman. Coupling small scale physical processes with biology. The Sea: Biological-Physical interaction in the Ocean, edited by A.R. Robinson, J.J. McCarthy and B.J. Rothschild, Chapter 3: 51-112, 2002.
[92] H. Yamazaki, K. Squires. Comparison of oceanic turbulence and copepod swimming. Mar. Ecol. Prog. Ser., 144 (1996), 299-301.
[93] L. Seuront, H. Yamazaki, S. Souissi. Hydrodynamic disturbance and zooplankton swimming behavior. Zoological Studies, 43 (2004), 377-388.
[94] L. E. Karp-Boss, E. Boss, P. A. Jumars. Nutrient fluxes to planktonic osmotrophs in the presence of fluid motion. Mar. Biol. Ann. Rev., 34 (1996), 71-107.
[95] M. C. Gregg. Uncertainties and limitations in measuring and {\(\chi\)}T. J. Atmos. Ocean. Tech., 16 (1990), 1483-1490. 40 L. SeurontMicroscale complexity in the ocean
[96] I. N. McCave. Size spectra and aggregation of suspended particles in the deep ocean. DeepSea Res., 31 (1990), 329-352.
[97] T. Kirboe. Small-scale turbulence, marine snow formation, and planktivorous feeding. Sci. Mar., 61 (1997), 141-158.
[98] W. D. Gardner. The flux of particles to the deep sea: methods, measurements and mechanisms. Oceanography, 10 (1997), 116-121.
[99] G. Jackson, A. Bird. Aggregation in the marine environment. Environ. Sci. Tech., 32 (1998), 2805-2814.
[100] T. Kirboe, , K. P. Andersen, H. Dam. Coagulation efficiency and aggregate formation in marine phytoplankton. Mar. Biol., 107 (1990), 235-245.
[101] B. J. Rothschild, T. R. Osborn. Small-scale turbulence and plankton contact rates. J. Plankton Res., 10 (1988), 465-474.
[102] T. Kirboe, E. Saiz. Planktivorous feeding in calm and turbulent environment, with emphasis on copepods. Mar. Ecol. Prog. Ser., 122 (1995), 135-145.
[103] A. W. Visser, B. R. MacKenzie. Turbulence-induced contact rates of plankton: the question of scale. Mar. Ecol. Prog. Ser., 166 (1998), 307-310. 41
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