Skip to main content Accessibility help
×
Home

Observations on the wavenumber spectrum and evolution of an internal wave attractor

  • JEROEN HAZEWINKEL (a1) (a2), PIETER VAN BREEVOORT (a3), STUART B. DALZIEL (a2) and LEO R. M. MAAS (a1) (a3)

Abstract

Reflecting internal gravity waves in a stratified fluid preserve their frequency and thus their angle with the gravitational direction. At boundaries that are neither horizontal nor vertical, this leads to a focusing or defocusing of the waves. Previous theoretical and experimental work has demonstrated how this can lead to internal wave energy being focused onto ‘wave attractors’ in relatively simple geometries. We present new experimental and theoretical results on the dynamics of wave attractors in a nearly two-dimensional trapezoidal basin. In particular, we demonstrate how a basin-scale mode forced by simple mechanical excitation develops an equilibrium spectrum. We find a balance between focusing of the basin-scale internal wave by reflection from a single sloping boundary and viscous dissipation of the waves with higher wavenumbers. Theoretical predictions using a simple ray-tracing technique are found to agree well with direct experimental observations of the waves. With this we explain the observed behaviour of the wave attractor during the initial development, steady forcing, and the surprising increase of wavenumber during the decay of the wave field after the forcing is terminated.

Copyright

References

Hide All
Benielli, D. & Sommeria, J. 1998 Excitation and breaking of internal gravity waves by parametric instability. J. Fluid Mech 374, 117144.
Dalziel, S.B., Hughes, G.O. & Sutherland, B.R. 2000 Whole field density measurements by ‘synthetic schlieren’. Exps. Fluids 28, 322335.
Lam, F.-P.A. & Maas, L. R.M. 2008 Internal wave focusing revisited; a reanalysis and new theoretical links. Fluid Dyn. Res 40, 95122.
LeBlond, P.H. & Mysak, L.A. 1978 Waves in the Ocean. Elsevier.
Maas, L. R. M. 2001 Wave focussing and ensuing mean flow due to symmetry breaking in rotating fluids. J. Fluid Mech 437, 1328.
Maas, L. R. M. 2005 Wave attractors: linear yet nonlinear. Intl J. Bifurcation Chaos 15, 27572782.
Maas, L. R. M., Benielli, D., Sommeria, J. & Lam, F.-P.A. 1997 Observation of an internal wave attractor in a confined stably-stratified fluid. Nature 388, 557561.
Maas, L. R. M. & Lam, F.-P.A. 1995 Geometric focusing of internal waves. J. Fluid Mech 300, 141.
Manders, A. M. M. & Maas, L. R. M. 2003 Observations of inertial waves in a rectangular basin with one sloping boundary. J. Fluid Mech 493, 5988.
Manders, A. M. M. & Maas, L. R. M. 2004 On the three-dimensional structure of the inertial wave field in a rectangular basin with one sloping boundary. Fluid Dyn. Res 35, 121.
Ogilvie, G.I. 2005 Wave attractors and the asymptotic dissipation rate of tidal disturbances. J. Fluid Mech 543, 1944.
Phillips, O.M. 1977 The Dynamics of the Upper Ocean, 2nd edn. Cambridge University Press.
Rieutord, M., Valdettaro, L. & Georgeot, B. 2001 Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum. J. Fluid Mech 435, 103144.
Rieutord, M., Valdettaro, L. & Georgeot, B. 2002 Analysis of singular inertial modes in a spherical shell: the slender toroidal shell model. J. Fluid Mech 463, 345360.
Stewartson, K. 1971 On trapped oscillations of a rotating fluid in a thin spherical shell. Tellus XXII (6), 506510.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Metrics

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