Abyssal Mixing through Critical Reflection of Equatorially Trapped Waves off Smooth Topography

Bertrand L. Delorme Earth System Science Department, Stanford University, Stanford, California

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Leif N. Thomas Earth System Science Department, Stanford University, Stanford, California

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Abstract

The inferred diapycnal upwelling in the abyssal meridional overturning circulation (AMOC) is intensified near the equator, but little is known as to why this is so. In this study, it is shown that the reflection of equatorially trapped waves (ETWs) off the bottom leads to seafloor-intensified mixing and substantial diapycnal upwelling near the equator when the full Coriolis force and the so-called nontraditional effects are taken into account. Using idealized simulations run with the MITgcm of downward-propagating ETWs of various types (i.e., inertia–gravity, Yanai, Kelvin, and Rossby waves) accounting for nontraditional effects, it is demonstrated that the reflection of ETWs off a flat seafloor generates beams of short inertia–gravity waves with strong vertical shear and low Richardson numbers that result in bottom-intensified, persistent, zonally invariant mixing at the inertial latitude of the ETW through the mechanism of critical reflection. The beams are more intense with weaker stratification and, for a given wave type, are stronger for waves with shorter periods and longer vertical wavelengths. The intensity of the beams also differs between wave types because their distinct meridional structures modulate the amount of energy fluxed to the bottom at the inertial latitude. As a result, equatorial inertia–gravity, Rossby, and eastward-propagating Yanai waves yield stronger mixing than Kelvin and westward-propagating Yanai waves in the simulations. It is estimated that this process can result in order 10 Sv (1 Sv ≡ 106 m3 s−1) of diapycnal upwelling per wavelength of ETW in the abyss and thus could play an important role in closing the AMOC.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Bertrand Delorme, bdelorme@stanford.edu

Abstract

The inferred diapycnal upwelling in the abyssal meridional overturning circulation (AMOC) is intensified near the equator, but little is known as to why this is so. In this study, it is shown that the reflection of equatorially trapped waves (ETWs) off the bottom leads to seafloor-intensified mixing and substantial diapycnal upwelling near the equator when the full Coriolis force and the so-called nontraditional effects are taken into account. Using idealized simulations run with the MITgcm of downward-propagating ETWs of various types (i.e., inertia–gravity, Yanai, Kelvin, and Rossby waves) accounting for nontraditional effects, it is demonstrated that the reflection of ETWs off a flat seafloor generates beams of short inertia–gravity waves with strong vertical shear and low Richardson numbers that result in bottom-intensified, persistent, zonally invariant mixing at the inertial latitude of the ETW through the mechanism of critical reflection. The beams are more intense with weaker stratification and, for a given wave type, are stronger for waves with shorter periods and longer vertical wavelengths. The intensity of the beams also differs between wave types because their distinct meridional structures modulate the amount of energy fluxed to the bottom at the inertial latitude. As a result, equatorial inertia–gravity, Rossby, and eastward-propagating Yanai waves yield stronger mixing than Kelvin and westward-propagating Yanai waves in the simulations. It is estimated that this process can result in order 10 Sv (1 Sv ≡ 106 m3 s−1) of diapycnal upwelling per wavelength of ETW in the abyss and thus could play an important role in closing the AMOC.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Bertrand Delorme, bdelorme@stanford.edu
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  • Adcroft, A., and Coauthors, 2016: MITgcm user manual. MIT Tech. Rep., 451 pp., http://mitgcm.org/public/r2_manual/final/online_documents/manual.html.

  • Alford, M. H., J. A. MacKinnon, H. L. Simmons, and J. D. Nash, 2016: Near-inertial internal gravity waves in the ocean. Annu. Rev. Mar. Sci., 8, 95123, https://doi.org/10.1146/annurev-marine-010814-015746.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Armi, L., 1978: Some evidence for boundary mixing in the deep ocean. J. Geophys. Res., 83, 19711979, https://doi.org/10.1029/JC083iC04p01971.

  • Ascani, F., E. Firing, P. Dutrieux, J. P. McCreary, and A. Ishida, 2010: Deep equatorial ocean circulation induced by a forced–dissipated Yanai beam. J. Phys. Oceanogr., 40, 11181142, https://doi.org/10.1175/2010JPO4356.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ascani, F., E. Firing, J. P. McCreary, P. Brandt, and R. J. Greatbatch, 2015: The deep equatorial ocean circulation in wind-forced numerical solutions. J. Phys. Oceanogr., 45, 17091734, https://doi.org/10.1175/JPO-D-14-0171.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Blandford, R., 1966: Mixed gravity-Rossby waves in the ocean. Deep-Sea Res. Oceanogr. Abstr., 13, 941961, https://doi.org/10.1016/0011-7471(76)90912-8.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Boyer, T. P., and Coauthors, 2013: World Ocean Database 2013. NOAA Tech. Rep. NESDIS 72, 208 pp., https://doi.org/10.7289/V5NZ85MT.

    • Crossref
    • Export Citation
  • Brandt, P., and C. Eden, 2005: Annual cycle and interannual variability of the mid-depth tropical Atlantic Ocean. Deep-Sea Res. I, 52, 199219, https://doi.org/10.1016/j.dsr.2004.03.011.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Callies, J., and R. Ferrari, 2018: Dynamics of an abyssal circulation driven by bottom-intensified mixing on slopes. J. Phys. Oceanogr., 48, 12571282, https://doi.org/10.1175/JPO-D-17-0125.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cane, M. A., and D. W. Moore, 1981: A note on low-frequency equatorial basin modes. J. Phys. Oceanogr., 11, 15781584, https://doi.org/10.1175/1520-0485(1981)011<1578:ANOLFE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cox, M., 1980: Generation and propagation of 30-day waves in a numerical model of the Pacific. J. Phys. Oceanogr., 10, 11681186, https://doi.org/10.1175/1520-0485(1980)010<1168:GAPODW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cravatte, S., E. Kestenare, F. Marin, P. Dutrieux, and E. Firing, 2017: Subthermocline and intermediate zonal currents in the tropical Pacific Ocean: Paths and vertical structure. J. Phys. Oceanogr., 47, 23052324, https://doi.org/10.1175/JPO-D-17-0043.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dauxois, T., and W. R. Young, 1999: Near-critical reflection of internal waves. J. Fluid Mech., 390, 271295, https://doi.org/10.1017/S0022112099005108.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Durland, T. S., and J. T. Farrar, 2012: The wavenumber–frequency content of resonantly excited equatorial waves. J. Phys. Oceanogr., 42, 18341858, https://doi.org/10.1175/JPO-D-11-0234.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Eriksen, C. C., 1980: Evidence for a continuous spectrum of equatorial waves in the Indian Ocean. J. Geophys. Res., 85, 32853303, https://doi.org/10.1029/JC085iC06p03285.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Eriksen, C. C., 1981: Deep currents and their interpretation as equatorial waves in the western Pacific Ocean. J. Phys. Oceanogr., 11, 4870, https://doi.org/10.1175/1520-0485(1981)011<0048:DCATIA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Eriksen, C. C., and J. G. Richman, 1988: An estimate of equatorial wave energy flux at 9- to 90-day periods in the central Pacific. J. Geophys. Res., 93, 15 45515 466, https://doi.org/10.1029/JC093iC12p15455.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Farrar, J. T., 2008: Observations of the dispersion characteristics and meridional sea level structure of equatorial waves in the Pacific Ocean. J. Phys. Oceanogr., 38, 16691689, https://doi.org/10.1175/2007JPO3890.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Feistel, R., 2008: A Gibbs function for seawater thermodynamics for −6 to 80°C and salinity up to 120 g kg−1. Deep-Sea Res. I, 55, 16391671, https://doi.org/10.1016/j.dsr.2008.07.004.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ferrari, R., 2014: What goes down must come up. Nature, 513, 179180, https://doi.org/10.1038/513179a.

  • Fruman, M. D., 2009: Equatorially bounded zonally propagating linear waves on a generalized β plane. J. Atmos. Sci., 66, 29372945, https://doi.org/10.1175/2009JAS2932.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gerkema, T., and V. I. Shrira, 2005: Near-inertial waves on the “nontraditional” β plane. J. Geophys. Res., 110, C01003, https://doi.org/10.1029/2004JC002519.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Harvey, R., and W. Patzert, 1976: Deep current measurements suggest long waves in the eastern equatorial Pacific. Science, 193, 883885, https://doi.org/10.1126/science.193.4256.883.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holmes, R. M., J. N. Moum, and L. N. Thomas, 2016: Evidence for seafloor-intensified mixing by surface-generated equatorial waves. Geophys. Res. Lett., 43, 12021210, https://doi.org/10.1002/2015GL066472.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Knox, R., and D. L. Anderson, 1985: Recent advances in the study of the low-latitude ocean circulation. Prog. Oceanogr., 14, 259317, https://doi.org/10.1016/0079-6611(85)90014-X.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Large, W. G., J. C. McWilliams, and S. C. Doney, 1994: Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization. Rev. Geophys., 32, 363403, https://doi.org/10.1029/94RG01872.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lumpkin, R., and K. Speer, 2007: Global ocean meridional overturning. J. Phys. Oceanogr., 37, 25502562, https://doi.org/10.1175/JPO3130.1.

  • Luyten, J. R., and J. C. Swallow, 1976: Equatorial undercurrents. Deep-Sea Res. Oceanogr. Abstr., 23, 9991001, https://doi.org/10.1016/0011-7471(76)90830-5.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J., C. Hill, L. Perelman, and A. Adcroft, 1997: Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling. J. Geophys. Res., 102, 57335752, https://doi.org/10.1029/96JC02776.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Matsuno, T., 1966: Quasi-geostrophic motions in the equatorial area. J. Meteor. Soc. Japan, 44, 2543, https://doi.org/10.2151/jmsj1965.44.1_25.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McCreary, J. P., 1984: Equatorial beams. J. Mar. Res., 42, 395430, https://doi.org/10.1357/002224084788502792.

  • McDougall, T. J., and R. Ferrari, 2017: Abyssal upwelling and downwelling driven by near-boundary mixing. J. Phys. Oceanogr., 47, 261283, https://doi.org/10.1175/JPO-D-16-0082.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ménesguen, C., B. L. Hua, M. D. Fruman, and R. Schopp, 2009: Dynamics of the combined extra-equatorial and equatorial deep jets in the Atlantic. J. Mar. Res., 67, 323346, https://doi.org/10.1357/002224009789954766.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Needler, G., and P. Leblond, 1973: On the influence of the horizontal component of the Earth’s rotation on long period waves. Geophys. Fluid Dyn., 5, 2345, https://doi.org/10.1080/03091927308236107.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Philander, S. G., 1978: Forced oceanic waves. Rev. Geophys., 16, 1546, https://doi.org/10.1029/RG016i001p00015.

  • Polzin, K., J. Toole, J. R. Ledwell, and R. W. Schmitt, 1997: Spatial variability of turbulent mixing in the abyssal ocean. Science, 276, 9396, https://doi.org/10.1126/science.276.5309.93.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raymond, W. H., 2000: Equatorial meridional flows: Rotationally induced circulations. Pure Appl. Geophys., 157, 17671779, https://doi.org/10.1007/PL00001060.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raymond, W. H., 2001: Kelvin waves: Rotationally induced circulations. Dyn. Atmos. Oceans, 34, 2343, https://doi.org/10.1016/S0377-0265(01)00058-6.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Roundy, P. E., and M. A. Janiga, 2012: Analysis of vertically propagating convectively coupled equatorial waves using observations and a non-hydrostatic Boussinesq model on the equatorial beta-plane. Quart. J. Roy. Meteor. Soc., 138, 10041017, https://doi.org/10.1002/qj.983.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schopf, P. S., D. L. Anderson, and R. Smith, 1981: Beta-dispersion of low-frequency Rossby waves. Dyn. Atmos. Oceans, 5, 187214, https://doi.org/10.1016/0377-0265(81)90011-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smyth, W. D., T. S. Durland, and J. N. Moum, 2015: Energy and heat fluxes due to vertically propagating Yanai waves observed in the equatorial Indian Ocean. J. Geophys. Res. Oceans, 120, 66306647, https://doi.org/10.1002/2014JC010152.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • St. Laurent, L., and C. Garrett, 2002: The role of internal tides in mixing the deep ocean. J. Phys. Oceanogr., 32, 28822899, https://doi.org/10.1175/1520-0485(2002)032<2882:TROITI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Waterhouse, A. F., and Coauthors, 2014: Global patterns of diapycnal mixing from measurements of the turbulent dissipation rate. J. Phys. Oceanogr., 44, 18541872, https://doi.org/10.1175/JPO-D-13-0104.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Weisberg, R. H., and A. M. Horigan, 1981: Low-frequency variability in the equatorial Atlantic. J. Phys. Oceanogr., 11, 913920, https://doi.org/10.1175/1520-0485(1981)011<0913:LFVITE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Winters, K. B., P. Bouruet-Aubertot, and T. Gerkema, 2011: Critical reflection and abyssal trapping of near-inertial waves on a β-plane. J. Fluid Mech., 684, 111136, https://doi.org/10.1017/jfm.2011.280.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wunsch, C., and A. E. Gill, 1976: Observations of equatorially trapped waves in Pacific sea level variations. Deep-Sea Res. Oceanogr. Abstr., 23, 371390, https://doi.org/10.1016/0011-7471(76)90835-4.

    • Crossref
    • Search Google Scholar
    • Export Citation
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