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Morphodynamics of reflective and dissipative beach and inshore systems: Southeastern Australia — Reply
373 REFERENCES Bowen, A.J., 1973. Edge waves and the littoral environment, Proc. 13th Coast. Eng. Conf., pp.1313--1320, Council on Wave Research, London. Bowen, A.J. and Guza, R.T., 1978. Edge waves and surf beat. J. Geophys. Res., 83: 1913--1920. Guza, R.T. and Inman, D.L., 1975. Edge waves and beach cusps. J. Geophys. Res., 80(21): 2997--3012. Hasselmann, K., Munk, W. and MacDonald, G., 1963. Bispectra of ocean waves, In: M. Rosenblatt (Editor), Time Series Analysis, Wiley, New York, N.Y. Huntley, D.A., 1976. Long-period waves on a natural beach. J. Geophys. Res., 81: 6441--6449. Huntley, D.A. and Bowen, A.J., 1979. Beach cusps and edge waves. In: Proc. 16th Coast. Eng. Conf., Hamburg, 1978, pp.1378--1393. ASCE, New York, N.Y. Wells, D.R. 1967. Beach equilibrium and second-order wave theory. J. Geophys. Res., 72 : 497--504. Wright, L.D,. Chappell, J., Thorn, D.G., Bradshaw, M.P. and Cowell, P. 1979. Morphodynamics of reflective and dissipative beach and inshore systems: southeastern Australia. Mar. Geol., 32 : 105--140.
MORPHODYNAMICS OF REFLECTIVE A N D DISSIPATIVE BEACH A N D INSHORE SYSTEMS: S O U T H E A S T E R N A U S T R A L I A - - REPLY
L.D. WRIGHT
Coastal Studies Unit, Department of Geography, University of Sydney, Sydney (Australia) (Received December 13, 1979)
Huntley's contributions to the literature on edge waves, especially in the realm o f field observations, have been substantial and his comments (Huntley, 1980, this issue) with regard to our recent paper are well taken. In a general sense, all of his points are valid; however, I feel that some clarification is required as to the implications for our results. Since submitting that paper, our field data base has greatly increased; the important points of our original conclusions are substantiated, b u t as Huntley has aptly judged, some of the interpretations of specific hydrodynamic processes appear to require modification. I will address Huntley's points in sequence. (1) Eq.3 is included in the review only for historical continuity and is n o t deployed in any of our arguments. Bowen and Inman (1969) employed surf zone width (xs) on a profile o f constant slope/~ in defining a dimensionless shore-normal length identical to that given b y eq.4 in our paper. For the case of linear beach/inshore profiles which abruptly flatten to horizontal offshore, Guza and Inman (1975) and Huntley (1976) defined the shore normal length on the basis o f the distance, which they termed "beach width", to the point at which ~ = 0. On the complex, natural topographies with which we have dealt, selection of this position is n o t so straightforward. As an objective and physically meaningful surrogate for "beach w i d t h " we used
374 surf-zone width on the grounds that on the beaches we studied the most sustained minimum bed gradients were developed beneath or immediately seaward of the outer edge of the breaker zone. This situation is most clearcut on reflective beaches where the " b r e a k " occurs at or immediately seaward of the step and the widths of the " s u r f z o n e " and upper beach segment (our fig.3) are virtually identical. However, a similar relationship between "beach w i d t h " and surf zone width is also approximated on the dissipative profiles as can be seen from an examination of our fig.6 and the inserts in figs.10 and 14. The next position at which the condition ~ -* 0 roughly obtains is about 15 km seaward on the outer continental shelf plain. Where pronounced bartrough topography is present, the distance to the inner edge of the flat-topped bar (i.e., trough width) probably provides a stricter measure o f critical inshore dimensions. In the absence of sufficient observational data to identify modes we used eq.5 to estimate the likely mode numbers which could have corresponded to the frequencies we observed, n o t for purposes of predicting the frequencies. (2) I can only offer m y most contrite apologies for our sloppy methodology in segregating onshore and offshore time series in an a t t e m p t to express the relative contributions o f different frequencies to shoreward versus seaward transport. We eventually realized, but u n f o r t u n a t e l y too late, t h a t we had erred. However, the essence of our argument stands and is further supported by our more recent results: (a) the strongest shoreward flows are associated with the bores of the broken incident waves themselves whereas the lower frequencies dominate the strongest seaward flows, and (b) seaward flows near the bed become more intense as low-frequency energy near the beach increases. The former tendency is visibly apparent from the raw or filtered time series. The latter t e n d e n c y is evident from a comparison for different runs and experiments of sl~ore-normal time-averaged current statistics including skewness. It still remains for us to quantify these relationships adequately. (3) I must note to clarify confusing wording in Huntley's point (3) that the ~ and u phase relationship of ~ clearly refers to ~ and u measured at spatially separate locations, n o t at the same position. The phase angle between and u at the s a m e position was ~/2 t h r o u g h o u t the frequency range from 0.06 to 0.12 Hz and as Huntley notes, this would suggest that incident waves as well as subharmonic motions were standing against the beach. I agree that the ~ phase angle between A and C at 0.12 Hz was attributable to longshore separation of sensors. From further, more comprehensive experiments on Bracken Beach as well as from analyses of different segments of the original 9 December, 1976 record, it is clear that we have little if any evidence of significant synchronous edge waves. Cross-spectra indicate t h a t the incident waves may be standing on reflective beaches under low-energy conditions but this effect disappears with moderate energy. The important feature of reflective beach spectra is the persistent recurrence of pronounced subharmonic resonance. Runs on Bracken Beach of 12 h and 30 h duration in May 1977, and December 1977, respectively, reveal that the subharmonic
375
resonance is present at b o t h high and low tide. A phase angle of ~/2 between and u is consistently observed for subharmonic frequencies. In addition, shore-normal and shore-parallel currents, u and v, were either in phase or antiphase at subharmonic frequency, a condition cited b y Huntley (1976) and Huntley and Bowen (1979) as evidence of standing edge waves (when the progressive incident wave possibility is eliminated). Furthermore, cusp spacings observed in the majority of cases were very close to one-half the predicted length of zero m o d e subharmonic edge waves. Our data thus strongly support the conclusions of Guza and Inman (1975) and Huntley and Bowen (1979) that subharmonic edge waves are probably the main cause of (small scale) cusps on the intertidal/subaerial beach. (4) Admittedly, the observed oscillations at frequencies close to onequarter of the incident-wave frequency in the presence of our T y p e 2 and 3 topography are n o t easily explained as they are not among.the edge wave pairs predicted by Guza and Davis (1974) and are n o t obvious members of resonant triads of infragravity frequency (Huntley, 1976). Nevertheless, I find Hun~ley's suggestions that these motions are artefacts produced by chance locations of sensors at the nodal positions of a specific frequency within a continuum of low frequencies difficult to accept for the following reasons: (a) these narrow-band peaks are n o t accompanied by significant energy at nearby frequencies; (b) the peaks recur consistently in 7, u and v at the same frequency at different locations within the wide trough and although the energy decays progressively away from the subaerial beach, they are significant at the 95% level, (c) the peaks recur and are dominant or subdominant in all runs of three separate experiments including a long experiment of 12--14 December, 1977, and (d) the peaks are only associated with well-developed bar-trough topography. I must stress that, whatever their generating mechanism m a y be, these oscillations at least exist. It also seems likely that they cause the crescentic bar patterns of Type 3. Subsequent experiments, as well as more comprehensive analyses of earlier data sets, do indicate that the original interpretations of Wright et al. {1979) deserve amendment. Invariably the motions near ¢oi/4 (¢oi is incidentwave frequency) occur in association with subharmonic edge waves which exist near and produce cusps on the subaerial beach. H o w e v e r , many of the runs, especially those from 12--14 December 1977, but also some of the runs from May 1977, disclose t w o additional but lower peaks at frequencies very close to the theoretical frequencies of the n = 1,0 edge wave pair predicted by Guza and Davis (1974), that is, at ~¢oJ1.58 and ~ w J 2 . 7 3 . The edge wave length associated with the n = 1,0 pair is intermediate between the length of a zero-mode subharmonic edge wave and a zero-mode edge wave near wi/4. The peaks near ¢oi/4 dominate in the presence of Types 2 and 3 topography but are weak or absent on Types 4 and 5. Experiments on Palm Beach with Types 4 and 5 show the peaks at ¢oJ1.58 and ¢oJ2.73 to be dominant. Examples are presented by Chappell and Wright (1979). Energy cascading to a low-frequency edge wave near ¢oi/4 involving an interaction between the three frequencies and t w o wave numbers of the
376
¢oj1.58, ¢oJ2.73, and subharmonic edge waves seem to offer a more feasible explanation for the wi/4 motions than the original suggestion of Wright et al. (1979) that the peaks represent some form of higher subharmonics, especially since the latter conjecture has no theoretical precedent. If it is in fact a mechanism similar to the alternative proposed above that is responsible, then the actual frequency is probably ¢oi/3.75 rather than ¢o~/4; however, the difference would be indistinguishable from field results involving a wide band width of incident-wave frequencies. Preferential amplification of resonance at ~¢oi/4 (or wi/3.75) may be related to the geometry of the trough as suggested by Chappell and Wright {1979). In view of the apparent fact that the possible edge waves described above are at frequencies ~ i / 3 . 7 5 , ¢~J2.73, ¢oi/2 (subharmonic) and ~ i / 1 . 5 8 it seems that the "j-series" terminology as proposed by Wright et al. (1979) must be abandoned, at least insofar as integer multiples of the incident-wave period are implied. However, the identification of the inferred n = 1,0 edge wave pair, subordinate on Types 2 and 3 but ascendant on 4 and 5, adds cogency to our general conclusion that there is a hierarchy of edge.wave frequencies and wave numbers with dominant lengths decreasing as surf-zone width and dissipativeness decrease. REFERENCES Bowen, A.J. and Inman, D.L., 1969. Rip currents, 2. Laboratory and field observations.
J. Geophys. Res., 74(23): 5479--5490. ChappeU, J. and Wright, L.D., 1979. Surf-zone resonance and coupled morphology. Proc.
16th Coast. Eng. Conf., Hamburg, 1978, pp.1359--1377. Guza, R.T. and Davis, R.E., I974. Excitation of edge waves by waves incident on a beach. J. Geophys. Res., 79(9): 1285--1291. Guza, R.T. and Inman, D.L., 1975. Edge waves and beach cusps. J, Geophys. Res., 80(21): 2997--3012. Huntley, D.A., 1976. Long-period waves on a natural beach. J. Geophys. Res., 81(36): 6441--6449. Huntley, D.A., 1980. Comments on "Morphodynamicsof reflective and dissipativebeach and inshore systems: southeastern Australia", Mar. Geol. (this issue). Huntley, D.A. and Bowen, A.J., 1979. Beach cusps and edge waves. Proc. 16th Conf. Coast. Eng., Hamburg, 1978, pp.1378--1393. Wright, L.D., Chappell, J,, Thorn, B,G., Bradshaw, M.P. and Cowell, P., 1979. Morphodynamics of reflective and dissipative beach and inshore systems: southeastern Australia. Mar. Geol., 32: 105--140.
MORPHODYNAMICS OF REFLECTIVE A N D DISSIPATIVE BEACH A N D INSHORE SYSTEMS: S O U T H E A S T E R N A U S T R A L I A - - REPLY
L.D. WRIGHT
Coastal Studies Unit, Department of Geography, University of Sydney, Sydney (Australia) (Received December 13, 1979)
Huntley's contributions to the literature on edge waves, especially in the realm o f field observations, have been substantial and his comments (Huntley, 1980, this issue) with regard to our recent paper are well taken. In a general sense, all of his points are valid; however, I feel that some clarification is required as to the implications for our results. Since submitting that paper, our field data base has greatly increased; the important points of our original conclusions are substantiated, b u t as Huntley has aptly judged, some of the interpretations of specific hydrodynamic processes appear to require modification. I will address Huntley's points in sequence. (1) Eq.3 is included in the review only for historical continuity and is n o t deployed in any of our arguments. Bowen and Inman (1969) employed surf zone width (xs) on a profile o f constant slope/~ in defining a dimensionless shore-normal length identical to that given b y eq.4 in our paper. For the case of linear beach/inshore profiles which abruptly flatten to horizontal offshore, Guza and Inman (1975) and Huntley (1976) defined the shore normal length on the basis o f the distance, which they termed "beach width", to the point at which ~ = 0. On the complex, natural topographies with which we have dealt, selection of this position is n o t so straightforward. As an objective and physically meaningful surrogate for "beach w i d t h " we used
374 surf-zone width on the grounds that on the beaches we studied the most sustained minimum bed gradients were developed beneath or immediately seaward of the outer edge of the breaker zone. This situation is most clearcut on reflective beaches where the " b r e a k " occurs at or immediately seaward of the step and the widths of the " s u r f z o n e " and upper beach segment (our fig.3) are virtually identical. However, a similar relationship between "beach w i d t h " and surf zone width is also approximated on the dissipative profiles as can be seen from an examination of our fig.6 and the inserts in figs.10 and 14. The next position at which the condition ~ -* 0 roughly obtains is about 15 km seaward on the outer continental shelf plain. Where pronounced bartrough topography is present, the distance to the inner edge of the flat-topped bar (i.e., trough width) probably provides a stricter measure o f critical inshore dimensions. In the absence of sufficient observational data to identify modes we used eq.5 to estimate the likely mode numbers which could have corresponded to the frequencies we observed, n o t for purposes of predicting the frequencies. (2) I can only offer m y most contrite apologies for our sloppy methodology in segregating onshore and offshore time series in an a t t e m p t to express the relative contributions o f different frequencies to shoreward versus seaward transport. We eventually realized, but u n f o r t u n a t e l y too late, t h a t we had erred. However, the essence of our argument stands and is further supported by our more recent results: (a) the strongest shoreward flows are associated with the bores of the broken incident waves themselves whereas the lower frequencies dominate the strongest seaward flows, and (b) seaward flows near the bed become more intense as low-frequency energy near the beach increases. The former tendency is visibly apparent from the raw or filtered time series. The latter t e n d e n c y is evident from a comparison for different runs and experiments of sl~ore-normal time-averaged current statistics including skewness. It still remains for us to quantify these relationships adequately. (3) I must note to clarify confusing wording in Huntley's point (3) that the ~ and u phase relationship of ~ clearly refers to ~ and u measured at spatially separate locations, n o t at the same position. The phase angle between and u at the s a m e position was ~/2 t h r o u g h o u t the frequency range from 0.06 to 0.12 Hz and as Huntley notes, this would suggest that incident waves as well as subharmonic motions were standing against the beach. I agree that the ~ phase angle between A and C at 0.12 Hz was attributable to longshore separation of sensors. From further, more comprehensive experiments on Bracken Beach as well as from analyses of different segments of the original 9 December, 1976 record, it is clear that we have little if any evidence of significant synchronous edge waves. Cross-spectra indicate t h a t the incident waves may be standing on reflective beaches under low-energy conditions but this effect disappears with moderate energy. The important feature of reflective beach spectra is the persistent recurrence of pronounced subharmonic resonance. Runs on Bracken Beach of 12 h and 30 h duration in May 1977, and December 1977, respectively, reveal that the subharmonic
375
resonance is present at b o t h high and low tide. A phase angle of ~/2 between and u is consistently observed for subharmonic frequencies. In addition, shore-normal and shore-parallel currents, u and v, were either in phase or antiphase at subharmonic frequency, a condition cited b y Huntley (1976) and Huntley and Bowen (1979) as evidence of standing edge waves (when the progressive incident wave possibility is eliminated). Furthermore, cusp spacings observed in the majority of cases were very close to one-half the predicted length of zero m o d e subharmonic edge waves. Our data thus strongly support the conclusions of Guza and Inman (1975) and Huntley and Bowen (1979) that subharmonic edge waves are probably the main cause of (small scale) cusps on the intertidal/subaerial beach. (4) Admittedly, the observed oscillations at frequencies close to onequarter of the incident-wave frequency in the presence of our T y p e 2 and 3 topography are n o t easily explained as they are not among.the edge wave pairs predicted by Guza and Davis (1974) and are n o t obvious members of resonant triads of infragravity frequency (Huntley, 1976). Nevertheless, I find Hun~ley's suggestions that these motions are artefacts produced by chance locations of sensors at the nodal positions of a specific frequency within a continuum of low frequencies difficult to accept for the following reasons: (a) these narrow-band peaks are n o t accompanied by significant energy at nearby frequencies; (b) the peaks recur consistently in 7, u and v at the same frequency at different locations within the wide trough and although the energy decays progressively away from the subaerial beach, they are significant at the 95% level, (c) the peaks recur and are dominant or subdominant in all runs of three separate experiments including a long experiment of 12--14 December, 1977, and (d) the peaks are only associated with well-developed bar-trough topography. I must stress that, whatever their generating mechanism m a y be, these oscillations at least exist. It also seems likely that they cause the crescentic bar patterns of Type 3. Subsequent experiments, as well as more comprehensive analyses of earlier data sets, do indicate that the original interpretations of Wright et al. {1979) deserve amendment. Invariably the motions near ¢oi/4 (¢oi is incidentwave frequency) occur in association with subharmonic edge waves which exist near and produce cusps on the subaerial beach. H o w e v e r , many of the runs, especially those from 12--14 December 1977, but also some of the runs from May 1977, disclose t w o additional but lower peaks at frequencies very close to the theoretical frequencies of the n = 1,0 edge wave pair predicted by Guza and Davis (1974), that is, at ~¢oJ1.58 and ~ w J 2 . 7 3 . The edge wave length associated with the n = 1,0 pair is intermediate between the length of a zero-mode subharmonic edge wave and a zero-mode edge wave near wi/4. The peaks near ¢oi/4 dominate in the presence of Types 2 and 3 topography but are weak or absent on Types 4 and 5. Experiments on Palm Beach with Types 4 and 5 show the peaks at ¢oJ1.58 and ¢oJ2.73 to be dominant. Examples are presented by Chappell and Wright (1979). Energy cascading to a low-frequency edge wave near ¢oi/4 involving an interaction between the three frequencies and t w o wave numbers of the
376
¢oj1.58, ¢oJ2.73, and subharmonic edge waves seem to offer a more feasible explanation for the wi/4 motions than the original suggestion of Wright et al. (1979) that the peaks represent some form of higher subharmonics, especially since the latter conjecture has no theoretical precedent. If it is in fact a mechanism similar to the alternative proposed above that is responsible, then the actual frequency is probably ¢oi/3.75 rather than ¢o~/4; however, the difference would be indistinguishable from field results involving a wide band width of incident-wave frequencies. Preferential amplification of resonance at ~¢oi/4 (or wi/3.75) may be related to the geometry of the trough as suggested by Chappell and Wright {1979). In view of the apparent fact that the possible edge waves described above are at frequencies ~ i / 3 . 7 5 , ¢~J2.73, ¢oi/2 (subharmonic) and ~ i / 1 . 5 8 it seems that the "j-series" terminology as proposed by Wright et al. (1979) must be abandoned, at least insofar as integer multiples of the incident-wave period are implied. However, the identification of the inferred n = 1,0 edge wave pair, subordinate on Types 2 and 3 but ascendant on 4 and 5, adds cogency to our general conclusion that there is a hierarchy of edge.wave frequencies and wave numbers with dominant lengths decreasing as surf-zone width and dissipativeness decrease. REFERENCES Bowen, A.J. and Inman, D.L., 1969. Rip currents, 2. Laboratory and field observations.
J. Geophys. Res., 74(23): 5479--5490. ChappeU, J. and Wright, L.D., 1979. Surf-zone resonance and coupled morphology. Proc.
16th Coast. Eng. Conf., Hamburg, 1978, pp.1359--1377. Guza, R.T. and Davis, R.E., I974. Excitation of edge waves by waves incident on a beach. J. Geophys. Res., 79(9): 1285--1291. Guza, R.T. and Inman, D.L., 1975. Edge waves and beach cusps. J, Geophys. Res., 80(21): 2997--3012. Huntley, D.A., 1976. Long-period waves on a natural beach. J. Geophys. Res., 81(36): 6441--6449. Huntley, D.A., 1980. Comments on "Morphodynamicsof reflective and dissipativebeach and inshore systems: southeastern Australia", Mar. Geol. (this issue). Huntley, D.A. and Bowen, A.J., 1979. Beach cusps and edge waves. Proc. 16th Conf. Coast. Eng., Hamburg, 1978, pp.1378--1393. Wright, L.D., Chappell, J,, Thorn, B,G., Bradshaw, M.P. and Cowell, P., 1979. Morphodynamics of reflective and dissipative beach and inshore systems: southeastern Australia. Mar. Geol., 32: 105--140.