Abstract
Three-dimensional simulations of the M2 and K1 internal tides using the MIT General Circulation Model (MITgcm) configured for the Luzon Ridge are presented. The energetics of M2 and K1 internal tides are studied by analyzing the full barotropic and baroclinic energy budgets and the barotropic and baroclinic kinetic energy budgets. The conversion rate of M2 tide is also investigated using the approximate expression by Nycander (J Geophys Res 110:C10028, 2005). The results show that about 15.10 GW is transferred from the M2 barotropic tide to the M2 baroclinic tide at the Luzon Ridge, which is about 88% of the loss by the barotropic tide. The net baroclinic energy flux is about 4.46 GW, and the total dissipation is about 11.33 GW. Additionally, it is found that the potential energy changes are small in the full energy budget when comparing the result between the full barotropic and baroclinic energy budgets and the barotropic and baroclinic kinetic energy budgets. The expression by Nycander (J Geophys Res 110:C10028, 2005) is found to be sensitive to the model resolution, but may underestimate the conversion rate at the Luzon Ridge at high resolution compared with the model results.
Similar content being viewed by others
References
Alford MH, Lien RC, Simmons H, Klymak J, Ramp S, Yang YG, Tang D, Chang MH (2010) Speed and evolution of nonlinear internal waves transiting the South China Sea. J Phys Oceanogr 40:1338–1355. https://doi.org/10.1175/2010JPO4388.1
Alford MH, Peacock T, MacKinnon JA, Nash JD, Buijsman MC, Centurioni LR, Chao SY, Chang MH, Farmer DM, Fringer OB, Fu KH, Gallacher PC, Graber HC, Helfrich KR, Jachec SM, Jackson CR, Klymak JM, Ko DS, Jan S, Johnston TMS, Legg S, Lee IH, Lien RC, Mercier MJ, Moum JN, Musgrave R, Park JH, Pickering AI, Pinkel R, Rainville L, Ramp SR, Rudnick DL, Sarkar S, Scotti A, Simmons HL, St Laurent LC, Venayagamoorthy SK, Wang YH, Wang J, Yang YJ, Paluszkiewicz T, (David) Tang TY (2015) The formation and fate of internal waves in the South China Sea. Nature 521:65–71. https://doi.org/10.1038/nature14399
Balmforth NJ, Ierley GR, Young WR (2002) Tidal conversion by subcritical topography. J Phys Oceanogr 32:2900–2914. https://doi.org/10.1175/15200485(2002)032<2900:TCBST>2.0.CO;2
Bell TH (1975a) Lee waves in stratified flows with simple harmonic time dependence. J Fluid Mech 67(4):705–722. https://doi.org/10.1017/S0022112075000560
Bell TH (1975b) Topographically generated internal waves in the open ocean. J Geophys Res 80(3):320–327. https://doi.org/10.1029/JC080i003p00320
Buijsman MC, McWilliams JC, Jackson CR (2010) East-west asymmetry in nonlinear internal waves from Luzon Strait. J Geophys Res 115:C10057. https://doi.org/10.1029/2009JC006004
Buijsman MC, Uchiyama Y, McWilliams JC, Hill-Lindsay CR (2012) Modeling semidiurnal internal tide variability in the Southern California Bight. J Phys Oceanogr 42:62–77. https://doi.org/10.1175/2011JPO4597.1
Buijsman MC, Klymak J, Legg S, Alford M, Farmer D, MacKinnon J, Nash J, Park J, Pickering A, Simmons H (2014) Three-dimensional double-ridge internal tide resonance in Luzon Strait. J Phys Oceanogr 44:850–869. https://doi.org/10.1175/JPO-D-13-024.1
Carter GS, Merrifield M, Becker J, Katsumata K, Gregg M, Luther D, Levine M, Boyd T, Firing Y (2008) Energetics of M2 barotropic-to-baroclinic tidal conversion at the Hawaiian Islands. J Phys Oceanogr 38:2205–2223. https://doi.org/10.1175/2008JPO3860.1
Duda TF, Lynch JF, Irish JD, Beardsley RC, Ramp SR, Chiu CS, Tang TY, Yang YJ (2004) Internal tide and nonlinear internal wave behavior at the continental slope in the northern South China Sea. IEEE J Ocean Eng 29(4):1105–1130. https://doi.org/10.1109/JOE.2004.836998
Egbert GD, Erofeeva SY (2002) Efficient inverse modeling of barotropic ocean tides. J Atmos Ocean Technol 19:183–204. https://doi.org/10.1175/1520-0426(2002)019<0183:EIMOBO>2.0.CO;2
Egbert GD, Ray RD (2001) Estimates of M2 tidal energy dissipation from TOPEX/Poseidon altimeter data. J Geophys Res 106(C10):22475–22502. https://doi.org/10.1029/2000JC000699
Egbert GD, Bennett AF, Foreman MG (1994) TOPEX/POSEIDON tides estimated using a global inverse model. J Geophys Res 99(C12):24821–24852. https://doi.org/10.1029/94JC01894
Falahat S, Nycander J, Roquet F, Zarroug M (2014) Global calculation of tidal energy conversion into vertical normal modes. J Phys Oceanogr 44:3225–3244. https://doi.org/10.1175/JPO-D-14-0002.1
Gouretski V, Koltermann KP (2004) WOCE global hydrographic climatology. Tech Rep 35:1–52
Green JM, Nycander J (2013) A comparison of tidal conversion parameterizations for tidal models. J Phys Oceanogr 43:104–119. https://doi.org/10.1175/JPO-D-12-023.1
Green JM, Simpson JH, Legg S, Palmer MR (2008) Internal waves, baroclinic energy fluxes and mixing at the European shelf edge. Cont Shelf Res 28(7):937–950. https://doi.org/10.1016/j.csr.2008.01.014
Jachec SM, Fringer OB, Gerritsen MG, Street RL (2006) Numerical simulation of internal tides and the resulting energetics within Monterey Bay and the surrounding area. Geophys Res Lett 33:L12605. https://doi.org/10.1029/2006GL026314
Jalali M, Rapaka NR, Sarkar S (2014) Tidal flow over topography: effect of excursion number on wave energetics and turbulence. J Fluid Mech 750:259–283. https://doi.org/10.1017/jfm.2014.258
Jan S, Chern CS, Wang J, Chao SY (2007) Generation of diurnal K1 internal tide in the Luzon Strait and its influence on surface tide in the South China Sea. J Geophys Res 112:C06019. https://doi.org/10.1029/2006JC004003
Jan S, Lien RC, Ting CH (2008) Numerical study of baroclinic tides in Luzon Strait. J Oceanogr 64:789–802. https://doi.org/10.1007/s10872-008-0066-5
Kang D, Fringer O (2012) Energetics of barotropic and baroclinic tides in the Monterey Bay area. J Phys Oceanogr 42:272–290. https://doi.org/10.1175/JPO-D-11-039.1
Kelly SM, Nash JD, Martini KI, Alford MH, Kunze E (2012) The cascade of tidal energy from low to high modes on a continental slope. J Phys Oceanogr 42:1217–1232. https://doi.org/10.1175/JPO-D-11-0231.1
Kerry CG, Powell BS, Carter GS (2014) The impact of subtidal circulation on internal tide generation and propagation in the Philippine Sea. J Phys Oceanogr 44:1386–1405. https://doi.org/10.1175/JPO-D-13-0142.1
Khatiwala S (2003) Generation of internal tides in an ocean of finite depth: analytical and numerical calculations. Deep-Sea Res I Oceanogr Res Pap 50(1):3–21. https://doi.org/10.1016/S0967-0637(02)00132-2
Large WG, McWilliams JC, Doney SC (1994) Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parameterization. Rev Geophys 32(4):363–403. https://doi.org/10.1029/94RG01872
Li Q, Farmer DM (2011) The generation and evolution of nonlinear internal waves in the deep basin of the South China Sea. J Phys Oceanogr 41:1345–1363. https://doi.org/10.1175/2011JPO4587.1
Li X, Zhao Z, Pichel WG (2008) Internal solitary waves in the northwestern South China Sea inferred from satellite images. Geophys Res Lett 35:L13605. https://doi.org/10.1029/2008GL034272
Llewellyn Smith SG, Young WR (2002) Conversion of the barotropic tide. J Phys Oceanogr 32:1554–1566. https://doi.org/10.1175/1520-0485(2002)032<1554:COTBT>2.0.CO;2
Llewellyn Smith SG, Young WR (2003) Tidal conversion at a very steep ridge. J Fluid Mech 495:175–191. https://doi.org/10.1017/S0022112003006098
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. https://doi.org/10.1029/96JC02775
Melet A, Nikurashin M, Muller C, Falahat S, Nycander J, Timko PG, Arbic BK, Goff JA (2013) Internal tide generation by abyssal hills using analytical theory. J Geophys Res 118:6303–6318. https://doi.org/10.1002/2013JC009212
Merrifield MA, Holloway PE (2002) Model estimates of M2 internal tide energetics at the Hawaiian Ridge. J Geophys Res 107(C8). https://doi.org/10.1029/2001JC000996
Munk W, Wunsch C (1998) Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res I Oceanogr Res Pap 45(12):1977–2010. https://doi.org/10.1016/S0967-0637(98)00070-3
Niwa Y, Hibiya T (2004) Three-dimensional numerical simulation of M2 internal tides in the East China Sea. J Geophys Res 109:C04027. https://doi.org/10.1029/2003JC001923
Niwa Y, Hibiya T (2011) Estimation of baroclinic tide energy available for deep ocean mixing based on three-dimensional global numerical simulations. J Oceanogr 67:493–502. https://doi.org/10.1007/s10872-011-0052-1
Niwa Y, Hibiya T (2014) Generation of baroclinic tide energy in a global three-dimensional numerical model with different spatial grid resolutions. Ocean Model 80:59–73. https://doi.org/10.1016/j.ocemod.2014.05.003
Nycander J (2005) Generation of internal waves in the deep ocean by tides. J Geophys Res 110:C10028. https://doi.org/10.1029/2004JC002487
Ponte AL, Cornuelle BD (2013) Coastal numerical modelling of tides: sensitivity to domain size and remotely generated internal tide. Ocean Model 62:17–26. https://doi.org/10.1016/j.ocemod.2012.11.007
Ramp SR, Tang TY, Duda TF, Lynch JF, Liu AK, Chiu CS, Bahr FL, Kim HR, Yang YJ (2004) Internal solitons in the northeastern South China Sea. Part I: sources and deep water propagation. IEEE J Ocean Eng 29:1157–1181. https://doi.org/10.1109/JOE.2004.840839
Rapaka NR, Gayen B, Sarkar S (2013) Tidal conversion and turbulence at a model ridge: direct and large eddy simulations. J Fluid Mech 715:181–209. https://doi.org/10.1017/jfm.2012.513
Smith WH, Sandwell DT (1997) Global sea floor topography from satellite altimetry and ship depth soundings. Science 277:1956–1962. https://doi.org/10.1126/science.277.5334.1956
St. Laurent L, Garrett C (2002) The role of internal tides in mixing the deep ocean. J Phys Oceanogr 32:2882–2899. https://doi.org/10.1175/1520-0485(2002)032<2882:TROITI>2.0.CO;2
Tanaka T, Yasuda I, Tanaka Y, Carter GS (2013) Numerical study on tidal mixing along the shelf break in the Green Belt in the southeastern Bering Sea. J Geophys Res 118:6525–6542. https://doi.org/10.1002/2013JC009113
Xu ZH, Liu K, Yin B, Zhao Z, Wang Y, Li Q (2016) Long-range propagation and associated variability of internal tides in the South China Sea. J Geophys Res 121:8268–8286. https://doi.org/10.1002/2016JC012105
Zaron ED, Egbert GD (2006) Verification studies for a z-coordinate primitive-equation model: tidal conversion at a mid-ocean ridge. Ocean Model 14:257–278. https://doi.org/10.1016/j.ocemod.2006.05.007
Zarroug M, Nycander J, Döös K (2010) Energetics of tidally generated internal waves for nonuniform stratification. Tellus Ser A 62:71–79
Zhang Z, Fringer OB, Ramp SR (2011) Three-dimensional, nonhydrostatic numerical simulation of nonlinear internal wave generation and propagation in the South China Sea. J Geophys Res 116:C05022. https://doi.org/10.1029/2010JC006424
Zhao Z (2014) Internal tide radiation from the Luzon Strait. J Geophys Res 119:5434–5448. https://doi.org/10.1002/2014JC010014
Zhao Z, Alford MH (2006) Source and propagation of internal solitary waves in the northeastern South China Sea. J Geophys Res 111:C11012. https://doi.org/10.1029/2006JC003644
Zilberman NV, Becker JM, Merrifield MA, Carter GS (2009) Model estimates of M2 internal tide generation over Mid-Atlantic Ridge topography. J Phys Oceanogr 39:2635–2651. https://doi.org/10.1175/2008JPO4136.1
Funding
Bing would like to thank the China Scholar Council (CSC) for providing the fund for the work, and the simulations were performed on the German Climate Computing Center (DKRZ). This work is also financially supported by the Open Project Program of State Key Laboratory of Tropical Oceanography (LTOZZ1801), the National Natural Science Foundation of China (41525019 and 41830538), the State Oceanic Administration of China (GASI-IPOVAI-02), and the Chinese Academy of Sciences (ZDRW-XH-2019-2).
Author information
Authors and Affiliations
Corresponding author
Additional information
Responsible Editor: Richard John Greatbatch
Rights and permissions
About this article
Cite this article
Han, B., Eden, C. The energetics of internal tides at the Luzon Ridge. Ocean Dynamics 69, 1009–1022 (2019). https://doi.org/10.1007/s10236-019-01297-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10236-019-01297-9