Experiments in Fluids

, 54:1454 | Cite as

3D Stereoscopic PIV visualization of the axisymmetric conical internal wave field generated by an oscillating sphere

Research Article


To date, experimental studies of internal wave velocity fields have been limited to two-dimensional investigations of planar or axisymmetric systems. Here, we present results of the first three-dimensional stereoscopic Particle Image Velocimetry (PIV) visualizations of an internal wave field. The experiments utilize the canonical arrangement of a vertically oscillating sphere, which enables rigorous comparison with recently published theoretical results. The excellent level of agreement between experiment and theory demonstrates the utility of using stereoscopic PIV to study three-dimensional internal waves. Furthermore, the ability to measure all three components of the velocity field gives an alternative perspective on the significance of harmonics generated via nonlinear processes in the vicinity of the oscillating sphere.


  1. Appleby JC, Crighton DG (1987) Internal gravity waves generated by oscillations of a sphere. J Fluid Mech 183:439–450MATHCrossRefGoogle Scholar
  2. Dalziel SB, Carr M, Sveen JK, Davies PA (2007) Simultaneous synthetic schlieren and PIV measurements for internal solitary waves. Meas Sci Technol 18:533–547CrossRefGoogle Scholar
  3. Echeverri P, Flynn MR, Winters KB, Peacock T (2009) Low-mode internal tide generation by topography: an experimental and numerical investigation. J Fluid Mech 636:91–108MathSciNetMATHCrossRefGoogle Scholar
  4. Ermanyuk EV, Flor J-B, Voisin B (2011) Spatial structure of first and higher harmonic internal waves from a horizontally oscillating sphere. J Fluid Mech 671:364–383MathSciNetMATHCrossRefGoogle Scholar
  5. Flynn MR, Onu K, Sutherland BR (2003) Internal wave excitation by a vertically oscillating sphere. J Fluid Mech 494:65–93MathSciNetMATHCrossRefGoogle Scholar
  6. Garrett C, Kunze E (2007) Internal tide generation in the deep ocean. Ann Rev Fluid Mech 39:57–87MathSciNetCrossRefGoogle Scholar
  7. Gortler VH (1943) Uber eine Schwingungserscheinung in Flussigkeiten. Zeitschrift fur angewandte mathematik und mechanik 23:65–71MathSciNetCrossRefGoogle Scholar
  8. Hazewinkel J, Maas LRM, Dalziel SB (2011) Tomographic reconstruction of internal wave patterns in a paraboloid. Exp Fluids 50:247–258CrossRefGoogle Scholar
  9. Hurley DG (1972) A general method for solving steady-state internal gravity wave problems. J Fluid Mech 56:721–740MathSciNetMATHCrossRefGoogle Scholar
  10. King B, Zhang HP, Swinney HL (2009) Tidal flow over three-dimensional topography in a stratified fluid. Phys Fluids 21:116601CrossRefGoogle Scholar
  11. Lighthill MJ (1978) Waves in fluids. Cambridge University Press, CambridgeMATHGoogle Scholar
  12. Mathur M, Peacock T (2009) Internal wave beam propagation in non-uniform stratifications. J Fluid Mech 639:133–152MATHCrossRefGoogle Scholar
  13. Mercier MJ, Garnier NB, Dauxois T (2008) Reflection and diffraction of internal waves analyzed with the Hilbert transform. Phys Fluids 20:086601CrossRefGoogle Scholar
  14. Mowbray DE (1967) The use of schlieren and shadowgraph techniques in the study of flow patterns in density stratified liquids. J Fluid Mech 27:595–608CrossRefGoogle Scholar
  15. Mowbray DE, Rarity BSH (1967) A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified liquid. J Fluid Mech 28:1–16CrossRefGoogle Scholar
  16. Oster G, Yamamoto M (1963) Density gradient techniques. Chem Rev 63(3):257–268CrossRefGoogle Scholar
  17. Peacock T, Echeverri P, Balmforth NJ (2008) An experimental investigation of internal tide generation by two-dimensional topography. J Phys Oceanogr 38:235–242CrossRefGoogle Scholar
  18. Scheimpflug T (1904) Method of distorting plane images by means of lenses or mirrors. Patent No. 751347, February 1904Google Scholar
  19. Sutherland BR, Dalziel SB, Hughes GO, Linden PF (1999) Visualization and measurement of internal waves by ‘synthetic schlieren’. Part 1. Vertically oscillating cylinder. J Fluid Mech 390:93–126MATHCrossRefGoogle Scholar
  20. Sutherland BR, Linden PF (2002) Internal wave excitation by a vertically oscillating elliptical cylinder. Phys Fluids 14:721–731MathSciNetCrossRefGoogle Scholar
  21. Thomas NH, Stevenson TN (1972) A similarity solution for viscous internal waves. J Fluid Mech 54:495–506MATHCrossRefGoogle Scholar
  22. Voisin B (2003) Limit states of internal wave beams. J Fluid Mech 496:243–293MathSciNetMATHCrossRefGoogle Scholar
  23. Voisin B, Ermanyuk EV, Flor J-B (2011) Internal wave generation by oscillation of a sphere, with application to internal tides. J Fluid Mech 666:308–357MathSciNetMATHCrossRefGoogle Scholar
  24. Wieneke B (2005) Stereo-PIV using self-calibration on particle images. Exp Fluids 39:267–280CrossRefGoogle Scholar
  25. Yick KY, Torres CR, Peacock T, Stocker R (2009) Enhanced drag of a sphere settling in a stratified fluid at small Reynolds numbers. J Fluid Mech 632:49–68MATHCrossRefGoogle Scholar
  26. Zhang HP, King B, Swinney HL (2007) Experimental study of internal gravity waves generated by supercritical topography. Phys Fluids 19:096602CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations