Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-25T07:21:54.969Z Has data issue: false hasContentIssue false
  • English
  • Français

Application of a model of internal hydraulic jumps

Published online by Cambridge University Press:  17 November 2017

S. A. Thorpe Open the ORCID record for S. A. Thorpe [Opens in a new window] ,
J. Malarkey ,
G. Voet ,
M. H. Alford ,
J. B. Girton  and
G. S. Carter
S. A. Thorpe*
Affiliation:
School of Ocean Sciences, Bangor University, Menai Bridge, Anglesey LL59 5AB, UK
J. Malarkey
Affiliation:
School of Ocean Sciences, Bangor University, Menai Bridge, Anglesey LL59 5AB, UK
G. Voet
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, CA 92093, USA
M. H. Alford
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, CA 92093, USA
J. B. Girton
Affiliation:
Applied Physics Laboratory, University of Washington, Seattle, WA 98105, USA
G. S. Carter
Affiliation:
Department of Oceanography, University of Hawaii, Honolulu, HI 96822, USA
*
†Email address for correspondence: s.a.thorpe@bangor.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

A model devised by Thorpe & Li (J. Fluid Mech., vol. 758, 2014, pp. 94–120) that predicts the conditions in which stationary turbulent hydraulic jumps can occur in the flow of a continuously stratified layer over a horizontal rigid bottom is applied to, and its results compared with, observations made at several locations in the ocean. The model identifies two positions in the Samoan Passage at which hydraulic jumps should occur and where changes in the structure of the flow are indeed observed. The model predicts the amplitude of changes and the observed mode 2 form of the transitions. The predicted dissipation of turbulent kinetic energy is also consistent with observations. One location provides a particularly well-defined example of a persistent hydraulic jump. It takes the form of a 390 m thick and 3.7 km long mixing layer with frequent density inversions separated from the seabed by some 200 m of relatively rapidly moving dense water, thus revealing the previously unknown structure of an internal hydraulic jump in the deep ocean. Predictions in the Red Sea Outflow in the Gulf of Aden are relatively uncertain. Available data, and the model predictions, do not provide strong support for the existence of hydraulic jumps. In the Mediterranean Outflow, however, both model and data indicate the presence of a hydraulic jump.

JFM classification

Geophysical and Geological Flows: Hydraulic control Geophysical and Geological Flows: Stratified flows Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 834 , 10 January 2018 , pp. 125 - 148
Check for updates
Copyright
© 2017 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

Afanasyev, YA.D. & Peltier, W. R. 1998 The three-dimensionalization of stratified flows over two-dimensional topography. J. Atmos. Sci. 55, 19–39.Google Scholar
Alford, M. H., Girton, J. B., Voet, G., Carter, G. S., Mickett, B. & Klymak, J. M. 2013 Turbulent mixing and hydraulic control of abyssal water in the Samoan Passage. Geophys. Res. Lett. 40, 4668–4674.CrossRefGoogle Scholar
Armi, L. & Mayr, G. T. 2011 The descending stratified flow and hydraulic jump in the lee of the Sierras. J. Appl. Meteorol. Climatol. 50, 1995–2011.Google Scholar
Baines, P. G. 1995 Topographic Effects in Stratified Flows, p. 482. Cambridge University Press.Google Scholar
Baines, P. G. 2016 Internal hydraulic jumps in two-layer systems. J. Fluid Mech. 787, 1–15.Google Scholar
Doyle, J. D. & Durran, D. R. 2007 Rotor and subrotor dynamics in the lee of three-dimensional terrain. J. Atmos. Sci. 64, 4202–4221.Google Scholar
Farmer, D. M. & Armi, L. 1999 Stratified flow over topography: the role of small-scale entrainment and mixing in flow establishment. Proc. R. Soc. Lond. A 455, 3221–3258.Google Scholar
Fer, I., Lemmin, U. & Thorpe, S. A. 2002 Winter cascading of cold water in Lake Geneva. J. Geophys. Res. 107 (C6), doi:10.1029/2001JC000828.Google Scholar
Gasser, M., Pelegi, J. I., Nash, J. D., Peters, H. & Garcia-Lafuente, J. 2011 Topographic control on the nascent Mediterranean outflow. Geo.-Mar. Lett. 31, 301–314.Google Scholar
Jagannathan, A., Winters, K. B. & Armi, L. 2017 Stability of stratified downslope flows with an overlying stagnant isolating layer. J. Fluid Mech. 810, 392–411.Google Scholar
Lawrie, A. G. W. & Dalziel, S. B. 2011 Rayleigh–Taylor instability in an otherwise stable stratification. J. Fluid Mech. 688, 507–527.Google Scholar
Miles, J. N. & Howard, L. N. 1963 Note on a heterogeneous shear flow. J. Fluid Mech. 20, 331–336.Google Scholar
Nash, J. D., Peters, H., Kelly, S. M., Pelegri, J. L., Emelianov, M. & Gasser, M. 2012 Turbulence and high-frequency variability in a deep gravity current outflow. Geophys. Res. Lett. 39, L18611.Google Scholar
Ogden, K. A. & Helfich, K. R. 2016 Internal hydraulic jumps in two-layer flows with upstream shear. J. Fluid Mech. 789, 64–92.Google Scholar
Peters, H. & Johns, W. E. 2005 Mixing and entrainment in the Red Sea outflow plume. Part II: turbulence characteristics. J. Phys. Oceanogr. 35, 584–600.Google Scholar
Peters, H., Johns, W. E., Bower, A. S. & Fratantoni, D. M. 2005 Mixing and entrainment in the Red Sea outflow plume. Part I: plume structure. J. Phys. Oceanogr. 35, 569–583.Google Scholar
Pettré, P. & André, J.-C. 1991 Surface pressure change through Loewe’s phenomena and katabatic flow jumps: study of two cases in Adélie Land, Antarctica. J. Atmos. Sci. 48, 557–571.Google Scholar
Polzin, K., Speer, K. G., Toole, J. M. & Schmitt, R. W. 1996 Intense mixing of Antarctic Bottom Water in the equatorial Atlantic Ocean. Nature 380, 54–56.Google Scholar
Rapp, R. J. & Melville, W. K. 1990 Laboratory measurements of deep water breaking waves. Phil. Trans. R. Soc. Lond. A 331, 735–800.Google Scholar
Rottman, J. W., Broutman, D. & Grimshaw, R. 1996 Numerical simulations of uniformly stratified fluid flow over topography. J. Fluid Mech. 306, 1–30.Google Scholar
Scorer, R. S. 1955 The theory of airflow over mountains – IV. Separation of flow from the surface. Q. J. R. Meteorol. Soc. 81, 340–350.CrossRefGoogle Scholar
Scorer, R. 1972 Clouds of the World, p. 176. David & Charles.Google Scholar
Smyth, W. D., Moum, J. N. & Caldwell, D. R. 2001 The efficiency of mixing in turbulent patches: inferences from direct simulations and microstructure observations. J. Phys. Oceanogr. 31, 1969–1992.2.0.CO;2>CrossRefGoogle Scholar
Thorpe, S. A. 1973 Experiments on instability and turbulence in a stratified shear flow. J. Fluid Mech. 61, 731–751.Google Scholar
Thorpe, S. A. 2010 Turbulent hydraulic jumps in a stratified shear flow. J. Fluid Mech. 654, 305–350.CrossRefGoogle Scholar
Thorpe, S. A. & Li, L. 2014 Turbulent hydraulic jumps in a stratified shear flow. Part 2. J. Fluid Mech. 758, 94–120; (referred to as ‘TL’).CrossRefGoogle Scholar
Voet, G., Alford, M. H., Girton, J. B., Carter, G. S., Mickett, J. B. & Klymak, J. M. 2016 Warming and weakening of the abyssal flow through the Samoan Passage. J. Phys. Oceanogr. 46, 2389–2401.Google Scholar
Voet, G., Girton, J. B., Alford, M. H., Carter, G. S., Klymak, J. M. & Mickett, J. B. 2015 Pathways, volume transport, and mixing of abyssal water in the Samoan Passage. J. Phys. Oceanogr. 45, 562–588.Google Scholar
Winters, K. B. & Armi, L. 2014 Topographic control and stratified flows: upstream jets, blocking and isolating layers. J. Fluid Mech. 753, 80–103.Google Scholar
Yakovenko, S. N., Thomas, T. G. & Castro, I. P. 2011 A turbulent patch arising from a breaking internal wave. J. Fluid Mech. 677, 103–133.Google Scholar
Yakovenko, S. N., Thomas, T. G. & Castro, I. P. 2014 Transition through Rayleigh–Taylor instabilities in a breaking internal lee wave. J. Fluid Mech. 760, 466–493.Google Scholar