Skip to main content

Temperature statistics above a deep-ocean sloping boundary

  • Andrea A. Cimatoribus (a1) and H. van Haren (a1)

We present a detailed analysis of temperature statistics in an oceanographic observational dataset. The data are collected using a moored array of thermistors, $100~\text{m}$ tall and starting $5~\text{m}$ above the bottom, deployed during four months above the slopes of a Seamount in the north-eastern Atlantic Ocean. Turbulence at this location is strongly affected by the semidiurnal tidal wave. Mean stratification is stable in the entire dataset. We compute structure functions, of order up to 10, of the distributions of temperature increments. Strong intermittency is observed, in particular, during the downslope phase of the tide, and farther from the solid bottom. In the lower half of the mooring during the upslope phase, the temperature statistics are consistent with those of a passive scalar. In the upper half of the mooring, the temperature statistics deviate from those of a passive scalar, and evidence of turbulent convective activity is found. The downslope phase is generally thought to be more shear-dominated, but our results suggest on the other hand that convective activity is present. High-order moments also show that the turbulence scaling behaviour breaks at a well-defined scale (of the order of the buoyancy length scale), which is however dependent on the flow state (tidal phase, height above the bottom). At larger scales, wave motions are dominant. We suggest that our results could provide an important reference for laboratory and numerical studies of mixing in geophysical flows.

Corresponding author
Email address for correspondence:
Hide All
Alford, M. H. & Pinkel, R. 2000 Observations of overturning in the thermocline: the context of ocean mixing. J. Phys. Oceanogr. 30, 805832.
Billant, P. & Chomaz, J.-M. 2001 Self-similarity of strongly stratified inviscid flows. Phys. Fluids 13, 16451651.
Brethouwer, G. & Lindborg, E. 2008 Passive scalars in stratified turbulence. Geophys. Res. Lett. 35, L06809.
Celani, A., Lanotte, A., Mazzino, A. & Vergassola, M. 2001 Fronts in passive scalar turbulence. Phys. Fluids 13, 17681783.
Celani, A., Matsumoto, T., Mazzino, A. & Vergassola, M. 2002 Scaling and universality in turbulent convection. Phys. Rev. Lett. 88, 054503.
Ching, E. S. 1991 Probabilities for temperature differences in Rayleigh–Bénard convection. Phys. Rev. A 44, 36223629.
Cimatoribus, A. A., van Haren, H. & Gostiaux, L. 2014 Comparison of Ellison and Thorpe scales from Eulerian ocean temperature observations. J. Geophys. Res.–Oceans 119, 70477065.
Costa Frola, E., Mazzino, A., Cassola, F., Mortarini, L. & Ferrero, E. 2014 An experimental study of the statistics of temperature fluctuations in the atmospheric boundary layer. Boundary-Layer Meteorol. 150, 91106.
Davis, A., Marshak, A., Wiscombe, W. & Cahalan, R. 1994 Multifractal characterizations of nonstationarity and intermittency in geophysical fields: observed, retrieved, or simulated. J. Geophys. Res.–Atmos. 99, 80558072.
Frisch, U. 1996 Turbulence. Cambridge University Press.
Garrett, C. 1990 The role of secondary circulation in boundary mixing. J. Geophys. Res.–Oceans 95, 31813188.
Garrett, C. 1991 Marginal mixing theories. Atmos. Ocean 29, 313339.
Gayen, B. & Sarkar, S. 2011a Boundary mixing by density overturns in an internal tidal beam. Geophys. Res. Lett. 38, L14608.
Gayen, B. & Sarkar, S. 2011b Negative turbulent production during flow reversal in a stratified oscillating boundary layer on a sloping bottom. Phys. Fluids 23, 101703.
van Haren, H. 2013 Stratified turbulence and small-scale internal waves above deep-ocean topography. Phys. Fluids 25, 106604.
van Haren, H. & Gostiaux, L. 2009 High-resolution open-ocean temperature spectra. J. Geophys. Res.–Oceans 114, C05005.
van Haren, H. & Gostiaux, L. 2010 A deep-ocean Kelvin–Helmholtz billow train. Geophys. Res. Lett. 37 (3), L03605.
van Haren, H. & Gostiaux, L. 2012 Detailed internal wave mixing above a deep-ocean slope. J. Mar. Res. 70, 173197.
van Haren, H., Laan, M., Buijsman, D.-J., Gostiaux, L., Smit, M. G. & Keijzer, E. 2009 NIOZ3: independent temperature sensors sampling yearlong data at a rate of 1 Hz. IEEE J. Ocean. Engng 34, 315322.
van Haren, H., Oakey, N. & Garrett, C. 1994 Measurements of internal wave band eddy fluxes above a sloping bottom. J. Mar. Res. 52, 909946.
Lamb, K. G. 2014 Internal wave breaking and dissipation mechanisms on the continental slope/shelf. Annu. Rev. Fluid Mech. 46, 231254.
Lindborg, E. & Fedina, E. 2009 Vertical turbulent diffusion in stably stratified flows. Geophys. Res. Lett. 36, L01605.
Moum, J. N., Perlin, A., Klymak, J. M., Levine, M. D., Boyd, T. & Kosro, P. M. 2004 Convectively driven mixing in the bottom boundary layer. J. Phys. Oceanogr. 34, 21892202.
Munk, W. H. 1966 Abyssal recipes. Deep-Sea Res. 13, 707730.
Munk, W. & Wunsch, C. 1998 Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res. I 45, 19772010.
Mydlarski, L. & Warhaft, Z. 1998 Passive scalar statistics in high-Péclet-number grid turbulence. J. Fluid Mech. 358, 135175.
Osborn, T. R. & Cox, C. S. 1972 Oceanic fine structure. Geophys. Fluid Dyn. 3, 321345.
Pinton, J.-F. & Labbé, R. 1994 Correction to the Taylor hypothesis in swirling flows. J. Phys. (Paris) II 4, 14611468.
Riley, J. J. & Lindborg, E. 2008 Stratified turbulence: a possible interpretation of some geophysical turbulence measurements. J. Atmos. Sci. 65, 24162424.
Rorai, C., Mininni, P. D. & Pouquet, A. 2014 Turbulence comes in bursts in stably stratified flows. Phys. Rev. E 89, 043002.
Seuront, L., Schmitt, F., Schertzer, D., Lagadeuc, Y. & Lovejoy, S. 1999 Multifractal intermittency of Eulerian and Lagrangian turbulence of ocean temperature and plankton fields. Nonlinear Process. Geophys. 3, 236246.
Shraiman, B. I. & Siggia, E. D. 2000 Scalar turbulence. Nature 405, 639646.
Slinn, D. N. & Levine, M. D.2003 Modeling internal tides and mixing over ocean ridges. In Near-Boundary Processes and Their Parameterization: Proceedings of 13th ‘Aha Huliko’, a Hawaiian Winter Workshop, pp. 59–68.
Smyth, W. & Moum, J. 2012 Ocean mixing by Kelvin–Helmholtz instability. Oceanography 25, 140149.
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Thoroddsen, S. T. & Van Atta, C. W. 1992 Exponential tails and skewness of density-gradient probability density functions in stably stratified turbulence. J. Fluid Mech. 244, 547566.
Thorpe, S. A. 2012 On the Kelvin–Helmholtz route to turbulence. J. Fluid Mech. 708, 14.
Thorpe, S. A., Curé, M. & White, M. 1991 The skewness of temperature derivatives in oceanic boundary layers. J. Phys. Oceanogr. 21, 428433.
Thorpe, S. A., Hall, P. & White, M. 1990 The variability of mixing at the continental slope. Phil. Trans. R. Soc. Lond. A 331 (1616), 183194.
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203240.
Winters, K. B. & D’Asaro, E. A. 1996 Diascalar flux and the rate of fluid mixing. J. Fluid Mech. 317, 179193.
Zhai, X., Johnson, H. L. & Marshall, D. P. 2010 Significant sink of ocean-eddy energy near western boundaries. Nat. Geosci. 3, 608612.
Zhou, S.-Q. & Xia, K.-Q. 2002 Plume statistics in thermal turbulence: mixing of an active scalar. Phys. Rev. Lett. 89, 184502.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed