Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 19
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Machicoane, Nathanaël Cortet, Pierre-Philippe Voisin, Bruno and Moisy, Frédéric 2015. Influence of the multipole order of the source on the decay of an inertial wave beam in a rotating fluid. Physics of Fluids, Vol. 27, Issue. 6, p. 066602.

    Wang, Gang Zheng, Quanan Lin, Min Dai, Dejun and Qiao, Fangli 2015. Three dimensional simulation of internal wave attractors in the Luzon Strait. Acta Oceanologica Sinica, Vol. 34, Issue. 11, p. 14.

    Clark di Leoni, P. Cobelli, P. J. Mininni, P. D. Dmitruk, P. and Matthaeus, W. H. 2014. Quantification of the strength of inertial waves in a rotating turbulent flow. Physics of Fluids, Vol. 26, Issue. 3, p. 035106.

    Jouve, Laurène and Ogilvie, Gordon I. 2014. Direct numerical simulations of an inertial wave attractor in linear and nonlinear regimes. Journal of Fluid Mechanics, Vol. 745, p. 223.

    Nurijanyan, S. Bokhove, O. and Maas, L. R. M. 2013. A new semi-analytical solution for inertial waves in a rectangular parallelepiped. Physics of Fluids, Vol. 25, Issue. 12, p. 126601.

    Nurijanyan, S. van der Vegt, J.J.W. and Bokhove, O. 2013. Hamiltonian discontinuous Galerkin FEM for linear, rotating incompressible Euler equations: Inertial waves. Journal of Computational Physics, Vol. 241, p. 502.

    Scolan, Hélène Ermanyuk, Eugeny and Dauxois, Thierry 2013. Nonlinear Fate of Internal Wave Attractors. Physical Review Letters, Vol. 110, Issue. 23,

    Boisson, Jean Lamriben, Cyril Maas, Leo R. M. Cortet, Pierre-Philippe and Moisy, Frédéric 2012. Inertial waves and modes excited by the libration of a rotating cube. Physics of Fluids, Vol. 24, Issue. 7, p. 076602.

    Li, L. Patterson, M. D. Zhang, K. and Kerswell, R. R. 2012. Spin-up and spin-down in a half cone: A pathological situation or not?. Physics of Fluids, Vol. 24, Issue. 11, p. 116601.

    Lamriben, Cyril Cortet, Pierre-Philippe Moisy, Frédéric and Maas, Leo R. M. 2011. Excitation of inertial modes in a closed grid turbulence experiment under rotation. Physics of Fluids, Vol. 23, Issue. 1, p. 015102.

    Swart, Arno Manders, Astrid Harlander, Uwe and Maas, Leo R.M. 2010. Experimental observation of strong mixing due to internal wave focusing over sloping terrain. Dynamics of Atmospheres and Oceans, Vol. 50, Issue. 1, p. 16.

    Ogilvie, Gordon I. 2009. Tidal dissipation in rotating fluid bodies: a simplified model. Monthly Notices of the Royal Astronomical Society, Vol. 396, Issue. 2, p. 794.

    Messio, Laura Morize, Cyprien Rabaud, Marc and Moisy, Frédéric 2008. Experimental observation using particle image velocimetry of inertial waves in a rotating fluid. Experiments in Fluids, Vol. 44, Issue. 4, p. 519.

    Bewley, Gregory P. Lathrop, Daniel P. Maas, Leo R. M. and Sreenivasan, K. R. 2007. Inertial waves in rotating grid turbulence. Physics of Fluids, Vol. 19, Issue. 7, p. 071701.

    Drijfhout, Sybren and Maas, Leo R. M. 2007. Impact of Channel Geometry and Rotation on the Trapping of Internal Tides. Journal of Physical Oceanography, Vol. 37, Issue. 11, p. 2740.

    Harlander, Uwe and Maas, Leo R.M. 2007. Internal boundary layers in a well-mixed equatorial atmosphere/ocean. Dynamics of Atmospheres and Oceans, Vol. 44, Issue. 1, p. 1.

    MAAS, LEO R. M. 2005. WAVE ATTRACTORS: LINEAR YET NONLINEAR. International Journal of Bifurcation and Chaos, Vol. 15, Issue. 09, p. 2757.

    van Haren, Hans and Millot, Claude 2005. Gyroscopic waves in the Mediterranean Sea. Geophysical Research Letters, Vol. 32, Issue. 24,

    Manders, Astrid M M and Maas, Leo R M 2004. On the three-dimensional structure of the inertial wave field in a rectangular basin with one sloping boundary. Fluid Dynamics Research, Vol. 35, Issue. 1, p. 1.

  • Journal of Fluid Mechanics, Volume 493
  • October 2003, pp. 59-88

Observations of inertial waves in a rectangular basin with one sloping boundary

  • ASTRID M. M. MANDERS (a1) and LEO R. M. MAAS (a1)
  • DOI:
  • Published online: 01 October 2003

Inertial waves in a homogeneous rotating fluid travel along rays that are inclined with respect to the rotation axis. The angle of inclination depends solely on the ratio of the wave frequency and twice the angular frequency. Because of this fixed angle, the waves can become focused when reflected at a sloping wall. In an infinitely long channel with a sloping wall, the repeated action of focusing may lead to the approach to a limit cycle, the so-called wave attractor, where the energy is concentrated. This effect is studied in the laboratory in a rectangular tank with one sloping wall, placed excentrically on a rotating table. The waves are excited by modulation of the background rotation. Several frequency ratios are used to study different wave attractors and one standing wave. The observations consist mainly of particle image velocimetry data in horizontal and vertical cross-sections in one half of the basin. The attractors are observed in the vertical cross-sections. They show continuous phase propagation, which distinguishes them from the standing wave where the phase changes at the same time over the whole cross-section. However, particle motion of inertial waves is three-dimensional and the actual basin is not an ideal two-dimensional channel but is of finite length. This implies that the waves must adapt to the vertical endwalls, although a prediction of the nature of these adaptations and the structure of the three-dimensional wave field is at present lacking. For critical waves, whose rays are parallel to the slope, clear three-dimensional behaviour is observed. The location of most intense motion along this critical slope attractor changes in the horizontal direction and horizontal phase propagation is observed, with a wavelength between 1/5 and 1/4 of the basin length. For the other attractors there is little evidence of phase propagation in the horizontal direction. The motion along the attractor is however stronger near the vertical endwalls for attractors with wave rays of slopes close to 1 or larger. The standing wave and the other attractors are more clearly visible near 1/5 of the tank length.

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? *