Abstract
A series of laboratory experiments has been carried out to investigate the passage of an internal solitary wave of depression over a bottom ridge, in a two-layer fluid system for which the upper and lower layer is linearly-stratified and homogeneous respectively. Density, velocity and vorticity fields induced by the wave propagation over the ridge have been measured simultaneously at three locations, namely upstream, downstream and over the ridge crest, for a wide range of model parameters. Results are presented to show that wave breaking may occur for a sufficiently large wave amplitude and a strong ridge blockage factor, with accompanying mixing and overturning. Density field data are presented (i) to illustrate the overturning and mixing processes that accompany the wave breaking and (ii) to quantify the degree of mixing in terms of the wave and ridge parameters. For weak encounters, good agreement is obtained between the laboratory experimental results (velocity and vorticity fields induced by the wave propagation) and the predictions of a recently-developed fully nonlinear theory. Discrepancies between theory and experiment are discussed for cases in which breaking and mixing occur.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Osborne, A.R. and Burch, T.L.: 1980, Internal solitons in the Andaman Sea, Science 208, 451–460.
Apel, J.R., Holbrook, J.R., Liu, A.K. and Tsai, J.J.: 1985, The Sulu Sea internal soliton experiment, J. Phys. Oceanogr. 15, 1625–1651.
Bole, J.B., Ebbesmayer, C.C. and Romea, R.D.: 1994, Soliton currents in the South China sea: Measurements and theoretical modeling, Paper OTC 7417, 26th Annual Offshore Technology Conference, Houston, USA, 2–5 May 1994.
Farmer, D. and Armi, L.: 1999, The generation and trapping of solitary waves over topography. Science 283, 188–190.
Keulegan, G.H.: 1953, Characteristics of internal solitary waves, J. Res. Natl. Bureau Standards 51, 133–140.
Long, R.R.: 1956, Solitary waves in one- and two-fluid systems, Tellus 8, 460–471.
Long, R.R.: 1965, On the Boussinesq approximation and its role in the theory of internal waves, Tellus 17, 46–52.
Benjamin, T.B.: 1966, Internal waves of finite amplitude and permanent form, J. Fluid. Mech. 25, 241–270.
Koop, C.G. and Butler, G.: 1981, An investigation of internal solitary waves in a two-fluid system, J. Fluid. Mech. 112, 225–251.
Segur, H. and Hammack, J.L.: 1982, Soliton models of long internal waves, J. Fluid Mech. 118, 285–304.
Kao, T.W., Pan F.-S. and Renouard, D.: 1985, Internal solitons on the pycnocline: Generation, propagation, and shoaling and breaking over a slope, J. Fluid Mech. 159, 19–53.
Michallet, H. and Barthélemy, E.: 1988, Experimental study of interfacial solitary waves, J. Fluid Mech. 366, 159–177.
Drazin, P.G. and Johnson, R.S.: 1993, Solitons: An Introduction, Cambridge University Press, Cambridge, U.K.
Grue, J., Jensen, A., Rusås, P.-O. and Sveen, J.K.: 1999, Properties of large-amplitude internal waves, J. Fluid Mech. 380, 159–177.
Helfrich, K.R. and Melville, W.K.: 1986, On long nonlinear internal waves over slope-shelf topography, J. Fluid Mech. 167, 285–308.
Helfrich, K.R.: 1992, Internal solitary wave breaking and run-up on a uniform slope, J. Fluid Mech. 243, 133–154.
Bogucki, D. and Garrett, C.: 1993, A simple model for the shear-induced decay of an internal solitary wave, J. Phys. Oceanogr. 23, 1767–1776.
Michallet, H. and Ivey, G.N.: 1989, Experiments on mixing due to internal solitary waves breaking on uniform slopes, J. Geophys. Res. C6, 104, 13467–13477.
Wessels, F. and Hutter, K.: 1996, Interaction of internal waves with a topographic sill in a two-layer fluid, J. Phys. Oceanogr. 26, 5–20.
Hütteman, H. and Hutter, K.: 2001, Baroclinic solitary waves in a two layer fluid system with diffusive interface, Exp. Fluids 30, 317–326.
Vlasenko, V.I. and Hutter, K.: 2001, Generation of second mode solitary waves by the interaction of a first mode soliton with a sill, Nonlin. Process. Phys. 8, 223–239.
Sveen, J.K., Guo, Y., Davies, P.A. and Grue, J.: 2002, Breaking of internal solitary waves at a bottom ridge, J. Fluid Mech. 469, 161–188.
Grue, J., Jensen, A., Rusås, P.-O. and Sveen, J.K.S.: 2000, Breaking and broadening of internal solitary waves, J. Fluid Mech. 413, 181–217.
Brown, D.J. and Christie, D.R.: 1998, Fully nonlinear solitary waves in continuously-stratified incompressible Boussinesq fluids Phys. Fluids 10, 2569–2586.
Oster, G.: 1965, Density gradients, Sci. Amer. 213, 70–76.
Head, M.J.: 1983, The Use of Four-Electrode Conductivity Probes for High-Resolution Measurement of Turbulent Density or Temperature Variation in Salt-Stratified Water Flows, Ph.D. Thesis, UCSD, USA
Dalziel, S.B.: 1992, Decay of rotating turbulence: Some particle tracking experiments, Appl. Sci. Res. 49, 217–235.
Dalziel, S.B.: 1993, Rayleigh-Taylor instability experiments with image analysis, Dyn. Oceans Atmos. 20, 127–153.
De Silva I.P.D., Imberger, J. and Ivey, G.N.: 1997, Localised mixing due to a breaking internal wave ray at a sloping bed, J. Fluid Mech. 350, 1–27.
Thorpe, S.A.: 1977, Turbulence and mixing in a Scottish loch, Phil. Trans. Roy. Soc. Lond., Ser A, 286, 125–181.
De Silva, I.P.D. and Fernando, H.J.S.: 1992, Some aspects of mixing in a stratified turbulent patch, J. Fluid Mech. 240, 601–625.
Folkard, A.M., Davies, P.A. and Fernando, H.J.S.: 1997, Measurements in a turbulent patch in a rotating, linearly-stratified fluid, Dyn. Atmos. Oceans 26, 27–51.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Guo, Y., Sveen, J.K., Davies, P.A. et al. Modelling the motion of an internal solitary wave over a bottom ridge in a stratified fluid. Environ Fluid Mech 4, 415–441 (2005). https://doi.org/10.1007/s10652-005-0485-4
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10652-005-0485-4