Skip to main content Accessibility help

Interference and transmission of spatiotemporally locally forced internal waves in non-uniform stratifications

  • Rohit Supekar (a1) and Thomas Peacock (a1)


Studies of the effects of constructive or destructive interference on the transmission of internal waves through non-uniform stratifications have typically been performed for internal wave fields that are spatiotemporally harmonic. To understand the impacts of spatiotemporal localization, we present a theoretical and experimental study of the transmission of two-dimensional internal waves that are generated by a boundary forcing that is localized in both space and time. The model analysis reveals that sufficient localization leads to the disappearance of transmission peaks and troughs that would otherwise be present for a harmonic forcing. The corresponding laboratory experiments that we perform provide clear demonstration of this effect. Based on the group velocity and angle of propagation of the internal waves, a practical criterion that assesses when the transmission peaks or troughs are evident is obtained.


Corresponding author

Email address for correspondence:


Hide All
Alford, M. H., MacKinnon, J. A., Simmons, H. L. & Nash, J. D. 2016 Near-inertial internal gravity waves in the ocean. Annu. Rev. Mar. Sci. 8, 95123.
Baines, P. G. & Hoinka, K. P. 1985 Stratified flow over two-dimensional topography in fluid of infinite depth: a laboratory simulation. J. Atmos. Sci. 42 (15), 16141630.
Bell, T. H. 1975 Lee waves in stratified flows with simple harmonic time-dependence. J. Fluid Mech. 67, 705722.
Cuypers, Y., Le Vaillant, X., Bouruet-Aubertot, P., Vialard, J. & McPhaden, M. J. 2013 Tropical storm-induced near-inertial internal waves during the Cirene experiment: energy fluxes and impact on vertical mixing. J. Geophys. Res. Oceans 118 (1), 358380.
Echeverri, P. M.2009 Internal tide generation by tall ocean ridges. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA.
Ghaemsaidi, S. J.2015 Interference and resonance of internal gravity waves. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA.
Ghaemsaidi, S. J., Dosser, H. V., Rainville, L. & Peacock, T. 2016a The impact of multiple layering on internal wave transmission. J. Fluid Mech. 789, 617629.
Ghaemsaidi, S. J., Joubaud, S., Dauxois, T., Odier, P. & Peacock, T. 2016b Nonlinear internal wave penetration via parametric subharmonic instability. Phys. Fluids 28 (1), 011703.
Gill, A. E. 1984 On the behavior of internal waves in the wakes of storms. J. Phys. Oceanogr. 14 (7), 11291151.
Gostiaux, L., Didelle, H., Mercier, S. & Dauxois, T. 2007 A novel internal waves generator. Exp. Fluids 42 (1), 123130.
Gregory, K. D. & Sutherland, B. R. 2010 Transmission and reflection of internal wave beams. Phys. Fluids 22 (10), 106601.
Kundu, P. K. 1993 On internal waves generated by travelling wind. J. Fluid Mech. 254, 529559.
Mathur, M. & Peacock, T. 2009 Internal wave beam propagation in non-uniform stratifications. J. Fluid Mech. 639, 133152.
Mathur, M. & Peacock, T. 2010 Internal wave interferometry. Phys. Rev. Lett. 104, 118501.
Mercier, M. J., Martinand, D., Mathur, M., Gostiaux, L., Peacock, T. & Dauxois, T. 2010 New wave generation. J. Fluid Mech. 657, 308334.
Nault, J. T. & Sutherland, B. R. 2007 Internal wave transmission in nonuniform flows. Phys. Fluids 19 (1), 016601.
Oster, G. 1965 Density gradients. Sci. Am. 213 (2), 7076.
Price, J. F. 1981 Upper ocean response to a hurricane. J. Phys. Oceanogr. 11, 153175.
Price, J. F. 1983 Internal wave wake of a moving storm. Part I. Scales, energy budget and observations. J. Phys. Oceonogr. 13, 949965.
Rayson, M. D., Ivey, G. N., Jones, N. L., Lowe, R. J., Wake, G. W. & McConochie, J. D. 2015 Near-inertial ocean response to tropical cyclone forcing on the Australian North-West Shelf. J. Geophys. Res. Oceans 120 (12), 77227751.
Supekar, R. B.2017 Interference and transmission of locally forced internal waves in non-uniform stratifications. Master’s thesis, Massachusetts Institute of Technology, Cambridge, MA.
Sutherland, B. R. 2010 Internal Gravity Waves. Cambridge University Press.
Sutherland, B. R. 2016 Internal wave transmission through a thermohaline staircase. Phys. Rev. Fluids 1 (1), 013701.
Sutherland, B. R. & Yewchuk, K. 2004 Internal wave tunnelling. J. Fluid Mech. 511, 125134.
Timmermans, M.-L., Toole, J., Krishfield, R. & Winsor, P. 2008 Ice-tethered profiler observations of the double-diffusive staircase in the Canada Basin thermocline. J. Geophys. Res. 113, C00A02.
Vailard, J., Duvel, J. P., McPhaden, M. J., Bouruet-Aubertot, P., Ward, B., Key, E., Bourras, D., Weller, R., Minnett, P., Weill, A. et al. 2009 Cirene: air–sea interactions in the Seychelles-Chagos thermocline ridge region. Bull. Am. Meteorol. Soc. 90 (1), 4561.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed