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

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


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.



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Baker, M. A. & Gibson, C. H. 1987 Sampling turbulence in the stratified ocean: statistical consequences of strong intermittency. J. Phys. Oceanogr. 17, 18171836.
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, 329358.
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, 167188.
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, 19691987.
Cimatoribus, A. A. & van Haren, H. 2015 Temperature statistics above a deep-ocean sloping boundary. J. Fluid Mech. 775, 415435.
Cimatoribus, A. A., van Haren, H. & Gostiaux, L. 2014 Comparison of Ellison and Thorpe scales from Eulerian ocean temperature observations. J. Geophys. Res. 119, 70477065.
Dillon, T. M. 1982 Vertical overturns: a comparison of Thorpe and Ozmidov length scales. J. Geophys. Res. 87, 96019613.
Gargett, A. E. 1989 Ocean turbulence. Annu. Rev. Fluid Mech. 21, 419451.
Gregg, M. C. 1987 Diapycnal mixing in the thermocline: a review. J. Geophys. Res. 92, 52495286.
van Haren, H., Cimatoribus, A. & Gostiaux, L. 2015 Where large deep-ocean waves break. Geophys. Res. Lett. 42 (7), 23512357.
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, 315322.
Holford, J. M. & Linden, P. F. 1999 Turbulent mixing in a stratified fluid. Dyn. Atmos. Oceans 30, 173198.
Itsweire, E. C. 1984 Measurements of vertical overturns in a stably stratified turbulent flow. Phys. Fluids 27, 764766.
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics, vol. 6. Elsevier.
Martin, J. E. & Rehmann, C. R. 2006 Layering in a flow with diffusively stable temperature and salinity stratification. J. Phys. Oceanogr. 36, 14571470.
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, 46464653.
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, 24972521.
Munk, W. H. 1966 Abyssal recipes. Deep-Sea Res. 13, 707730.
Osborn, T. R. & Cox, C. S. 1972 Oceanic fine structure. Geophys. Fluid Dyn. 3, 321345.
Park, Y.-G., Whitehead, J. A. & Gnanadeskian, A. 1994 Turbulent mixing in stratified fluids: layer formation and energetics. J. Fluid Mech. 279, 279311.
Phillips, O. M. 1972 Turbulence in a strongly stratified fluid – is it unstable? Deep-Sea Res. 19, 7981.
Pinton, J.-F. & Labbé, R. 1994 Correction to the Taylor hypothesis in swirling flows. J. Phys. II 4, 14611468.
Posmentier, E. S. 1977 The generation of salinity finestructure by vertical diffusion. J. Phys. Oceanogr. 7, 298300.
Prandtl, L. 1935 The mechanics of viscous fluids. In Aeordynamics Theory (ed. Durand, W. F.), vol. 3, pp. 34208. Springer.
Ruddick, B., Anis, A. & Thompson, K. 2000 Maximum likelihood spectral fitting: the Batchelor spectrum. J. Atmos. Ocean. Technol. 17, 15411555.
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, 597609.
Scotti, A. 2015 Biases in Thorpe-scale estimates of turbulence dissipation. Part II: energetics arguments and turbulence simulations. J. Phys. Oceanogr. 45, 25222543.
Thorpe, S. A. 1977 Turbulence and mixing in a Scottish loch. Phil. Trans. R. Soc. Lond. A 286, 125181.
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.
Wunsch, S. & Kerstein, A. 2001 A model for layer formation in stably stratified turbulence. Phys. Fluids 13, 702712.
Zhou, X. H. & Gao, S. 1997 Confidence intervals for the log-normal mean. Stat. Med. 16, 783790.
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Estimates of the temperature flux–temperature gradient relation above a sea floor

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


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