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Estimates of the temperature flux–temperature gradient relation above a sea floor

Published online by Cambridge University Press:  18 March 2016

Andrea A. Cimatoribus Open the ORCID record for Andrea A. Cimatoribus [Opens in a new window]  and
H. van Haren
Andrea A. Cimatoribus
Affiliation:
Royal Netherlands Institute for Sea Research, Landsdiep 4, 1797SZ, ’t Horntje, NH, The Netherlands
H. van Haren
Affiliation:
Royal Netherlands Institute for Sea Research, Landsdiep 4, 1797SZ, ’t Horntje, NH, The Netherlands
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Abstract

The relation between the flux of temperature (or buoyancy), the vertical temperature gradient and the height above the bottom is investigated in an oceanographic context, using high-resolution temperature measurements. The model for the evolution of a stratified layer by Balmforth et al. (J. Fluid Mech., vol. 355, 1998, pp. 329–358) is reviewed and adapted to the case of a turbulent flow above a wall. Model predictions are compared with the average observational estimates of the flux, exploiting a flux estimation method proposed by Winters & D’Asaro (J. Fluid Mech., vol. 317, 1996, pp. 179–193). This estimation method enables the disentanglement of the dependence of the average flux on the height above the bottom and on the background temperature gradient. The classical N-shaped flux–gradient relation is found in the observations. The model and the observations show similar qualitative behaviour, despite the strong simplifications used in the model. The results shed light on the modulation of the temperature flux by the presence of the boundary, and support the idea of a turbulent flux following a mixing-length argument in a stratified flow. Furthermore, the results support the use of Thorpe scales close to a boundary, if sufficient averaging is performed, suggesting that the Thorpe scales are affected by the boundary in a similar way to the mixing length.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Turbulent Flows: Stratified turbulence
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Papers
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Journal of Fluid Mechanics , Volume 793 , 25 April 2016 , pp. 504 - 523
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© 2016 Cambridge University Press 

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References

Baker, M. A. & Gibson, C. H. 1987 Sampling turbulence in the stratified ocean: statistical consequences of strong intermittency. J. Phys. Oceanogr. 17, 1817–1836.2.0.CO;2>CrossRefGoogle Scholar
Balmforth, N. J., Llewellyn Smith, S. G. & Young, W. R. 1998 Dynamics of interfaces and layers in a stratified turbulent fluid. J. Fluid Mech. 355, 329–358.CrossRefGoogle Scholar
Billant, P. & Chomaz, J.-M. 2000 Experimental evidence for a new instability of a vertical columnar vortex pair in a strongly stratified fluid. J. Fluid Mech. 418, 167–188.CrossRefGoogle Scholar
Chalamalla, V. K. & Sarkar, S. 2015 Mixing, dissipation rate, and their overturn-based estimates in a near-bottom turbulent flow driven by internal tides. J. Phys. Oceanogr. 45, 1969–1987.CrossRefGoogle Scholar
Cimatoribus, A. A. & van Haren, H. 2015 Temperature statistics above a deep-ocean sloping boundary. J. Fluid Mech. 775, 415–435.CrossRefGoogle Scholar
Cimatoribus, A. A., van Haren, H. & Gostiaux, L. 2014 Comparison of Ellison and Thorpe scales from Eulerian ocean temperature observations. J. Geophys. Res. 119, 7047–7065.CrossRefGoogle Scholar
Dillon, T. M. 1982 Vertical overturns: a comparison of Thorpe and Ozmidov length scales. J. Geophys. Res. 87, 9601–9613.CrossRefGoogle Scholar
Gargett, A. E. 1989 Ocean turbulence. Annu. Rev. Fluid Mech. 21, 419–451.CrossRefGoogle Scholar
Gregg, M. C. 1987 Diapycnal mixing in the thermocline: a review. J. Geophys. Res. 92, 5249–5286.Google Scholar
van Haren, H., Cimatoribus, A. & Gostiaux, L. 2015 Where large deep-ocean waves break. Geophys. Res. Lett. 42 (7), 2351–2357.CrossRefGoogle Scholar
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. Oceanic Engng 34, 315–322.CrossRefGoogle Scholar
Holford, J. M. & Linden, P. F. 1999 Turbulent mixing in a stratified fluid. Dyn. Atmos. Oceans 30, 173–198.CrossRefGoogle Scholar
Itsweire, E. C. 1984 Measurements of vertical overturns in a stably stratified turbulent flow. Phys. Fluids 27, 764–766.CrossRefGoogle Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics, vol. 6. Elsevier.Google Scholar
Martin, J. E. & Rehmann, C. R. 2006 Layering in a flow with diffusively stable temperature and salinity stratification. J. Phys. Oceanogr. 36, 1457–1470.CrossRefGoogle Scholar
Mater, B. D. & Venayagamoorthy, S. K. 2014 The quest for an unambiguous parameterization of mixing efficiency in stably stratified geophysical flows. Geophys. Res. Lett. 41, 4646–4653.CrossRefGoogle Scholar
Mater, B. D., Venayagamoorthy, S. K., Laurent, L. St & Moum, J. N. 2015 Biases in Thorpe-scale estimates of turbulence dissipation. Part I: Assessments from large-scale overturns in oceanographic data. J. Phys. Oceanogr. 45, 2497–2521.CrossRefGoogle Scholar
Munk, W. H. 1966 Abyssal recipes. Deep-Sea Res. 13, 707–730.Google Scholar
Osborn, T. R. & Cox, C. S. 1972 Oceanic fine structure. Geophys. Fluid Dyn. 3, 321–345.CrossRefGoogle Scholar
Park, Y.-G., Whitehead, J. A. & Gnanadeskian, A. 1994 Turbulent mixing in stratified fluids: layer formation and energetics. J. Fluid Mech. 279, 279–311.CrossRefGoogle Scholar
Phillips, O. M. 1972 Turbulence in a strongly stratified fluid – is it unstable? Deep-Sea Res. 19, 79–81.Google Scholar
Pinton, J.-F. & Labbé, R. 1994 Correction to the Taylor hypothesis in swirling flows. J. Phys. II 4, 1461–1468.Google Scholar
Posmentier, E. S. 1977 The generation of salinity finestructure by vertical diffusion. J. Phys. Oceanogr. 7, 298–300.2.0.CO;2>CrossRefGoogle Scholar
Prandtl, L. 1935 The mechanics of viscous fluids. In Aeordynamics Theory (ed. Durand, W. F.), vol. 3, pp. 34–208. Springer.CrossRefGoogle Scholar
Ruddick, B., Anis, A. & Thompson, K. 2000 Maximum likelihood spectral fitting: the Batchelor spectrum. J. Atmos. Ocean. Technol. 17, 1541–1555.2.0.CO;2>CrossRefGoogle Scholar
Ruddick, B. R., Mcdougall, T. J. & Turner, J. S. 1989 The formation of layers in a uniformly stirred density gradient. Deep-Sea Res. A 36, 597–609.CrossRefGoogle Scholar
Scotti, A. 2015 Biases in Thorpe-scale estimates of turbulence dissipation. Part II: energetics arguments and turbulence simulations. J. Phys. Oceanogr. 45, 2522–2543.CrossRefGoogle Scholar
Thorpe, S. A. 1977 Turbulence and mixing in a Scottish loch. Phil. Trans. R. Soc. Lond. A 286, 125–181.Google Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–240.CrossRefGoogle Scholar
Winters, K. B. & D’Asaro, E. A. 1996 Diascalar flux and the rate of fluid mixing. J. Fluid Mech. 317, 179–193.CrossRefGoogle Scholar
Wunsch, S. & Kerstein, A. 2001 A model for layer formation in stably stratified turbulence. Phys. Fluids 13, 702–712.CrossRefGoogle Scholar
Zhou, X. H. & Gao, S. 1997 Confidence intervals for the log-normal mean. Stat. Med. 16, 783–790.3.0.CO;2-2>CrossRefGoogle ScholarPubMed