Kinematic Undertow Model with Logarithmic Boundary Layer
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 123, Issue 6
Abstract
A new kinematic undertow profile model is developed to relate the mean horizontal velocity, bottom shear stress, and boundary layer thickness in a simple but general manner. The model combines a logarithmic profile in the bottom boundary layer with a parabolic profile in the interior layer. Use of a logarithmic profile is justified using our laboratory measurements for regular waves spilling on a rough, impermeable slope. Two forms of the model are presented, each with one calibration coefficient associated with the mean bottom shear stress. By adjusting the calibration coefficient at each measuring line, the model is shown to be capable of predicting the measured undertow profiles both inside and outside the surf zone for our rough slope case and for smooth slope cases from the literature. The model does not predict the overshoot in the bottom boundary layer for the rough slope case outside the surf zone. The predicted velocity profile for the smooth slope case in the bottom boundary could not be verified due to a lack of data. The predicted boundary layer thickness agrees with the measurements for the rough slope case and appears to be reasonable for the smooth slope cases. The model predicts the shear velocity in the transition region and inner surf zone reasonably well for the rough slope case, and it underpredicts the shear velocity outside the surf zone. This model is shown to be simple and versatile, but it will need further validation using irregular wave data and varying bottom geometry before it can be used in practical applications.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Battjes, J. A. (1974). “Surf similarity.”Proc., 14th Coast. Engrg. Conf., ASCE, New York, N.Y., 466–480.
2.
Bauer, O. B., Sherman, D. J., and Wolcott, J. F.(1992). “Sources of uncertainty in shear stress and roughness length estimates derived from velocity profiles.”Profl. Geographer, 44(4), 453–464.
3.
Cox, D. T., and Kobayashi, N. (1996). “Undertow profiles in the bottom boundary layer under breaking waves.”Proc., 25th Coast. Engrg. Conf., ASCE, New York, N.Y., 3194–3206.
4.
Cox, D. T., Kobayashi, N., and Okayasu, A. (1995). “Experimental and numerical modeling of surf zone hydrodynamics.”Rep. No. CACR-95-97, Center for Applied Coastal Research, University of Delaware, Newark, Del.
5.
Cox, D. T., Kobayashi, N., and Okayasu, A. (1996). “Bottom shear stress in the surf zone.”J. Geophys. Res., 101(C6), 14337–14348.
6.
Dally, W. B., and Brown, C. A. (1995). “A modeling investigation of the breaking wave roller with application to cross-shore currents.”J. Geophys. Res., 110(C12), 24873–24883.
7.
Dally, W. B., and Dean, R. G.(1984). “Suspended sediment transport and beach evolution.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 110(1), 15–33.
8.
Deigaard, R., and Fredsøe, J. (1989). “Shear stress distribution in dissipative water waves.”Coast. Engrg., 13, Elsevier Science Publishing Co., Inc., New York, N.Y., 357–378.
9.
Deigaard, R., Justesen, P., and Fredsøe, J. (1991). “Modeling of undertow by a one-equation turbulence model.”Coast. Engrg., 15, Elsevier Science Publishing Co., Inc., New York, N.Y., 431–458.
10.
Dyhr-Nielsen, M., and Sørensen, T. (1970). “Sand transport phenomena on coasts with bars.”Proc., 12th Coast. Engrg. Conf., ASCE, New York, N.Y., 182–192.
11.
Grant, W. D., and Madsen, O. S. (1979). “Combined wave and current interaction with a rough bottom.”J. Geophys. Res., 84(C4), 1797–1808.
12.
Haines, J. W., and Sallenger, A. H. (1994). “Vertical structure of mean cross-shore currents across a barred beach.”J. Geophys. Res., 99(C7), 14223–14242.
13.
Hansen, J. B., and Svendsen, I. A. (1984). “A theoretical and experimental study of undertow.”Proc., 19th Coast. Engrg. Conf., ASCE, New York, N.Y., 2246–2262.
14.
Jonsson, I. G. (1966). “Wave boundary layers and friction factors.”Proc., 10th Coast. Engrg. Conf., ASCE, New York, N.Y., 127–148.
15.
Kamphuis, J. W.(1975). “Friction factor under oscillatory waves.”J. Wtrwy., Harb., and Coastal Engrg. Div., 101(2), 135–144.
16.
Nadaoka, K., and Kondoh, T.(1982). “Laboratory measurements of velocity field structure in the surf zone by LDV.” Coast. Engrg. in Japan, Tokyo, Japan, 25, 125–145.
17.
Nielsen, P. (1992). Coastal bottom boundary layers and sediment transport, Advanced Series on Ocean Engineering, Vol. 4, World Scientific Publishing Co., River Edge, N.J.
18.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T. (1989). Numerical recipes: The art of scientific computing. Cambridge University Press, New York, N.Y.
19.
Putrevu, U., and Svendsen, I. A. (1993). “Vertical structure of the undertow outside the surf zone.”J. Geophys. Res., 98(C12), 22707–22716.
20.
Schlichting, H. (1979). Boundary-layer theory, 7th Ed., McGraw-Hill, Inc., New York, N.Y.
21.
Stive, M. J. F., and De Vriend, H. J.(1994). “Shear stresses and mean flow in shoaling and breaking waves.”Proc., 24th Coast. Engrg. Conf., ASCE, New York, N.Y., 1, 594–608.
22.
Stive, M. J. F., and Wind, H. G. (1982). “A study of radiation stress and set-up in the nearshore region.”Coast. Engrg., 6, Elsevier Science Publishing Co., Inc., New York, N.Y., 1–26.
23.
Stive, M. J. F., and Wind, H. G. (1986). “Cross-shore mean flow in the surf zone.”Coast. Engrg., 10, Elsevier Science Publishing Co., Inc., New York, N.Y., 325–340.
24.
Svendsen, I. A. (1984). “Mass flux and undertow in a surf zone.”Coast. Engrg., 8, Elsevier Science Publishing Co., Inc., New York, N.Y., 247–365.
25.
Svendsen, I. A., Schäffer, H. A., and Hansen, J. B. (1987). “The interaction between the undertow and the boundary layer flow on a beach.”J. Geophys. Res., 92(C11), 11845–11856.
Information & Authors
Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 123 • Issue 6 • November 1997
Pages: 354 - 360
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Nov 1, 1997
Published in print: Nov 1997
Authors
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.