Abstract
Mass, momentum and energy conservation laws, including the radiation stress, are used to derive an equation of the eigenvalues of rip current spacing.
A coastal region with linear bottom slope is divided into two parts: Offshore region and surfzone separated by the breaker line. Wave set-up, wave energy and mean current are assumed to be composed of basic state, which is a function of the distance from the coast to offshore only, and of superposed two-dimensional perturbations.
In the case of normal incidence of waves, basic steady current system vanishes and perturbations are found to be of cellular shape. According to the boundary conditions at the coast, stream function of perturbed motion in the surfzone can be represented by the confluent hypergeometric function, while in the offshore zone it is approximated by the modified Bessel function.
Interpolation of the stream functions in the surf and offshore regions enables us to obtain a characteristic relation which gives the eigenvalues of nondimensional alongshore spacing of rip current system as a function of a parameter determined by the bottom friction coefficient, width of the surfzone and breaker height.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bowen, A. J. (1969): Rip currents, 1. Theoretical investigations. J. Geophy. Res.,74, 5467–5478.
Bowen, A. J. andD. L. Inman (1969): Rip current, 2. Laboratory and field observations. J. Geophy. Res.,74, 5479–5490.
Hino, M. (1974): Theory on formation of ripcurrent and cuspidal coast. Proc. 14th Int. Conf. on Coastal Engineering, Copenhagen.
Inman, D.L., R.J. Tait andC.E. Nordstrom (1971): Mixing in the surfzone. J. Geophy. Res.,76, 3493–3514.
Iwata, N. (1974): Energy-momentum tensor and conservation laws for water waves. J. Oceanog. Soc. Japan,30, 222–231.
Kajiura, K. (1968): A model of the bottom boundary layer in water waves. Bull. Earthquake Res. Inst.,46, 75–123.
LeBlond, P. H. andC. L. Tang (1974): On energy coupling between waves and rip currents. J. Geophy. Res.,79, 811–816.
Longuet-Higgins, M. S. (1970a): Longshore currents generated by obliquely incident waves, 1. J. Geophy. Res.,75, 6778–6789.
Longuet-Higgins, M. S. (1970b): Longshore currents generated by obliquely incident waves, 2. J. Geophy. Res.,75, 6790–6801.
Longuet-Higgins, M. S. (1972): Recent progress in the study of longshore currents.In, Waves on Beaches. Academic Press, New York, London, 203–248.
Noda, E. K. (1974): Wave-induced nearshore circulation. J. Geophy. Res.,79, 4097–4106.
Phillips, O. M. (1966): The Dynamics of the Upper Ocean. Cambridge U. P., Cambridge, pp. 261.
Public Works Research Institute (1974): Field observations on waves and coastal currents. Tech. Memo. No. 916, 125–167 (in Japanese).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Iwata, N. Rip current spacing. Journal of the Oceanographical Society of Japan 32, 1–10 (1976). https://doi.org/10.1007/BF02107651
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02107651