Advertisement

Laboratory Modeling on Transformation of Large-Amplitude Internal Waves by Topographic Obstructions

  • N. Gorogedtska
  • V. Nikishov
  • K. Hutter
Chapter
Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM)

Abstract

In this chapter, the results of laboratory investigations of the generation and propagation of large-amplitude solitary internal waves in two-layer systems with complex topography are presented. The influence of the shape and size of underwater obstacles and localized constrictions of the channel on the transformation, reflection, and fission of solitary waves is studied. Interaction of solitary wave with different types of slopes is analyzed.

Keywords

Solitary Wave Incident Wave Wave Amplitude Internal Wave Vortical Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The authors thank their colleagues from IHM NASU: Dr. Oleksandr Stetsenko for fruitful discussions and for assisting with the experiments; we also thank Dr. Vitaliy Oleksiuk, Mr. Oleksiy Kulik, and Mr Sergey Pihur for help when conducting the experiments.

This research was supported by INTAS Grant No. 03-51-3728.

References

  1. Ablowitz M.J., Segur H. Solitons and the Inverse Scattering Transform. SIAM, 1981, 438 p.Google Scholar
  2. Armi, L.: The hydraulics of two flowing layers with different densities. J. Fluid Mech. 163, 27–58 (1986)CrossRefGoogle Scholar
  3. Benjamin, T.B.: Internal waves of permanent form in fluid of great depth. J. Fluid Mech. 29, 559–592 (1967)CrossRefGoogle Scholar
  4. Boegman, L., Ivey, G.N., Imberger, J.: The degeneration of internal waves in lakes with sloping topography. Limnol. Oceanogr. 50, 1620–1637 (2005)CrossRefGoogle Scholar
  5. Bogucki, D., Garrett, C.:A simple model for the shear-induced decay of an internal solitary wave. J. Phys. Oceanogr. 8, 1767–1776 (1993)Google Scholar
  6. Bourgault, D., Kelley, D.E.: On the reflectance of uniform slopes for normally incident interfacial solitary nwaves. J. Phys. Oceanogr. 37, 1156–1162 (2007)CrossRefGoogle Scholar
  7. Bourgault, D., Kelley, D.E., Galbraith, P.S.: Interfacial solitary wave run-up in the St. Lawrence estuary. J. Mar. Res. 63, 1001–1015 (2005)CrossRefGoogle Scholar
  8. Bukreev, V.I., Gavrilov, N.V.: Experimental investigation of solitary internal waves in a two-layer fluid. Zh. Prikl. Mekh. Tekhn. Fiziki (PMTF) N.5, 51–56 (1983) (in Russian) 1983 [English translation: Sov. Phys. J. Appl. Mech. Tech. Phys. n.5 (1983)].Google Scholar
  9. Cacchione, D., Wünch, C.: Experimental study of internal waves over a slope. J. Fluid Mech. 66, 223–239 (1974)CrossRefGoogle Scholar
  10. Carr, M., Davies, P.A.: The motion of an internal solitary wave of depression over a fixed bottom bouddary in a shallow, two-layer fluid. Phys. Fluids 18, 016601 (2006)CrossRefGoogle Scholar
  11. Chen, C.-Y., Hsu, J.R.-C., Chen, H.-H., Kuo, C.-F., Cheng, M.-H.: Laboratory observations on internal solitary wave evolution on steep and inverse uniform slopes. Ocean Eng. 34, 157–170 (2007a)CrossRefGoogle Scholar
  12. Chen, C.-Y., Hsu, J.R.-C., Chen, H.-H., Kuo, C.-F., Cheng, M.-H.: An investigation on internal solitary waves in a two-layer fluid: Propagation and reflection from steep slope. Ocean Eng. 34, 171–184 (2007b)CrossRefGoogle Scholar
  13. Dauxious, T., Didier, A., Falcon, E.: Observations of near-critical reflection of internal waves in a stably stratified fluid. Phys. Fluids 16, 1936–1941 (2004)CrossRefGoogle Scholar
  14. Diebels, S., Schuster, B. & Hutter, K.: Nonlinear internal waves over variable bottom topography. Geophys. Astrophys. Fluid Dyn. 76, 165–192 (1994)CrossRefGoogle Scholar
  15. Djordjevic, V.D., Redekopp, L.G.: The fission and disintegration of internal solitary waves moving over two-dimensional topography. J. Phys. Oceanogr. 8, 1016–1024 (1978)CrossRefGoogle Scholar
  16. Drazin P.G., Reid W.H. Hydrodynamic stability. Cambridge University Press, 2004, 605 p.Google Scholar
  17. Evans, W.A.B., Ford, M.J.: An integral equation approach to internal (2-layer) solitary waves. Phys. Fluids 8, 2032–2047 (1996)CrossRefGoogle Scholar
  18. Funakoshi, M.: Long internal waves in a two-layer fluid. J. Phys. Soc. Japan 54, 2470–2476 (1985).CrossRefGoogle Scholar
  19. Funakoshi, M., Oikawa, M.: Long internal waves of large amplitude in a two-layer fluid. J. Phys. Soc. Japan 55,128-144 (1986)CrossRefGoogle Scholar
  20. Gavrilov, N.V.: Viscous damping of solitary internal waves in two-layer fluid. Zh. Prikl. Mekh. i Tekhn. Fiziki N.4, 51–54 (1988)(in Russian)Google Scholar
  21. Gear, J., Grimshaw, R.: A second-order theory for solitary waves in shallow fluids. Phys. Fluids 26, 14–29 (1983)CrossRefGoogle Scholar
  22. Grue, J., Jensen, P.O., Rusas, P.-O., Sveen, J.K.: Properties of large-amplitude internal waves. J. Fluid Mech. 380, 257–278 (1999)CrossRefGoogle Scholar
  23. Grue J. Generation, propagation, and breaking of internal waves. Chaos, 15, 037110 (2005)CrossRefGoogle Scholar
  24. Guo, Y., Sveen, J.K., Davies, P.A., Grue, J., Dong, P.: Modelling the motion of an internal solitary wave over a bottom ridge in a stratified fluid. Environ. Fluid Mech. 4, 415–441 (2004)CrossRefGoogle Scholar
  25. Helfrich, K.R.: Internal solitary wave breaking and run-up on a uniform slope. J. Fluid Mech. 243, 133–154 (1992)CrossRefGoogle Scholar
  26. Helfrich, K.R., Melville, W.K.: On long nonlinear internal waves over slope-shelf topography. J. Fluid Mech. 167, 285–308 (1986)CrossRefGoogle Scholar
  27. Helfrich, K.R., Melville, W.K., Miles, J.W.: On interfacial solitary waves over slowly varying top[pgraphy. J. Fluid Mech. 149, 305–317 (1984)CrossRefGoogle Scholar
  28. Horn, D.A., Redekopp, L.G., Imberger, J., Ivey, G.N.: Internal wave evolution in a space- time varying field. J. Fluid Mech. 424, 279–301 (2000)CrossRefGoogle Scholar
  29. Horn, D.A., Imberger, J., Ivey, G.N.: The degeneration of large-scale interfacial gravity waves in lakes. J. Fluid Mech. 434, 181–207 (2001)CrossRefGoogle Scholar
  30. Hüttemann, H.: Modulation interner Wasserwellen durch Variation der Bodentopographie. Diploma Thesis, Department of Mechanics, Darmstadt University of Technology, 110 p. (1997)Google Scholar
  31. Hüttemann, H., Hutter, K.: Baroclinic solitary water waves in two-layer fluid system with diffusive interface. Exp.Fluids 30, 317–326 (2001)CrossRefGoogle Scholar
  32. Ivey, G.N., Nokes, R.I.: Vertical mixing due to the breaking of critical internal waves on slope boundaries. J. Fluid Mech. 204, 479–500 (1989)CrossRefGoogle Scholar
  33. Joseph R.I. Solitary waves in a finite depth fluid. J.Fluid Mech., 10, L225-L227 (1977)Google Scholar
  34. Kakutani, T., Yamazaki, N.: Solitary waves on a two-layer fluid. J. Phys. Soc. Japan 45, 674–679 (1978)CrossRefGoogle Scholar
  35. Kao, T.W., Pan, F.S. Renouard, D.: Internal soliton on the pycnocline : Generation, propagation, and shoaling and breaking over a slope. J. Fluid Mech.159, 19–53 (1985)CrossRefGoogle Scholar
  36. Keulegan, G.H.: Gradual damping of solitary waves. J. Res. Natl. Bur. Stand. 40, 480–487 (1948)CrossRefGoogle Scholar
  37. Keulegan, G.H.: Characteristics of internal solitary waves. J. Res. Natl. Bur. Stand. 51, 133–140 (1953)CrossRefGoogle Scholar
  38. Koop, C.G., Butler, G.: An investigation of internal solitary waves in a two-fluid system. J. Fluid Mech. 112, 225–251 (1981)CrossRefGoogle Scholar
  39. Kocsis, O., Mathis, B., Gloor, M., Schurter, M., Wüest, A.: Enhanced mixing in narrows: A case study at the Mainau sill (Lake Constance). Aquat.sci. 60, 236–252 (1998)Google Scholar
  40. Kubota, T., Ko, D.R.S., Dobbs, L.D.: Weakly-nonlinear, long internal gravity waves in stratified fluids of finite depth. J. Hydronautics 12, 157–165 (1978)CrossRefGoogle Scholar
  41. Lawrence, G.A.: On the hydraulics of Boussinesq and non-Boussinesq two-layer flows. J. Fluid Mech. 215, 457–480 (1990)CrossRefGoogle Scholar
  42. Lee, C.-Y., Beardsley, R.C.: The generation of long nonlinear internal waves in a weakly stratified shear flow. J. Geophys. Res. 79, 453–457 (1974)CrossRefGoogle Scholar
  43. Leone, C., Segur, H., Hammack, J.L.: Viscous decay of long internal solitary waves. Phys. Fluids 25, 942–944 (1982)CrossRefGoogle Scholar
  44. Maurer, J.: Skaleneffekte bei internen Wellen im Zweischichten-Fluid mit topographischen Erhebungen. Diploma Thesis, Department of Mechanics, Darmstadt University of Technology, 112 p (1993)Google Scholar
  45. Maurer, J., Hutter, K., Diebels, S.: Viscous effects in internal waves of a two-layered fluid with variable depth. Eur. J. Mech., B/Fluids 15, 445–470 (1986)Google Scholar
  46. Michallet, H., Barthelemy, E.: Ultrasonic probe and data processing to study interrfacial solitary waves. Exp.Fluids 22, 380–386 (1997)CrossRefGoogle Scholar
  47. Michallet, H., Barthelemy, E. Experimental study of interfacial solitary waves. J. Fluid Mech. 366, 159–177 (1998)CrossRefGoogle Scholar
  48. Michallet, H., Ivey, G.N.: Experiments on mixing due to internal solitary waves breaking on uniform slopes. J. Geophys. Res.104, 13467–13477 (1999)CrossRefGoogle Scholar
  49. Ono, H.: Algebraic solitary waves in stratified fluids. J. Phys. Soc. Japan 39, 1082–1091 (1975)CrossRefGoogle Scholar
  50. Ostrovsky, L.A., Grue, J.: Evolution equations for strongly nonlinear waves. Phys. Fluids 15, 2934–2948 (2003)CrossRefGoogle Scholar
  51. Ostrovsky, L.A., Stepanyants, Y.A.: Internal solitons in laboratory experiments: Comparison with theoretical models. Chaos 15, 037111 (2005)CrossRefGoogle Scholar
  52. Segur, H., Hammack, J.L.: Soliton models of long internal waves. J. Fluid Mech. 118, 285–304 (1982)CrossRefGoogle Scholar
  53. Schuster, B.: Experimente zu nicht-linaren Wellen grosser Amplitude in einem Rechteckkanal mit variabler Bodentopographie. Ph. D. Dissertation, Department of Mechanics, Darmstadt University of Technology, 165 p (1992)Google Scholar
  54. Stevens, C., Imberger, J.: The initial response of a stratified lake to a surface shear stress. J. Fluid Mech. 342, 39–66 (1996)CrossRefGoogle Scholar
  55. Sveen, J.K., Guo, Y., Davies, P.A., Grue, J.: On the breaking of internal solitary waves at a ridge. J. Fluid Mech. 469, 161–188 (2002)CrossRefGoogle Scholar
  56. Troy, C.D., Koseff, J.R.: The generation and quantitative visualization of breaking internal waves. Exp. Fluids 38, 549–562 (2005)CrossRefGoogle Scholar
  57. Troy, C.D., Koseff, J.R.: The viscous decay of progressive interfacial waves. Phys. Fluids 18, 026602 (2006)CrossRefGoogle Scholar
  58. Turner J.S. Buoyancy effects in fluids. Cambridge University Press, 1973, 367 p.Google Scholar
  59. Umeyama, M,: Experimental and theoretical analyses of internal waves of finite amplitude. J. Waterway, Port, Coastal and Ocean Eng. 128, 133–141 (2002)Google Scholar
  60. Umeyama, M, Shintani, T.: Visualization analysis of runup and mixing of internal waves on an upper slope. J. Waterway, Port, Coastal and Ocean Eng.130, 89–97 (2004)Google Scholar
  61. Vlasenko, V.I., Hutter, K.: Generation of second mode solitary waves by the interaction of a first mode soliton with a sill. Nonlinear Proc. Geophys. 8, 223–239 (2001)CrossRefGoogle Scholar
  62. Vlasenko, V.I., Hutter, K.: Transformation and disintegration of strongly nonlinear internal waves by topography in stratified lakes. Ann.Geophys. 20, 2087–2103 (2002a)CrossRefGoogle Scholar
  63. Vlasenko, V.I., Hutter, K.: Numerical experiments on the breaking of solitary internal waves over a slope-shelf topography. J. Phys. Oceanogr. 32, 1779–1793 (2002b)CrossRefGoogle Scholar
  64. Walker, S.A., Martin, A.J., Easson, W.J., Evans, W.A.B.: Comparison of laboratory and theoretical internal solitary wave kinematics. J. Waterway, Port, Coastal and Ocean Eng. 129, 210–218 (2003)Google Scholar
  65. Wallace, B.C., Wilkinson, D.L.: Run-up of internal waves on a gentle slope in a two-layered system. J. Fluid Mech. 191, 419–442 (1988)CrossRefGoogle Scholar
  66. Wessel, F.: Wechselwirkung interner Wellen im Zweischichtenfluid mit topographischen Erhebungen. Diploma Thesis, Department of Mechanics, Darmstadt University of Technology, 69 p. (1993)Google Scholar
  67. Wessel, F., Hutter, K.: Interaction of internal waves with topographic sill in a two-layer fluid. J. Phys. Oceanogr. 26, 5–20 (1996)CrossRefGoogle Scholar
  68. Wood, I.R., Simpson, J.E.: Jumps in layered miscible fluids. J. Fluid Mech.140, 329–342 (1984)CrossRefGoogle Scholar
  69. Wüest, A., Lorke, A.: Small-scale hydrodynamics in lakes. Ann. Rev. Fluid Mech. 35 373–412 (2003)CrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of Hydromechanics of National Academy of Sciences of UkraineKievUkraine

Personalised recommendations