Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-05-05T06:11:24.425Z Has data issue: false hasContentIssue false
  • English
  • Français

Surface reflection of bottom generated oceanic lee waves

Published online by Cambridge University Press:  05 August 2021

L.E. Baker Open the ORCID record for L.E. Baker [Opens in a new window]  and
A. Mashayek Open the ORCID record for A. Mashayek [Opens in a new window]
L.E. Baker*
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK
A. Mashayek
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: l.baker18@imperial.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Lee waves generated by stratified flow over rough bottom topography in the ocean extract momentum and energy from the geostrophic flow, causing drag and enhancing turbulence and mixing in the interior ocean when they break. Inviscid linear theory is generally used to predict the generation rate of lee waves, but the location and mechanism of wave breaking leading to eventual dissipation of energy and irreversible mixing are poorly constrained. In this study, a linear model with viscosity, diffusivity and an upper boundary is used to demonstrate the potential importance of the surface in reflecting lee wave energy back into the interior, making the case for treating lee waves as a full water-column process. In the absence of critical levels, it is shown that lee waves can be expected to interact with the upper ocean, resulting in enhanced vertical velocities and dissipation and mixing near the surface. The impact of the typical oceanic conditions of increasing background velocity and stratification with height above bottom are investigated and shown to contribute to enhanced upper ocean vertical velocities and mixing.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Topographic effects Geophysical and Geological Flows: Waves in rotating fluids
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 924 , 10 October 2021 , A17
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

Andrews, D.G. & McIntyre, M.E. 1976 Planetary waves in horizontal and vertical shear: the generalized Eliassen–Palm relation and the mean zonal acceleration. J. Atmos. Sci. 33 (11), 2031–2048.2.0.CO;2>CrossRefGoogle Scholar
Bachman, S.D., Taylor, J.R., Adams, K.A. & Hosegood, P.J. 2017 Mesoscale and submesoscale effects on mixed layer depth in the Southern Ocean. J. Phys. Oceanogr. 47 (9), 2173–2188.CrossRefGoogle Scholar
Baines, P.G. 1995 Topographic Effects in Stratified Flows. Cambridge University Press.Google Scholar
Bell, T.H. 1975 Topographically generated internal waves in the open ocean. J. Geophys. Res. 80 (3), 320–327.CrossRefGoogle Scholar
Booker, J.R. & Bretherton, F.P. 1967 The critical layer for internal gravity waves in a shear flow. J. Fluid Mech. 27 (3), 513–539.CrossRefGoogle Scholar
Brearley, J.A., Sheen, K.L., Naveira Garabato, A.C., Smeed, D.A. & Waterman, S. 2013 Eddy-induced modulation of turbulent dissipation over rough topography in the Southern Ocean. J. Phys. Oceanogr. 43 (11), 2288–2308.CrossRefGoogle Scholar
Bretherton, F.P. 1969 Momentum transport by gravity waves. Q. J. R. Meteorol. Soc. 95, 125–135.CrossRefGoogle Scholar
Bretherton, F.P. & Garrett, C. 1969 Wavetrains in inhomogeneous moving media. Proc. R. Soc. A 302, 529–554.Google Scholar
Cessi, P. 2019 The global overturning circulation. Annu. Rev. Mar. Sci. 11, 249–270.CrossRefGoogle ScholarPubMed
Charney, J.G. & Drazin, P.G. 1961 Propagation of planetary-scale disturbances from the lower into the upper atmosphere. J. Geophys. Res. 66, 83–109.CrossRefGoogle Scholar
Cusack, J.M., Naveira Garabato, A.C., Smeed, D.A. & Girton, J.B. 2017 Observation of a large lee wave in the Drake Passage. J. Phys. Oceanogr. 47 (4), 793–810.CrossRefGoogle Scholar
Cusack, J.M., Brearley, J.A., Naveira Garabato, A.C., Smeed, D.A., Polzin, K.L., Velzeboer, N. & Shakespeare, C.J. 2020 Observed eddy-internal wave interactions in the Southern Ocean. J. Phys. Oceanogr. 50, 3043–3062.CrossRefGoogle Scholar
Dossmann, Y., Shakespeare, C., Stewart, K. & Hogg, A. 2020 Asymmetric internal tide generation in the presence of a steady flow. J. Geophys. Res. Ocean. 125, e2020JC016503.CrossRefGoogle Scholar
Eliassen, A. & Palm, E. 1960 On the transfer of energy in stationary mountain waves. Geophys. Nor. XXII (3), 1–23.Google Scholar
Fox-Kemper, B. & Menemenlis, D. 2008 Can large eddy simulation techniques improve mesoscale rich ocean models? Geophys. Monogr. Ser. 177, 319–337.Google Scholar
Gill, A.E. 1982 Atmosphere-Ocean Dynamics. Academic Press.Google Scholar
Goff, J.A. & Jordan, T.H. 1988 Stochastic modeling of seafloor morphology. J. Geophys. Res. 93 (B11), 13589–13608.CrossRefGoogle Scholar
Grimshaw, R. 1975 Internal gravity waves: critical layer absorption in a rotating fluid. J. Fluid Mech. 70 (2), 287–304.CrossRefGoogle Scholar
Jones, W.L. 1967 Propagation of internal gravity waves in fluids with shear flow and rotation. J. Fluid Mech. 30 (3), 439–448.CrossRefGoogle Scholar
Klymak, J.M. 2018 Nonpropagating form drag and turbulence due to stratified flow over large-scale Abyssal Hill Topography. J. Phys. Oceanogr. 48 (10), 2383–2395.CrossRefGoogle Scholar
Kunze, E. & Lien, R.C. 2019 Energy sinks for lee waves in shear flow. J. Phys. Oceanogr. 49, 2851–2865.CrossRefGoogle Scholar
Large, W.G., McWilliams, J.C. & Doney, S.C. 1994 Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parameterization. Rev. Geophys. 32 (4), 363–403.CrossRefGoogle Scholar
Legg, S. 2021 Mixing by oceanic lee waves. Annu. Rev. Fluid Mech. 53, 173–201.CrossRefGoogle Scholar
Leith, C.E. 1996 Stochastic models of chaotic systems. Phys. D: Nonlinear Phenom. 98 (2–4), 481–491.CrossRefGoogle Scholar
MacKinnon, J.A., et al. 2017 Climate process team on internal wave–driven ocean mixing. Bull. Am. Meteorol. Soc. 98 (11), 2429–2454.CrossRefGoogle Scholar
de Marez, C., Lahaye, N. & Gula, J. 2020 Interaction of the Gulf Stream with small scale topography: a focus on lee waves. Sci. Rep. 10, 2332.CrossRefGoogle ScholarPubMed
Marshall, J., Adcroft, A., Hill, C., Perelman, L. & Heisey, C. 1997 A finite-volume, incompressible Navier–Stokes model for studies of the ocean on parallel computers. J. Geophys. Res. 102 (C3), 5753–5766.CrossRefGoogle Scholar
Mashayek, A., Ferrari, R., Merrifield, S., Ledwell, J.R., St Laurent, L. & Naveira Garabato, A. 2017 Topographic enhancement of vertical turbulent mixing in the Southern Ocean. Nat. Commun. 8, 14197.CrossRefGoogle ScholarPubMed
Maslowe, S. 1986 Critical layers in shear flows. Annu. Rev. Fluid Mech. 18, 405–432.CrossRefGoogle Scholar
Mayer, F.T. & Fringer, O.B. 2017 An unambiguous definition of the Froude number for lee waves in the deep ocean. J. Fluid Mech. 831, R3.CrossRefGoogle Scholar
McIntyre, M.E. 1972 On Long's hypothesis of no upstream influence in uniformly stratified or rotating flow. J. Fluid Mech. 52 (2), 209–243.CrossRefGoogle Scholar
Melet, A., Hallberg, R., Legg, S. & Nikurashin, M. 2014 Sensitivity of the ocean state to lee wave–driven mixing. J. Phys. Oceanogr. 44 (3), 900–921.CrossRefGoogle Scholar
Naveira Garabato, A.C., Nurser, A.J., Scott, R.B. & Goff, J.A. 2013 The impact of small-scale topography on the dynamical balance of the ocean. J. Phys. Oceanogr. 43, 647–668.CrossRefGoogle Scholar
Neeck, S.P., Lindstrom, E.J., Vaze, P.V. & Fu, L.L. 2012 Surface water and ocean topography (SWOT) mission. Sens. Syst. Next-Gen. Satell. XVI 8533 (November 2012), 85330G.Google Scholar
Nikurashin, M. & Ferrari, R. 2010 a Radiation and dissipation of internal waves generated by geostrophic motions impinging on small-scale topography: application to the Southern Ocean. J. Phys. Oceanogr. 40 (9), 2025–2042.CrossRefGoogle Scholar
Nikurashin, M. & Ferrari, R. 2010 b Radiation and dissipation of internal waves generated by geostrophic motions impinging on small-scale topography: theory. J. Phys. Oceanogr. 40, 1055–1074.CrossRefGoogle Scholar
Nikurashin, M. & Ferrari, R. 2011 Global energy conversion rate from geostrophic flows into internal lee waves in the deep ocean. Geophys. Res. Lett. 38 (8), L08610.CrossRefGoogle Scholar
Nikurashin, M. & Ferrari, R. 2013 Overturning circulation driven by breaking internal waves in the deep ocean. Geophys. Res. Lett. 40 (12), 3133–3137.CrossRefGoogle Scholar
Nikurashin, M., Ferrari, R., Grisouard, N. & Polzin, K. 2014 The impact of finite-amplitude bottom topography on internal wave generation in the Southern Ocean. J. Phys. Oceanogr. 44 (11), 2938–2950.CrossRefGoogle Scholar
Nikurashin, M., Vallis, G.K. & Adcroft, A. 2012 Routes to energy dissipation for geostrophic flows in the Southern Ocean. Nat. Geosci. 6 (1), 48–51.CrossRefGoogle Scholar
Peltier, W. & Clark, T. 1979 The evolution and stability of finite-amplitude mountain waves. Part II: surface wave drag and severe downslope windstorms. J. Atmos. Sci. 36, 1498–1529.2.0.CO;2>CrossRefGoogle Scholar
Rosso, I., Hogg, A.M., Kiss, A.E. & Gayen, B. 2015 Topographic influence on submesoscale dynamics in the Southern Ocean. Geophys. Res. Lett. 42 (4), 1139–1147.CrossRefGoogle Scholar
Scorer, R.S. 1949 Theory of waves in the lee of mountains. Q. J. R. Meteorol. Soc. 75, 41–56.CrossRefGoogle Scholar
Scott, R.B., Goff, J.A., Naveira Garabato, A.C. & Nurser, A.J. 2011 Global rate and spectral characteristics of internal gravity wave generation by geostrophic flow over topography. J. Geophys. Res. 116, C09029.Google Scholar
Shakespeare, C.J. 2020 Interdependence of internal tide and lee wave generation at abyssal hills: global calculations. J. Phys. Oceanogr. 50 (3), 655–677.CrossRefGoogle Scholar
Shakespeare, C.J. & Hogg, A.M. 2017 The viscous lee wave problem and its implications for ocean modelling. Ocean Model. 113, 22–29.CrossRefGoogle Scholar
Sheen, K.L., et al. 2013 Rates and mechanisms of turbulent dissipation and mixing in the Southern Ocean: results from the diapycnal and isopycnal mixing experiment in the Southern Ocean (DIMES). J. Geophys. Res. Ocean. 118 (6), 2774–2792.CrossRefGoogle Scholar
Smith, R.B. 1989 Mountain-induced stagnation points in hydrostatic flow. Tellus A 41A (3), 270–274.CrossRefGoogle Scholar
St. Laurent, L.C., Simmons, H.L. & Jayne, S.R. 2002 Estimating tidally driven mixing in the deep ocean. Geophys. Res. Lett. 29 (23), 19–22.CrossRefGoogle Scholar
Talley, L., et al. 2016 Changes in ocean heat, carbon content, and ventilation: a review of the first decade of GO-SHIP global repeat hydrography. Annu. Rev. Mar. Sci. 8, 185–215.CrossRefGoogle ScholarPubMed
Teixeira, M.A.C. 2014 The physics of orographic gravity wave drag. Front. Phys. 2, 43.CrossRefGoogle Scholar
Teixeira, M.A.C., Argaiń, J.L. & Miranda, P.M.A. 2013 Orographic drag associated with lee waves trapped at an inversion. J. Atmos. Sci. 70 (9), 2930–2947.CrossRefGoogle Scholar
Teixeira, M.A.C., Miranda, P.M.A., Argain, J.L. & Valente, M.A. 2005 Resonant gravity-wave drag enhancement in linear stratified flow over mountains. Q. J. R. Meteorol. Soc. 131 (609), 1795–1814.CrossRefGoogle Scholar
Waterman, S., Naveira Garabato, A.C. & Polzin, K.L. 2013 Internal waves and turbulence in the antarctic circumpolar current. J. Phys. Oceanogr. 43 (2), 259–282.CrossRefGoogle Scholar
Waterman, S., Polzin, K.L., Naveira Garabato, A.C., Sheen, K.L. & Forryan, A. 2014 Suppression of internal wave breaking in the antarctic circumpolar current near topography. J. Phys. Oceanogr. 44 (5), 1466–1492.CrossRefGoogle Scholar
Winters, K.B. & Armi, L. 2012 Hydraulic control of continuously stratified flow over an obstacle. J. Fluid Mech. 700, 502–513.CrossRefGoogle Scholar
Wright, C.J., Scott, R.B., Ailliot, P. & Furnival, D. 2014 Lee wave generation rates in the deep ocean. Geophys. Res. Lett. 41 (7), 2434–2440.CrossRefGoogle Scholar
Wurtele, M.G. 1996 Atmospheric lee waves. Annu. Rev. Fluid Mech. 28 (1), 429–476.CrossRefGoogle Scholar
Wurtele, M.G., Datta, A. & Sharman, R.D. 1996 The propagation of gravity-inertia waves and lee waves under a critical level. J. Atmos. Sci. 53 (11), 1505–1522.2.0.CO;2>CrossRefGoogle Scholar
Yang, L., Nikurashin, M., Hogg, A.M. & Sloyan, B.M. 2018 Energy loss from transient eddies due to lee wave generation in the Southern Ocean. J. Phys. Oceanogr. 48 (12), 2867–2885.CrossRefGoogle Scholar
Zheng, K. & Nikurashin, M. 2019 Downstream propagation and remote dissipation of internal waves in the southern ocean. J. Phys. Oceanogr. 49, 1873–1887.CrossRefGoogle Scholar
Zheng, Q., Holt, B., Li, X., Liu, X., Zhao, Q., Yuan, Y. & Yang, X. 2012 Deep-water seamount wakes on SEASAT SAR image in the Gulf Stream region. Geophys. Res. Lett. 39, L16604.CrossRefGoogle Scholar