Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T05:04:42.715Z Has data issue: false hasContentIssue false
  • English
  • Français

New wave generation

Published online by Cambridge University Press:  19 July 2010

MATTHIEU J. MERCIER ,
DENIS MARTINAND ,
MANIKANDAN MATHUR ,
LOUIS GOSTIAUX ,
THOMAS PEACOCK  and
THIERRY DAUXOIS
MATTHIEU J. MERCIER*
Affiliation:
Laboratoire de Physique de l'École Normale Supérieure de Lyon, CNRS–Université de Lyon, Lyon 69364, France
DENIS MARTINAND
Affiliation:
Laboratoire M2P2, UMR 6181 CNRS–Universités Aix-Marseille, Marseille 13451, France
MANIKANDAN MATHUR
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 01239, USA
LOUIS GOSTIAUX
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels (LEGI), CNRS, Grenoble 38000, France
THOMAS PEACOCK
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 01239, USA
THIERRY DAUXOIS
Affiliation:
Laboratoire de Physique de l'École Normale Supérieure de Lyon, CNRS–Université de Lyon, Lyon 69364, France
*
†Email address for correspondence: matthieu.mercier@ens-lyon.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

We present the results of a combined experimental and numerical study of the generation of internal waves using the novel internal wave generator design of Gostiaux et al. (Exp. Fluids, vol. 42, 2007, pp. 123–130). This mechanism, which involves a tunable source composed of oscillating plates, has so far been used for a few fundamental studies of internal waves, but its full potential is yet to be realized. Our study reveals that this approach is capable of producing a wide variety of two-dimensional wave fields, including plane waves, wave beams and discrete vertical modes in finite-depth stratifications. The effects of discretization by a finite number of plates, forcing amplitude and angle of propagation are investigated, and it is found that the method is remarkably efficient at generating a complete wave field despite forcing only one velocity component in a controllable manner. We furthermore find that the nature of the radiated wave field is well predicted using Fourier transforms of the spatial structure of the wave generator.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 657 , 25 August 2010 , pp. 308 - 334
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aguilar, D. A. & Sutherland, B. R. 2006 Internal wave generation from rough topography. Phys. Fluids 18, 066603.CrossRefGoogle Scholar
Alexander, M. J., Richter, J. H. & Sutherland, B. R. 2006 Generation and trapping of gravity waves from convection with comparison to parameterization. J. Atmos. Sci. 63, 2963–2977.CrossRefGoogle Scholar
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, 1614–1630.2.0.CO;2>CrossRefGoogle Scholar
Bell, T. H. 1975 Lee waves in stratified flows with simple harmonic time dependence. J. Fluid Mech. 67, 705–722.CrossRefGoogle Scholar
Dalziel, S. B., Hughes, G. O. & Sutherland, B. R. 2000 Whole-field density measurements by ‘synthetic schlieren’. Exp. Fluids 28, 322–335.CrossRefGoogle Scholar
Dauxois, T. & Young, W. R. 1999 Near-critical reflection of internal waves. J. Fluid Mech. 390, 271–295.CrossRefGoogle Scholar
Delisi, D. P. & Orlanski, I. 1975 On the role of density jumps in the reflection and breaking of internal gravity waves. J. Fluid Mech. 69, 445–464.CrossRefGoogle Scholar
Echeverri, P., Flynn, M. R., Peacock, T. & Winters, K. B. 2009 Low-mode internal tide generation by topography: an experimental and numerical investigation. J. Fluid Mech. 636, 91–108.CrossRefGoogle Scholar
Ermanyuk, E. V. & Gavrilov, N. V. 2008 On internal waves generated by large-amplitude circular and rectilinear oscillations of a circular cylinder in a uniformly stratified fluid. J. Fluid Mech. 613, 329–356.CrossRefGoogle Scholar
Fincham, A. & Delerce, G. 2000 Advanced optimization of correlation imaging velocimetry algorithms. Exp. Fluids 29, S1.CrossRefGoogle Scholar
Garrett, C. & Kunze, E. 2007 Internal tide generation in the deep ocean. Annu. Rev. Fluid Mech. 39, 57–87.CrossRefGoogle Scholar
Gavrilov, N. V. & Ermanyuk, E. V. 1996 Internal waves generated by circular translational motion of a cylinder in a linearly stratified fluid. J. Appl. Mech. Tech. Phys. 38, 224–227.CrossRefGoogle Scholar
Gerkema, T. 2001 Internal and interfacial tides: beam scattering and local generation of solitary waves. J. Mar. Res. 59, 227–255.CrossRefGoogle Scholar
Gilbert, N. 1988 Transition von der laminaren in die turbulente Kanalströmung. PhD thesis, DFVLR Institut für Strömungsmechanik, Göttingen, Germany.Google Scholar
Gill, A. E. 1982 Atmosphere–Ocean Dynamics. Academic.Google Scholar
Gostiaux, L. 2006 Etude expérimentale des ondes de gravité internes en présence de topographie. émission, propagation, réflexion. PhD thesis, École Normale Supérieure, Lyon, France.Google Scholar
Gostiaux, L. & Dauxois, T. 2007 Laboratory experiments on the generation of internal tidal beams over steep slopes. Phys. Fluids 19, 028102.CrossRefGoogle Scholar
Gostiaux, L., Didelle, H., Mercier, S. & Dauxois, T. 2007 A novel internal wave generator. Exp. Fluids 42, 123–130.CrossRefGoogle Scholar
Hurley, D. G. & Keady, G. 1997 The generation of internal waves by vibrating elliptic cylinders. Part 2. Approximate viscous solution. J. Fluid Mech. 351, 119–138.CrossRefGoogle Scholar
Ivey, G. N., Winters, K. B. & De Silva, I. P. D. 2000 Turbulent mixing in a sloping benthic boundary layer energized by internal waves. J. Fluid Mech. 418, 59–76.CrossRefGoogle Scholar
Johnston, T. M. S. & Merrifield, M. A. 2003 Internal tide scattering at seamounts, ridges and islands. J. Geophys. Res. 108 (C6), 3180.Google Scholar
Kleiser, L. & Schumann, U. 1980 Treatment of incompressibility and boundary conditions in 3-D numerical spectral simulations of plane channel flows. In Proceedings of Third GAMM Conference on Numerical Methods in Fluid Mechanics (ed. Hirschel, E. H.), pp. 165–173. Vieweg.CrossRefGoogle Scholar
Kleiser, L. & Schumann, U. 1984 Spectral simulations of the laminar–turbulent transition process in plane poiseuille flow. In Spectral Methods for Partial Differential Equations (ed. Voigt, R. G., Gottlieb, D. & Hussaini, M. Y.), pp. 141–163. SIAM.Google Scholar
Lam, F. P. A., Maas, L. R. M. & Gerkema, T. 2004 Spatial structure of tidal and residual currents as observed over the shelf break in the bay of biscay. Deep-Sea Res. I 51, 1075–1096.CrossRefGoogle Scholar
Lighthill, J. 1978 Waves in Fluids. Cambridge University Press.Google Scholar
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, 557–561.CrossRefGoogle Scholar
Martin, J. P., Rudnick, D. L. & Pinkel, R. 2006 Spatially broad observations of internal waves in the upper ocean at the hawaiian ridge. J. Phys. Oceanogr. 36, 1085–1103.CrossRefGoogle Scholar
Martinand, D., Carrière, Ph. & Monkewitz, P. A. 2006 Three-dimensional global instability modes associated with a localized hot spot in Rayleigh–Bénard–Poiseuille convection. J. Fluid Mech. 551, 275–301.CrossRefGoogle Scholar
Mathur, M. & Peacock, T. 2009 Internal wave beam propagation in nonuniform stratifications. J. Fluid Mech. 639, 133–152.CrossRefGoogle Scholar
McEwan, A. D. & Baines, P. G. 1974 Shear fronts and an experimental stratified shear flow. J. Fluid Mech. 63, 257–272.CrossRefGoogle Scholar
Mercier, M. J., Garnier, N. B. & Dauxois, T. 2008 Reflection and diffraction of internal waves analyzed with the Hilbert transform. Phys. Fluids 20, 086601.CrossRefGoogle Scholar
Mowbray, D. E. & Rarity, B. S. H. 1967 A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified fluid. J. Fluid Mech. 28, 1–16.CrossRefGoogle Scholar
Naito, S. 2006 Wave generation and absorption – theory and application. In Proceedings of the Sixteenth International Offshore and Polar Engineering Conference (ed. Chung, J. S., Kashiwagi, M., Ferrant, J., Mizutani, N. & Chien, L. K.), pp. 1–9. International Society of Offshore and Polar Engineers.Google Scholar
Nault, J. T. & Sutherland, B. R. 2007 Internal wave transmission in non-uniform flows. Phys. Fluids 19, 016601.CrossRefGoogle Scholar
New, A. L. & Da Silva, J. C. B. 2002 Remote sensing evidence for the local generation of internal soliton packets in the central Bay of Biscay. Deep-Sea Res. I 49, 915–934.CrossRefGoogle Scholar
New, A. L. & Pingree, R. D. 1990 Evidence for internal tidal mixing near the shelf break in the bay of biscay. Deep-Sea Res. 37, 1783–1803.CrossRefGoogle Scholar
Nicolaou, D., Liu, R. & Stevenson, T. N. 1993 The evolution of thermocline waves from an oscillatory disturbance. J. Fluid Mech. 254, 401–416.CrossRefGoogle Scholar
Osborne, A. R., Burch, T. L. & Scarlet, R. I. 1978 The influence of internal waves on deep-water drilling. J. Petrol. Engng 30, 1497–1504.Google Scholar
Oster, C. 1965 Density gradients. Sci. Am. 213, 70–76.CrossRefGoogle Scholar
Peacock, T. & Tabei, A. 2005 Visualization of nonlinear effects in reflecting internal wave beams. Phys. Fluids 17, 061702.CrossRefGoogle Scholar
Ray, R. D. & Mitchum, G. T. 1997 Surface manifestation of internal tides in the deep ocean: observations from altimetry and island gauges. Prog. Oceangr. 40, 135–162.CrossRefGoogle Scholar
Tabaei, A. & Akylas, T. R. 2003 Nonlinear internal gravity wave beams. J. Fluid Mech. 482, 141–161.CrossRefGoogle Scholar
Tabaei, A., Akylas, T. R. & Lamb, K. G. 2005 Nonlinear effects in reflecting and colliding internal wave beams. J. Fluid Mech. 526, 217–243.CrossRefGoogle Scholar
Thomas, N. H. & Stevenson, T. N. 1972 A similarity solution for viscous internal waves. J. Fluid Mech. 54, 495–506.CrossRefGoogle Scholar
Thorpe, S. A. 1968 On the shape of progressive internal waves. Phil. Trans. R. Soc. Lond. A 263, 563–614.Google Scholar
Thorpe, S. A. 1987 On the reflection of a train of finite-amplitude internal waves from a uniform slope. J. Fluid Mech. 178, 279–302.CrossRefGoogle Scholar
Thorpe, S. A. 1998 Nonlinear reflection of internal waves at a density discontinuity at the base of a mixed layer. J. Phys. Oceanogr. 28, 1853–1860.2.0.CO;2>CrossRefGoogle Scholar
Voisin, B. 2003 Limit states of internal wave beams. J. Fluid Mech. 496, 243–293.CrossRefGoogle Scholar
Walterscheid, R. L., Schubert, G. & Brinkman, D. G. 2001 Small scale gravity waves in the upper mesosphere and lower thermosphere generated by deep tropical convection. J. Geophys. Res. 106 (D23), 31825–31832.CrossRefGoogle Scholar