Abstract
The three-dimensional Massachusetts Institute of Technology general circulation model (MITgcm) with time-dependent forcing is implemented to investigate the spatial and temporal variability of internal tides over the eastern coast of India. Numerical simulations are conducted for a number of different months of the year for which in situ observations are available at high temporal resolution. During the months of November–December and March–April, peak spectral estimates of density variability are evident in the semidiurnal frequency band in both observations and simulations, while during August, variability is dominantly in the near-inertial frequency band. Empirical orthogonal functions (EOF) analysis is applied to decompose the baroclinic tidal currents into vertical modes. The results show that about 70–80% of the total variance is in the first mode, while the first three modes represent 90–95% of the total variance in all seasons. Internal tide characteristics such as phase speed, group speed, and wavelength are largest in the postmonsoon season. The magnitude of the computed energy flux is greatest during November, while the direction of propagation of internal tides is almost unchanged through the year. The available potential energy peaks in November (20 kJ m−2) and is smallest in August (14 kJ m−2). Calculation of the energy budget shows that the energy conversion rate from barotropic forcing to internal tides is about 85% in November but only about 46% in August.
Similar content being viewed by others
References
Carter, G. S., Gregg, M. C., & Lien, R. C. (2005). Internal waves, solitary-like waves, and mixing on the Monterey Bay shelf. Continental Shelf Research,25(12), 1499–1520.
Carter, G. S., Merrifield, M. A., Becker, J. M., Katsumata, K., Gregg, M. C., Luther, D. S., et al. (2008). Energetics of M 2 barotropic-to-baroclinic tidal conversion at the Hawaiian Islands. Journal of Physical Oceanography,38(10), 2205–2223.
Cooley, J. W., & Tukey, J. W. (1965). An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation,19(90), 297–301.
D’Asaro, E. A., Lien, R. C., & Henyey, F. (2007). High-frequency internal waves on the Oregon continental shelf. Journal of Physical Oceanography,37(7), 1956–1967.
Egbert, G. D., & Erofeeva, S. Y. (2002). Efficient inverse modeling of barotropic ocean tides. Journal of Atmospheric and Oceanic Technology,19(2), 183–204.
Holloway, P. E. (1996). A numerical model of internal tides with application to the Australian North West Shelf. Journal of Physical Oceanography,26(1), 21–37.
Hsu, M. K., Liu, A. K., & Liu, C. (2000). A study of internal waves in the China Seas and Yellow Sea using SAR. Continental Shelf Research,20(4), 389–410.
Joshi, M., Rao, A. D., Mohanty, S., Pradhan, H. K., Murty, V. S., & Prasad, K. V. S. R. (2017). Internal waves over the shelf in the western Bay of Bengal: A case study. Ocean Dynamics,67(1), 147–161.
Kang, D., & Fringer, O. (2012). Energetics of barotropic and baroclinic tides in the Monterey Bay area. Journal of Physical Oceanography,42(2), 272–290.
Kunze, E., Rosenfeld, L. K., Carter, G. S., & Gregg, M. C. (2002). Internal waves in Monterey submarine canyon. Journal of Physical Oceanography,32(6), 1890–1913.
LaFond, E. C., & LaFond, K. G. (1968). Studies of oceanic circulation in the Bay of Bengal. Bulletin of National Institute of Sciences of India,38, 164–183.
LaFond, K. G., & Rao, C. P. (1954). Vertical oscillations of tidal periods in the temperature structure of the sea. Andhra University Memoirs,1, 109–116.
Large, W. G., McWilliams, J. C., & Doney, S. C. (1994). Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization. Reviews of Geophysics,32(4), 363–403.
Locarnini, R. A., et al. (2013). World ocean atlas 2013, volume 1: Temperature. NOAA Atlas NESDIS,73, 40.
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. Journal of Geophysical Research: Oceans,102(C3), 5753–5766.
Merrifield, M. A., & Holloway, P. E. (2002). Model estimates of M2 internal tide energetics at the Hawaiian Ridge. Journal of Geophysical Research: Oceans,107(C8), 1–12.
Mohanty, S., Rao, A. D., & Latha, G. (2018). Energetics of semidiurnal internal tides in the Andaman Sea. Journal of Geophysical Research-Oceans. https://doi.org/10.1029/2018jc013852.
Mohanty, S., Rao, A. D., & Pradhan, H. K. (2017a). Effect of seasonal and cyclonic winds on internal tides over the Bay of Bengal. Natural Hazards,87(2), 1109–1124.
Mohanty, S., Rao, A. D., & Pradhan, H. K. (2017b). Estimates of internal tide energetics in the western Bay of Bengal. IEEE Journal of Oceanic Engineering,99, 1–9.
Morozov, E. G. (2018). Oceanic internal tides: Observations, analysis and modeling: A global view. Berlin: Springer.
Munk, Walter, & Wunsch, Carl. (1998). Abyssal recipes II: Energetics of tidal and wind mixing. Deep Sea Research Part I: Oceanographic Research Papers,45(12), 1977–2010.
Nagai, T., & Hibiya, T. (2015). Internal tides and associated vertical mixing in the Indonesian Archipelago. Journal of Geophysical Research: Oceans,120(5), 3373–3390.
Nash, J. D., Alford, M. H., & Kunze, E. (2005). Estimating internal wave energy fluxes in the ocean. Journal of Atmospheric and Oceanic Technology,22(10), 1551–1570.
Nash, J. D., Kunze, E., Toole, J. M., & Schmitt, R. W. (2004). Internal tide reflection and turbulent mixing on the continental slope. Journal of Physical Oceanography,34(5), 1117–1134.
Niwa, Y., & Hibiya, T. (2004). Three-dimensional numerical simulation of M2 internal tides in the East China Sea. Journal of Geophysical Research: Oceans, 109(C4).
Pradhan, H. K., Rao, A. D., & Mohanty, S. (2016). Inter-seasonal variability of internal tides in the western Bay of Bengal. Natural Hazards,84(2), 809–820.
Prasad, K. V. S. R., & Rajasekhar, M. (2011). Space borne SAR observations of oceanic internal waves in North Bay of Bengal. Natural Hazards,57(3), 657–667.
Rao, A. D., Babu, S. V., Prasad, K. V. S. R., Murty, T. R., Sadhuram, Y., & Mahapatra, D. K. (2010). Investigation of the generation and propagation of low frequency internal waves: A case study for the east coast of India. Estuarine, Coastal and Shelf Science,88(1), 143–152.
Rudnick, D. L., Boyd, T. J., Brainard, R. E., Carter, G. S., Egbert, G. D., Gregg, M. C., et al. (2003). From tides to mixing along the Hawaiian Ridge. Science,301(5631), 355–357.
Sindhu, B., Suresh, I., Unnikrishnan, A. S., Bhatkar, N. V., Neetu, S., & Michael, G. S. (2007). Improved bathymetric datasets for the shallow water regions in the Indian Ocean. Journal of Earth System Science,116(3), 261–274.
Smagorinsky, J. (1963). General circulation experiments with the primitive equations: I. The basic experiment. Monthly Weather Review,91(3), 99–164.
Vlasenko, V., Stashchuk, N., & Hutter, K. (2005). Baroclinic tides: Theoretical modeling and observational evidence. Cambridge: Cambridge University Press.
Zhao, Z., Alford, M. H., Lien, R. C., Gregg, M. C., & Carter, G. S. (2012). Internal tides and mixing in a submarine canyon with time-varying stratification. Journal of Physical Oceanography,42(12), 2121–2142.
Acknowledgements
The work was funded by the Naval Research Board (NRB), New Delhi for investigations on IWs in the Bay of Bengal through a collaborative project between the IITD, CSIR-National Institute of Oceanography Regional Centre, Visakhapatnam, and Andhra University, Visakhapatnam. The authors thank the Indian Institute of Technology Delhi HPC facility and Department of Science and Technology, Government of India for sanctioning a financial grant (DST-FIST, 2014) for computational resources. The bathymetry data were obtained through the website (http://apdrc.soest.hawaii.edu/datadoc/io_etopo.php). The barotropic tidal velocity data obtained from the TOPEX/Poseidon global tidal model (http://volkov.oce.orst.edu/tides/tpxo8_atlas.html) are gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Mohanty, S., Rao, A.D. & Yadidya, B. Spatial and Temporal Variability of Semidiurnal Internal Tide Energetics in the Western Bay of Bengal. Pure Appl. Geophys. 176, 5203–5215 (2019). https://doi.org/10.1007/s00024-019-02221-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00024-019-02221-4