Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-06-02T06:15:20.466Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of tidal force and topography on horizontal convection

Published online by Cambridge University Press:  09 December 2021

Guang-Yu Ding Open the ORCID record for Guang-Yu Ding [Opens in a new window] ,
Yu-Hao He  and
Ke-Qing Xia Open the ORCID record for Ke-Qing Xia [Opens in a new window]
Guang-Yu Ding
Affiliation:
Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China Department of Physics, The Chinese University of Hong Kong, Hong Kong, PR China
Yu-Hao He
Affiliation:
Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China Department of Physics, The Chinese University of Hong Kong, Hong Kong, PR China
Ke-Qing Xia*
Affiliation:
Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China Department of Physics, The Chinese University of Hong Kong, Hong Kong, PR China Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology, Shenzhen518055, PR China
*
†Email address for correspondence: xiakq@sustech.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a numerical study on how tidal force and topography influence flow dynamics, transport and mixing in horizontal convection. Our results show that local energy dissipation near topography will be enhanced when the tide is sufficiently strong. Such enhancement is related to the height of the topography and increases as the tidal frequency $\omega$ decreases. The global dissipation is found to be less sensitive to the changes in $\omega$ when the latter becomes small and asymptotically approaches a constant value. We interpret the behaviour of the dissipation as a result of the competition among the dominant forces in the system. According to which mechanism prevails, the flow state of the system can be divided into three regimes, which are the buoyancy-, tide- and drag-control regimes. We show that the mixing efficiency $\eta$ for different tidal energy and topography height can be well described by a universal function $\eta \approx \eta _{HC}/(1+\mathcal {R})$, where $\eta _{HC}$ is the mixing efficiency in the absence of tide and $\mathcal {R}$ is the ratio between tidal and available potential energy inputs. With this, one can also determine the dominant mechanism at a certain ocean region. We further derive a power law relationship connecting the mixing coefficient and the tidal Reynolds number.

JFM classification

Convection: Buoyancy-driven instability Geophysical and Geological Flows: Topographic effects
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 932 , 10 February 2022 , A38
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

Bretherton, F.P. 1966 The propagation of groups of internal gravity waves in a shear flow. Q. J. R. Meteorol. Soc. 92 (394), 466–480.CrossRefGoogle Scholar
Caldwell, D.R. & Mourn, J.N. 1995 Turbulence and mixing in the ocean. Rev. Geophys. 33 (2 S), 1385–1394.CrossRefGoogle Scholar
Chong, K.-L., Ding, G. & Xia, K.-Q. 2018 Multiple-resolution scheme in finite-volume code for active or passive scalar turbulence. J. Comput. Phys. 375, 1045–1058.CrossRefGoogle Scholar
Egbert, G.D. & Ray, R.D. 2000 Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data. Nature 405 (6788), 775–778.CrossRefGoogle ScholarPubMed
Fadlun, E.A., Verzicco, R., Orlandi, P. & Mohd-Yusof, J. 2000 Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161 (1), 35–60.CrossRefGoogle Scholar
Garrett, C. & Kunze, E. 2007 Internal tide generation in the deep ocean. Annu. Rev. Fluid Mech. 39 (1), 57–87.CrossRefGoogle Scholar
Gayen, B., Griffiths, R.W., Hughes, G.O. & Saenz, J.A. 2013 Energetics of horizontal convection. J. Fluid Mech. 716, R10.CrossRefGoogle Scholar
Gregg, M.C., D'Asaro, E.A., Riley, J.J. & Kunze, E. 2018 Mixing efficiency in the ocean. Annu. Rev. Mar. Sci. 10 (1), 443–473.CrossRefGoogle ScholarPubMed
Hazewinkel, J., Paparella, F. & Young, W.R. 2012 Stressed horizontal convection. J. Fluid Mech. 692, 317–331.CrossRefGoogle Scholar
Heywood, K.J., Naveira Garabato, A.C. & Stevens, D.P. 2002 High mixing rates in the abyssal Southern Ocean. Nature 415 (6875), 1011–1014.CrossRefGoogle ScholarPubMed
Huang, R.X. 1999 Mixing and energetics of the oceanic thermohaline circulation. J. Phys. Oceanogr. 29 (4), 727–746.2.0.CO;2>CrossRefGoogle Scholar
Hughes, G.O. & Griffiths, R.W. 2008 Horizontal convection. Annu. Rev. Fluid Mech. 40 (1), 185–208.CrossRefGoogle Scholar
Hughes, G.O., Hogg, A.M. & Griffiths, R.W. 2009 Available potential energy and irreversible mixing in the meridional overturning circulation. J. Phys. Oceanogr. 39 (12), 3130–3146.CrossRefGoogle Scholar
Kaczorowski, M., Chong, K.-L. & Xia, K.-Q. 2014 Turbulent flow in the bulk of Rayleigh–Bénard convection: aspect-ratio dependence of the small-scale properties. J. Fluid Mech. 747, 73–102.CrossRefGoogle Scholar
Kaczorowski, M. & Xia, K.-Q. 2013 Turbulent flow in the bulk of Rayleigh–Bénard convection: small-scale properties in a cubic cell. J. Fluid Mech. 722, 596–617.CrossRefGoogle Scholar
Killworth, P.D. & Manins, P.C. 1980 A model of confined thermal convection driven by non-uniform heating from below. J. Fluid Mech. 98 (03), 587–607.CrossRefGoogle Scholar
Kuhlbrodt, T., Griesel, A., Montoya, M., Levermann, A., Hofmann, M. & Rahmstorf, S. 2007 On the driving processes of the Atlantic meridional overturning circulation. Atlantic 45 (2004), RG2001.Google Scholar
Kundu, P.K., Cohen, I.M. & Dowling, D.R. 2016 Fluid Mechanics, 6th edn, pp. 349–407. Academic.CrossRefGoogle Scholar
Lamb, K.G. 2014 Internal wave breaking and dissipation mechanisms on the continental slope/shelf. Annu. Rev. Fluid Mech. 46 (1), 231–254.CrossRefGoogle Scholar
Ledwell, J.R., Montgomery, E.T., Polzin, K.L., St. Laurent, L.C., Schmitt, R.W. & Toole, J.M. 2000 Evidence for enhanced mixing over rough topography in the abyssal ocean. Nature 403 (6766), 179–182.CrossRefGoogle ScholarPubMed
Li, G., Cheng, L., Zhu, J., Trenberth, K.E., Mann, J.E. & Abraham, J.P. 2020 Increasing ocean stratification over the past half-century. Nat. Clim. Change 10 (12), 1116–1123.CrossRefGoogle Scholar
Lorenz, E.N. 1955 Available potential energy and the maintenance of the general circulation. Tellus 7 (2), 157–167.CrossRefGoogle Scholar
Mashayek, A., Ferrari, R., Vettoretti, G. & Peltier, W.R. 2013 The role of the geothermal heat flux in driving the abyssal ocean circulation. Geophys. Res. Lett. 40 (12), 3144–3149.CrossRefGoogle Scholar
Mathur, M. & Peacock, T. 2009 Internal wave beam propagation in non-uniform stratifications. J. Fluid Mech. 639, 133–152.CrossRefGoogle Scholar
Monismith, S.G., Koseff, J.R. & White, B.L. 2018 Mixing efficiency in the presence of stratification: when is it constant? Geophys. Res. Lett. 45 (11), 5627–5634.CrossRefGoogle Scholar
Mullarney, J.C., Griffiths, R.W. & Hughes, G.O. 2004 Convection driven by differential heating at a horizontal boundary. J. Fluid Mech. 516, 181–209.CrossRefGoogle Scholar
Munk, W. & Wunsch, C. 1998 Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res. 45 (12), 1977–2010.CrossRefGoogle Scholar
Munk, W.H. 1966 Abyssal recipes. Deep-Sea Res. 13 (4), 707–730.Google Scholar
Nycander, J. 2005 Generation of internal waves in the deep ocean by tides. J. Geophys. Res. 110 (10), 1–9.Google Scholar
Paparella, F. & Young, W.R. 2002 Horizontal convection is non-turbulent. J. Fluid Mech. 466, 205–214.CrossRefGoogle Scholar
Peltier, W.R. & Caulfield, C.P. 2003 Mixing efficiency in stratified shear flows. Annu. Rev. Fluid Mech. 35 (1), 135–167.CrossRefGoogle Scholar
Polzin, K.L., Toole, J.M., Ledwell, J.R. & Schmitt, R.W. 1997 Spatial variability of turbulent mixing in the abyssal ocean. Science 276 (5309), 93–96.CrossRefGoogle ScholarPubMed
Poulain, P.-M. & Centurioni, L. 2015 Direct measurements of World Ocean tidal currents with surface drifters. J. Geophys. Res. 120 (10), 6986–7003.CrossRefGoogle Scholar
Rossby, H.T. 1965 On thermal convection driven by non-uniform heating from below: an experimental study. Deep-Sea Res. 12 (1), 9–16.Google Scholar
Saenz, J.A., Hogg, A.M., Hughes, G.O. & Griffiths, R.W. 2012 Mechanical power input from buoyancy and wind to the circulation in an ocean model. Geophys. Res. Lett. 39 (13), L13605.CrossRefGoogle Scholar
Salehipour, H. & Peltier, W.R. 2015 Diapycnal diffusivity, turbulent Prandtl number and mixing efficiency in Boussinesq stratified turbulence. J. Fluid Mech. 775 (May), 464–500.CrossRefGoogle Scholar
Sarkar, S. & Scotti, A. 2017 From topographic internal gravity waves to turbulence. Annu. Rev. Fluid Mech. 49 (1), 195–220.CrossRefGoogle Scholar
Scott, J.R., Marotzke, J. & Adcroft, A. 2001 Geothermal heating and its influence on the meridional overturning circulation. J. Geophys. Res. 106 (C12), 31141–31154.CrossRefGoogle Scholar
Scotti, A. & White, B. 2011 Is horizontal convection really non-turbulent? Geophys. Res. Lett. 38 (21), L21609.CrossRefGoogle Scholar
Shishkina, O. 2017 Mean flow structure in horizontal convection. J. Fluid Mech. 812, 525–540.CrossRefGoogle Scholar
Shishkina, O., Grossmann, S. & Lohse, D. 2016 Heat and momentum transport scalings in horizontal convection. Geophys. Res. Lett. 43 (3), 1219–1225.CrossRefGoogle Scholar
Siggers, J.H., Kerswell, R.R. & Balmforth, N.J. 2004 Bounds on horizontal convection. J. Fluid Mech. 517, 55–70.CrossRefGoogle Scholar
Smyth, W.D. & Moum, J.N. 2000 Length scales of turbulence in stably stratified mixing layers. Phys. Fluids 12 (6), 1327–1342.CrossRefGoogle Scholar
Sohail, T., Gayen, B. & Hogg, A.M.C. 2018 Convection enhances mixing in the Southern Ocean. Geophys. Res. Lett. 45 (9), 4198–4207.CrossRefGoogle Scholar
Tailleux, R. 2009 On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models and the ocean heat engine controversy. J. Fluid Mech. 638, 339–382.CrossRefGoogle Scholar
Wang, F., Huang, S.-D. & Xia, K.-Q. 2018 Contribution of surface thermal forcing to mixing in the ocean. J. Geophys. Res. 123 (2), 855–863.CrossRefGoogle Scholar
Wang, F., Huang, S.-D., Zhou, S.-Q. & Xia, K.-Q. 2016 Laboratory simulation of the geothermal heating effects on ocean overturning circulation. J. Geophys. Res. 121 (10), 7589–7598.CrossRefGoogle Scholar
Wang, W. & Huang, R.X. 2005 An experimental study on thermal circulation driven by horizontal differential heating. J. Fluid Mech. 540, 49–73.CrossRefGoogle Scholar
Waterhouse, A.F., et al. 2014 Global patterns of diapycnal mixing from measurements of the turbulent dissipation rate. J. Phys. Oceanogr. 44 (7), 1854–1872.CrossRefGoogle Scholar
Whitehead, J.A. 1995 Thermohaline ocean processes and models. Annu. Rev. Fluid Mech. 27 (1), 89–113.CrossRefGoogle Scholar
Winters, K.B., Lombard, P.N., Riley, J.J. & D'Asaro, E.A. 1995 Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. 289, 115–128.CrossRefGoogle Scholar
Winters, K.B. & Young, W.R. 2009 Available potential energy and buoyancy variance in horizontal convection. J. Fluid Mech. 629, 221–230.CrossRefGoogle Scholar
Wunsch, C. 2000 Moon, tides and climate. Nature 405 (6788), 743–744.CrossRefGoogle ScholarPubMed
Wunsch, C. & Ferrari, R. 2004 Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36 (1), 281–314.CrossRefGoogle Scholar