Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 24
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Ghaemsaidi, S. J. Joubaud, S. Dauxois, T. Odier, P. and Peacock, T. 2016. Nonlinear internal wave penetration via parametric subharmonic instability. Physics of Fluids, Vol. 28, Issue. 1, p. 011703.


    Sutherland, Bruce R. 2016. Internal wave transmission through a thermohaline staircase. Physical Review Fluids, Vol. 1, Issue. 1,


    Wunsch, Scott Delwiche, Ian Frederick, Gary and Brandt, Alan 2015. Experimental study of nonlinear harmonic generation by internal waves incident on a pycnocline. Experiments in Fluids, Vol. 56, Issue. 5,


    Zhou, Qi and Diamessis, Peter J. 2015. Lagrangian flows within reflecting internal waves at a horizontal free-slip surface. Physics of Fluids, Vol. 27, Issue. 12, p. 126601.


    Diamessis, P.J. Wunsch, S. Delwiche, I. and Richter, M.P. 2014. Nonlinear generation of harmonics through the interaction of an internal wave beam with a model oceanic pycnocline. Dynamics of Atmospheres and Oceans, Vol. 66, p. 110.


    Dossmann, Yvan Paci, Alexandre Auclair, Francis Lepilliez, Mathieu and Cid, Emmanuel 2014. Topographically induced internal solitary waves in a pycnocline: Ultrasonic probes and stereo-correlation measurements. Physics of Fluids, Vol. 26, Issue. 5, p. 056601.


    Mathur, Manikandan Carter, Glenn S. and Peacock, Thomas 2014. Topographic scattering of the low-mode internal tide in the deep ocean. Journal of Geophysical Research: Oceans, Vol. 119, Issue. 4, p. 2165.


    Smith, S. and Crockett, J. 2014. Experiments on nonlinear harmonic wave generation from colliding internal wave beams. Experimental Thermal and Fluid Science, Vol. 54, p. 93.


    Stevens, CL Consalvey, M Devine, JA and Clark, MR 2014. Mixing and transport near the shallow-crested Rumble III seamount and the implications for plankton distribution. New Zealand Journal of Marine and Freshwater Research, Vol. 48, Issue. 2, p. 194.


    Sutherland, Bruce Dauxois, Thierry and Peacock, Thomas 2014. Modeling Atmospheric and Oceanic Flows.


    Dossmann, Y. Auclair, F. and Paci, A. 2013. Topographically induced internal solitary waves in a pycnocline: Secondary generation and selection criteria. Physics of Fluids, Vol. 25, Issue. 8, p. 086603.


    Gayen, B. and Sarkar, S. 2013. Degradation of an internal wave beam by parametric subharmonic instability in an upper ocean pycnocline. Journal of Geophysical Research: Oceans, Vol. 118, Issue. 9, p. 4689.


    Ghaemsaidi, Sasan John and Peacock, Thomas 2013. 3D Stereoscopic PIV visualization of the axisymmetric conical internal wave field generated by an oscillating sphere. Experiments in Fluids, Vol. 54, Issue. 2,


    Hall, Rob A. Huthnance, John M. and Williams, Richard G. 2013. Internal Wave Reflection on Shelf Slopes with Depth-Varying Stratification. Journal of Physical Oceanography, Vol. 43, Issue. 2, p. 248.


    Zhou, Qi and Diamessis, Peter J. 2013. Reflection of an internal gravity wave beam off a horizontal free-slip surface. Physics of Fluids, Vol. 25, Issue. 3, p. 036601.


    King, Benjamin Stone, Mark Zhang, H. P. Gerkema, Theo Marder, M. Scott, Robert B. and Swinney, Harry L. 2012. Buoyancy frequency profiles and internal semidiurnal tide turning depths in the oceans. Journal of Geophysical Research: Oceans, Vol. 117, Issue. C4, p. n/a.


    Wunsch, Scott and Brandt, Alan 2012. Laboratory experiments on internal wave interactions with a pycnocline. Experiments in Fluids, Vol. 53, Issue. 6, p. 1663.


    Dossmann, Yuan Paci, Alexandre Auclair, Francis and Floor, Jochem W. 2011. Simultaneous velocity and density measurements for an energy-based approach to internal waves generated over a ridge. Experiments in Fluids, Vol. 51, Issue. 4, p. 1013.


    GRISOUARD, N. STAQUET, C. and GERKEMA, T. 2011. Generation of internal solitary waves in a pycnocline by an internal wave beam: a numerical study. Journal of Fluid Mechanics, Vol. 676, p. 491.


    GRISOUARD, N. STAQUET, C. and GERKEMA, T. 2011. Generation of internal solitary waves in a pycnocline by an internal wave beam: a numerical study. Journal of Fluid Mechanics, Vol. 676, p. 491.


    ×
  • Journal of Fluid Mechanics, Volume 639
  • November 2009, pp. 133-152

Internal wave beam propagation in non-uniform stratifications

  • MANIKANDAN MATHUR (a1) and THOMAS PEACOCK (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112009991236
  • Published online: 30 October 2009
Abstract

In addition to being observable in laboratory experiments, internal wave beams are reported in geophysical settings, which are characterized by non-uniform density stratifications. Here, we perform a combined theoretical and experimental study of the propagation of internal wave beams in non-uniform density stratifications. Transmission and reflection coefficients, which can differ greatly for different physical quantities, are determined for sharp density-gradient interfaces and finite-width transition regions, accounting for viscous dissipation. Thereafter, we consider even more complex stratifications to model geophysical scenarios. We show that wave beam ducting can occur under conditions that do not necessitate evanescent layers, obtaining close agreement between theory and quantitative laboratory experiments. The results are also used to explain recent field observations of a vanishing wave beam at the Keana Ridge, Hawaii.

Copyright
Corresponding author
Email address for correspondence: manims@mit.edu
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

M. J. Alexander , J. R. Holton & D. R. Durran 1995 The gravity wave response above deep convection in a squall line simulation. J. Atmos. Sci. 52, 22122226.

A. Barcilon , S. Blumsack & J. Lau 1972 Reflection of internal gravity waves by small density variations. J. Phys. Ocean. 2, 104107.

G. L. Brown & B. R. Sutherland 2007 Internal wave tunnelling through non-uniformly stratified shear flow. Atmos. Ocean 45, 4756.

S. T. Cole , D. L. Rudnick , B. A. Hodges & J. P. MArtin 2009 Observations of tidal internal wave beams at Kauai Channel, Hawaii. J. Phys. Ocean. 39, 421436.

S. B. Dalziel , G. O. Hughes & B. R. Sutherland 2000 Whole-field density measurements by ‘synthetic schlieren’. Expts. Fluids 28, 322335.

C. Eckart 1961 Internal waves in the ocean. Phys. Fluids. 4, 791799.

D. C. Fritts & L. Yuan 1989 An analysis of gravity wave ducting in the atmosphere: Eckart's resonances in thermal and Doppler ducts J. Geophys. Res. 94 (D15), 1845518466.

T. Gerkema 2001 Internal and interfacial tides: beam scattering and local generation of solitary waves. J. Mar. Res. 59 (2), 227255.

A. E. Gill 1982 Atmosphere–Ocean Dynamics. Academic Press Inc.

L. Gostiaux & T. Dauxois 2007 Laboratory experiments on the generation of internal tidal beams over steep slopes. Phys. Fluids 19, 028102.

L. Gostiaux , H. Didelle , S. Mercier & T. Dauxois 2007 A novel internal waves generator. Expts. Fluids 42, 123130.

Y. V. Kistovich & Y. D. Chacheshkin 1998 Linear theory of the propagation of internal wave beams in an arbitrarily stratified liquid. J. Appl. Mech. & Tech. Phys. 39 (5), 729737.

R.-C. Lien & M. C. Gregg 2001 Observations of turbulence in a tidal beam and across a coastal ridge. J. Geophys. Res. 106, 45754591.

J. P. Martin , D. L. Rudnick & R. Pinkel 2006 Spatially broad observations of internal waves in the upper ocean at the Hawaiian ridge. J. Phys. Ocean. 36 (6), 10851103.

J. T. Nault & B. R. Sutherland 2007 Internal wave transmission in non-uniform flows. Phys. Fluids 19, 016601.

T. Peacock , P. Echeverri & N. J. B. Balmforth 2008 Experimental investigation of internal tide generation by two-dimensional topography. J. Phys. Ocean. 38, 235242.

T. Peacock & A. Tabaei 2005 Visualization of nonlinear effects in reflecting internal wave beams. Phys. Fluids 17, 061702.

T. Peacock & P. Weidman 2005 The effect of rotation on conical wave beams in a stratified fluid. Expts. Fluids 39, 3237.

S. A. Thorpe 1999 On the breaking of internal waves in the ocean. J. Phys. Ocean. 29, 24332441.

R. L. Walterscheid , G. Schubert & D. G. Brinkman 2001 Small-scale gravity waves in the upper mesosphere and lower thermosphere generated by deep tropical convection J. Geophys. Res. 106 (D23), 3182531832.

H. P. Zhang , B. King & H. L. Swinney 2007 Experimental study of internal gravity waves generated by supercritical topography Phys. Fluids 19, 096602.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax