doi:10.1016/S0378-3839(99)00061-7 
Copyright © 2000 Elsevier Science B.V. All rights reserved.
Breakpoint generated surf beat induced by bichromatic wave groups
T. E. Baldocka, *, D. A. Huntley1, b, P. A. D. Bird2, a, T. O'Hare3, b and G. N. Bullock4, a
a School of Civil and Structural Engineering, University of Plymouth, Palace Street, Plymouth, PL1 2DE, UK
b Institute of Marine Studies, University of Plymouth, Drake Circus, Plymouth, PL4 8AA, UK
Received 26 May 1999;
revised 7 October 1999;
accepted 1 November 1999.
Available online 23 February 2000.
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Abstract
This paper presents new experimental data on 2-D surf beat generation by a time-varying breakpoint induced by bichromatic wave groups. The experimental investigation covers a broad range of wave amplitudes, short wave frequencies, group frequencies and modulation rates. The data include measurements of incident and outgoing wave amplitudes, breakpoint position, shoreline run-up and the cross-shore structure of both the short and long wave motion. Surf beat generation is shown to be in good agreement with theory [Symonds, G., Huntley, D.A., Bowen, A.J., 1982. Two dimensional surf beat: long wave generation by a time-varying breakpoint. J. Geophys. Res. 87, 492–498]. In particular, surf beat generation is dependent on the normalised surf zone width, which is a measure of the phase relationship between the seaward and shoreward breakpoint forced long waves, and linearly dependent on the short wave amplitude. The cross-shore structure of the long wave motion is also consistent with theory; at maximum and minimum surf beat generation, the mean breakpoint coincides with the nodal and anti-nodal points, respectively, for a free long wave standing at the shoreline. A numerical solution, using measured data as input, additionally shows that the phase relationship between the incident bound long wave and the outgoing breakpoint forced wave is consistent with the time-varying breakpoint mechanism.
Author Keywords: Surf beat; Wave groups; Long waves; Breakpoint; Bound waves; Coastal
Fig. 1. Expected long wave phase due to surf beat generation by a time-varying breakpoint. IBFLW, RBFLW, OBFLW — incident, reflected and outgoing breakpoint forced long wave. IBLW — incident bound long wave, RBLW — released/reflected “bound” long wave. (a) Maximum response, mean breakpoint at a nodal point for a free standing long wave. (b) Minimum response, mean breakpoint at an antinode of a free standing long wave.
Fig. 2. Wave flume and instrumentation.
Fig. 3. (a) Comparison of measured incident boundwave amplitude with theory. □□□□ Data points, series A–E. (b) Measured incident boundwave amplitude vs. χ. ——□—— series A, – –
– – series B, ——·
·—— series C, ——··×··—— series D, ——Δ—— series E.
Fig. 4. (a) Outgoing free wave amplitude vs. group frequency/slope, series D. ——□—— Madsen et al. (1997) (β=1/20), ——··×··—— series D. (b) Outgoing free wave amplitude vs. group frequency/slope, series E. ——□—— Madsen et al. (1997) (β=1/40), ——
—— series E. (c) Outgoing free wave amplitude vs. group frequency/slope, series A–E. ——□—— series A, – –– - series B, – –– – series C, ——··×··—— series D, ——Δ—— series E.
Fig. 5. (a) Normalised outgoing free wave amplitude at the group frequency vs. χ. ——□—— series A, – –– - series B, ——— theory, Δa=0.2, Symonds et al. (1982). (b) Normalised outgoing free wave amplitude at the group frequency vs. χ. ——··—— series C, ——··×··—— series D, ———— series E, ——— theory, Δa=0.2, Symonds et al. (1982).
Fig. 6. (a) Ratio of outgoing to incident free wave amplitude at the group frequency vs. χ. ——□—— Series A, – –– - series B. (b) Ratio of outgoing to incident free wave amplitude at the group frequency vs. χ. ——··—— series C, ——··×··—— series D, ——Δ—— series E.
Fig. 7. Normalised outgoing free wave amplitude at f≠fG vs. χ. ——□—— Data, - - - - approximate theory, δ=1, after Symonds et al. (1982). (a) series A, (b) series C, (c) series D, (d) series E.
Fig. 8. (a) Amplitude spectra at x=−11.15 m, x=−1.25 m (
outer breakpoint) and run-up, case b1025/A. ——— x=−11.15 m, - - - - x=−1.25 m, □□□□ run-up. (b) Amplitude spectra at x=−11.15 m, x=−1.25 m (outer breakpoint) and run-up, case b6020/C. ——— x=−11.15 m, - - - - x=−1.25 m, □□□□ run-up.
Fig. 9. (a) Cross-shore variation in short wave amplitude, case b1025/A, fG=0.244 Hz. ———— f1, - -□- - f2, ——··—— 2f1, ——··—— 2f2, ——×—— f1+f2. (b) Cross-shore variation in wave amplitude at the group frequency, case b1025/A. - -□- - Data (fG), ——— IBLW, —— —— IBLW (scaled), ——·—— OFLW (inverse shoaling). (c) Cross-shore variation in wave amplitude at the group frequency compared to nodal structure of free standing wave and IBLW+OBFLW, case b1025/A, xbo=−0.9 m, xbi=−0.15 m. □□□□ Data (fG), ——— J0, - - - - IBLW+OBFLW.
Fig. 10. (a) Cross-shore variation in short wave amplitude, case b6020/C, fG=0.195 Hz. ———— f1, - -□- - f2, ——··—— 2f1, ——··—— 2f2, ——×—— f1+f2. (b) Cross-shore variation in wave amplitude at the group frequency, case b6020/C. - -□- - Data (fG), ——— IBLW, —— —— IBLW (scaled), ——·—— OFLW (inverse shoaling). (c) Cross-shore variation in wave amplitude at the group frequency compared to nodal structure of free standing wave and IBLW+OBFLW, case b6020/C, xbo=−0.95 m, xbi=−0.2 m. □□□□ Data (fG), ——— J0, - - - - IBLW+OBFLW.
Fig. 11. (a) Cross-shore variation in short wave amplitude, case b1060A, fG=0.586 Hz. ———— f1, - -□- - f2, ——·—— 2f1, ——··—— 2f2, ——×—— f1+f2. (b) Cross-shore variation in wave amplitude at the group frequency, case b1060/A. - -□- - Data (fG), ——— IBLW, ——·—— OFLW (inverse shoaling). (c) Cross-shore variation in wave amplitude at the group frequency compared to nodal structure of free standing wave and IBLW+OBFLW, case b1060/A, xbo=−0.9 m, xbi=−0.3 m. □□□□ Data (fG), ——— J0, - - - - IBLW+OBFLW.
Fig. 12. (a) Cross-shore variation in short wave amplitude, case b6055/C, fG=0.537 Hz. ———— f1, - -□- - f2, ——··—— 2f1, ——··—— 2f2, ——×—— f1+f2. (b) Cross-shore variation in wave amplitude at the group frequency, case b6055/C. - -□- - Data (fG), ——— IBLW, —— —— IBLW (scaled), ——·—— OFLW (inverse shoaling). (c) Cross-shore variation in wave amplitude at the group frequency compared to nodal structure of free standing wave and IBLW+OBFLW, case b6055/C, xbo=−1.05 m, xbi=−0.05 m. □□□□ Data (fG), ——— J0, - - - - IBLW+OBFLW.
Fig. 13. (a) Cross-shore variation in wave amplitude at the group frequency, case b1010A, fG=0.098 Hz, xbo=−1.1 m, xbi=−0.15 m. □□□□ Data (fG), ——— J0, - - - - IBLW, ——·—— OFLW (inverse shoaling). (b) Cross-shore variation in wave amplitude at the group frequency, case b6010C, fG=0.098 Hz, xbo=−0.9 m, xbi=−0.15 m. □□□□ Data (fG), ——— J0, - - - - IBLW, ——·—— OFLW (inverse shoaling).
Table 1. Bichromatic wave group frequencies
Amplitudes: (A) a1=a2=0.025 m, (B) a1=a2=0.0125 m, (C) a1=a2=0.025 m, (D) a1=a2=0.04 m, (E) a1+a2=0.08 m, a2/a1=0.2.
Table 2. Bichromatic wave group characteristics, x positive onshore from SWL
(A) a1=a2=0.025 m, (B) a1=a2=0.0125 m, (C) a1=a2=0.025 m, (D) a1=a2=0.04 m, (E) a1+a2=0.08 m, a2/a1=0.2.
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