TECHNICAL PAPERS
Sep 1, 2008

PIV Techniques for Velocity Fields of Internal Waves over a Slowly Varying Bottom Topography

Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 134, Issue 5

Abstract

This paper reviews transformation processes and nonlinear properties of internal waves over a uniform slope in a two-fluid system, attempting to reveal water particle kinematics by using particle image velocimetry (PIV). Attenuation and setup induced by wave breaking are predicted using an energy-dissipation model including the radiation stress. In the present paper, the radiation stress is associated with the time-averaged momentum flux owing to the interaction between incident and reflected internal waves. These predictions agree with experimental data obtained by an image processing technique with which the boundary plane between the upper and lower layers could be detected as a density interface. A set of halogen lamps and three high-definition digital video cameras are used to illustrate velocity vector fields during one wave period. Instantaneous velocity fields measured by the PIV system are compared with the calculated velocity distribution by the method of characteristics in combination with the first-order Stokes theory. The rundown behavior is then investigated, and its influence upon the undertow in the lower layer is explained with a simple turbulent-jet model. Furthermore, the theoretical approach for examining mass transport and undertow is discussed in relation to the measured mean velocity.

Get full access to this article

View all available purchase options and get full access to this article.

References

Bogucki, D., Dickey, T., and Redekopp, L. G. (1997). “Localized mixing due to a breaking internal wave ray at a sloping bed.” J. Phys. Oceanogr., 27(7), 1181–1196.
Cacchione, D., and Wunsch, C. (1974). “Experimental study of internal waves over a slope.” J. Fluid Mech., 66, 223–239.
Dore, B. D. (1970). “Mass transport in layered fluid systems.” J. Fluid Mech., 40, 113–126.
Friedrichs, C. T., and Wright, L. D. (1995). “Resonant internal waves and their role in transport and accumulation of fine sediment in Eckernforde Bay, Baltic Sea.” Cont. Shelf Res., 15(13), 1697–1721.
Gemmrich, J. R., and van Haren, H. (2001). “Thermal fronts generated by internal waves propagating obliquely along the continental slope.” J. Phys. Oceanogr., 31(3), 649–655.
Gerritsen, F. (1981). “Wave attenuation and wave set-up on a coastal reef.” Proc., Int. Conf. on Coastal Engineering, ASCE, New York, 444–461.
Greslou, L., and Mahe, Y. (1954). “Etude du coefficient de reflexion d’une houle sur un obstacle constitue par un plan incline.” Proc., Int. Conf. on Coastal Engineering, Vol. 5, ASCE, New York, 68–84.
Grue, F., Jensen, A., Rusas, P.-O., and Sveen, J. K. (2000). “Breaking and broadening of internal solitary waves.” J. Fluid Mech., 413, 181–217.
Helfrich, K. R. (1992). “Internal solitary wave breaking and run-up on a uniform slope.” J. Fluid Mech., 243, 133–154.
Ivey, G. N., and Nokes, R. I. (1989). “Vertical mixing due to the breaking of critical internal waves on sloping boundaries.” J. Fluid Mech., 204, 479–500.
Jonsson, I. G. (1966). “Wave boundary layers and friction forces.” Proc., Int. Conf. on Coastal Engineering, ASCE, New York, 127–148.
Keulegan, G. H. (1949). “Interfacial instability and mixing in stratified flows.” J. Res. Natl. Bur. Stand., 43, 487–500.
Koop, C. G., and Butler, G. (1981). “An investigation of internal solitary waves in a two-fluid system.” J. Fluid Mech., 112, 225–251.
Lamb, K. G. (1997). “Particle transport by nonbreaking solitary internal waves.” J. Geophys. Res., 102(C8), 18641–18660.
Longuet-Higgins, M. S. (1953). “Mass transport in waters.” Philos. Trans. R. Soc. London, 245, 535–581.
Longuet-Higgins, M. S., and Stewart, R. W. (1964). “Radiation stress in water waves: A physical discussion, with applications.” Deep-Sea Res., 11, 529–562.
Mei, C. C. (1989). The applied dynamics of ocean surface waves, World Scientific, Singapore.
Melville, W. K., and Helfrich, K. R. (1987). “Transcritical two-layer flow over topography.” J. Fluid Mech., 178, 31–52.
Michallet, H., and Ivey, G. N. (1999). “Experiments on mixing due to internal solitary waves breaking on uniform slopes.” J. Geophys. Res., C: Oceans Atmos., 104(C6), 13467–13477.
Munk, W., and Wunsch, C. (1998). “Abyssal recipes II: Enegetics of tidal and wind mixing.” Deep-Sea Res., Part I, 45(12), 1977–2010.
Petruncio, E. T., Rosenfeld, L. K., and Paduan, J. D. (1998). “Observations of the internal tide in Monterey Canyon.” J. Phys. Oceanogr., 28(10), 1873–1903.
Pienda, J. (1991). “Predictable upwelling and the shoreward transport of planktonic larvae by internal tidal bore.” Science, 253(5019), 548–551.
Polzin, K. L., Toole, J. M., Ledwell, J. R., and Schmitt, R. W. (1997). “Spatial variability of turbulent mixing in the abyssal ocean.” Science, 276(5309), 93–96.
Segur, H., and Hammack, J. L. (1982). “Soliton models of long internal waves.” J. Fluid Mech., 118, 285–304.
Shimizu, R., Shintani, T., and Umeyama, M. (2006). “Instantaneous and Lagrangian velocity fields of internal waves on a slope by PIV measurement and numerical simulation.” Annu. J. Coastal Eng., 52, 1–5 (in Japanese).
Stanton, T. P., and Ostrovsky, L. A. (1998). “Observations of highly nonlinear internal solitons over the continental shelf.” Geophys. Res. Lett., 25(14), 2695–2698.
Stoker, J. J. (1957). Water waves, Interscience, New York.
Thorpe, S. A. (1966). “Internal gravity waves.” Ph.D. thesis, University of Cambridge, Cambridge, U.K.
Thorpe, S. A. (1968). “On standing internal gravity waves of finite amplitude.” J. Fluid Mech., 32, 489–528.
Tollmien, W. (1926). “Berechnung turbulenter Ausbreitungsvorgange.” ZAMM, 6, 468–478.
Troy, C. D., and Koseff, J. R. (2005). “The generation and quantitative visualization of breaking internal waves.” Exp. Fluids, 38(5), 549–562.
Umeyama, M. (1998). “Second-order internal wave theory by a perturbation method.” Memoirs, Tokyo Met. Univ., Tokyo, 48, 137–145.
Umeyama, M. (2002). “Experimental and theoretical analyses of internal waves of finite amplitude.” J. Waterway, Port, Coastal, Ocean Eng., 128(3), 133–141.
Umeyama, M., and Shintani, T. (2004). “Visualization analysis of runup and mixing of internal waves on an upper slope.” J. Waterway, Port, Coastal, Ocean Eng., 130(2), 89–97.
Umeyama, M., and Shintani, T. (2006). “Transformation, attenuation, setup and undertow of internal waves on a gentle slope.” J. Waterway, Port, Coastal, Ocean Eng., 132(6), 477–486.
Wunsch, C. (1969). “Progressive internal waves on slopes.” J. Fluid Mech., 35, 131–144.

Information & Authors

Information

Published In

Go to Journal of Waterway, Port, Coastal, and Ocean Engineering
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 134Issue 5September 2008
Pages: 286 - 298

History

Received: Aug 28, 2006
Accepted: Mar 21, 2008
Published online: Sep 1, 2008
Published in print: Sep 2008

Permissions

Request permissions for this article.

Authors

Affiliations

Motohiko Umeyama
Professor, Dept. of Civil and Environmental Engineering, Tokyo Metropolitan Univ., 1-1 Minamiohsawa, Hachioji, Tokyo 192-0397, Japan. E-mail: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share