Field observations of edge waves and their effect on beach material D. A. HUNTLEY & A. J. BOWEN SUMMARY Observations of wave motion are described, length of 34 4- 6 m. The implications of these particularly of the horizontal particle velocities, observations are discussed in the light of recent up to a maximum of 25 m from the shoreline laboratory experiments and theories of edge on Slapton Beach, Start Bay. For the first time wave generation, and a possible swash inter- on a natural beach, the observed velocities action mechanism for generating subharmonic reveal directly the presence of short period wave motion on Slapton beach is described. edge waves, modes of wave motion trapped to A steady longshore current prevented these the shoreline by refraction. These edge waves subharmonic edge waves from forming cuspate occurred at the first subharmonic (a/2) of the or crescentic features in the nearshore beach incident wave frequency a, and their expon- material. Small shoreline cusps observed on ential decay in amplitude with distance from Slapton beach on other occasions were con- the shoreline was consistent with edge waves of sistent with edge waves at the frequency of the mode number zero with a longshore wave- incident waves themselves. SMOOTH SANDY COASTLINES commonly form large regular rhythmic sedi- mentary features at the shoreline and in the nearshore subaqueous region, and recent work has shown that many of these features can be related to the action of water waves. Edge waves provide a satisfactory explanation for the formation of sedimentary features which have a rhythmic pattern in the longshore direction, such as submerged crescentic sand bars and regular cuspate shorelines (Bowen & Inman x97I ). Edge waves are free modes of water motion trapped against a shoaling beach by refraction. Their amplitude varies sinusoidally along the shore and diminishes rapidly seawards from the shoreline. Surface waves incident on the beach, on the other hand, can explain the formation of long sand bars with crests parallel to the shore (Carter et al. 1973, Lau & Travis I973). A common aspect of these theoretical ideas is the need for standing rather than progressive waves, in order to provide the spatial differentiation in the hydro- dynamic regime necessary for the formation of rhythmic topography. However Sonu (I973) has questioned the possibility of standing edge waves on beaches which are very long compared to the edge wave wavelengths, since there is no obvious reason why edge waves should not migrate along the coast on such beaches. We have therefore conducted field experiments on a long beach with two primary aims" (i) to make direct measurements of the nearshore velocity field in an attempt to identify edge wave motion directly. Short period edge waves have been directly observed on laboratory beaches (Bowen & Inman I969), but their existence in the field has previously been inferred only from the success of edge wave interaction theories in explaining observed periodic ,sedimentary features and nearshore circulation patterns (Bowen & Inman I969, I97I). Jl geol. Soc. Lond. vol. x3x , t975, pp. 69-8I , 6 figs. PHnted in Northern Ireland. Downloaded from http://pubs.geoscienceworld.org/jgs/article-pdf/131/1/69/4896796/gsjgs.131.1.0069.pdf by guest on 28 September 2021 7o D. A. Huntley & A. J. Bowen (ii) to associate measurements of the nearshore hydrodynamics with the formation of regular sedimentary features. The first aim has been achieved, with the first direct observation of edge waves on a natural beach. This has important implications for the possible generation mechanisms of edge waves. The second aim has not yet been achieved however. Some rhythmic sedimentary features observed are in satisfactory agreement with theoretical predictions, but no features were observed associated with the measured edge waves, due to the presence of a steady longshore current close to the shore, caused by obliquely incident wind waves. I. Edge waves The theory of edge waves is well established (Stokes 1846, Lamb 1932 para. 260, Eekart t95t , Ursell t952 , Ball i967). Using the shallow water equations, Eckart (195I) found edge wave solutions for a beach of linear slope, h -- x tan/~, and Ball (i967) for a beach of exponential slope h = h0(t --e--~'), where h is the local water depth, x is the distance from the shoreline and/~ is the angle of the beach face to the horizontal. Their solutions predict a family of edge wave modes whose amplitudes decay in the offshore direction and vary sinusoidally in the longshore direction. The lowest order mode, with mode number n --o, decays exponentially offshore, while for higher order modes the mode number n gives the number of zero crossings of the amplitude in the offshore direction. Fig. t shows the offshore decay of the onshore, u, and longshore, v, edge wave velocities for modes n = I and 2, using Eckart's solutions. Another feature of the solutions is the existence of a dispersion relation linking the edge wave period T to the longshore wavelength L. Fig. 2 shows the dis- persion curves for an exponential beach (Ball 1967) , the exponential parameters 0~ and h0 being chosen to fit the beach profile at Slapton, South Devon. This shows the existence of a family of dispersion curves, one for each mode number, each mode except n =-o ceasing to exist above a cut-off period. For a given period each mode has a predicted wavelength, but several modes with different longshore wavelengths may occur with the same wave period. Some possible mechanisms for generating edge waves have been studied in a number of recent papers but none has yet gained general acceptance. In fact, several different mechanisms may be able to generate edge waves on a natural coastline, since the effective trapping of the energy against the shore means that a relatively weak coupling between a driving force and the edge wave modes should induce the edge wave motion. Munk et al. (I956) have suggested that edge waves with periods of several hours may be generated by sudden changes in the wind and atmospheric pressure, and show results from the Californian coast to support this idea. Much shorter periods appear to be generated by the wind and swell waves incident on the shore, however. Gallagher (i971) has attempted to explain 'surf-beat' energy, in the range of periods 25-i oo seconds, in terms of edge wave motion generated by non- linear interaction between two incident wave trains. When the beat frequency Act between the two incident wave trains and the difference A;t between their Downloaded from http://pubs.geoscienceworld.org/jgs/article-pdf/131/1/69/4896796/gsjgs.131.1.0069.pdf by guest on 28 September 2021 Field observations of edge waves and their effect on beach material 7 z longshore wave numbers are related by an edge wave dispersion relation, the incident waves and the edge waves can form a resonant triad, transferring energy from the incident waves to the edge waves. Interactions of this kind however cannot explain the existence of edge waves when only one incident wave train is present. Bowen & Inman (1969) for example found that edge waves could be generated on a laboratory beach from normally incident waves of a single fre- quency. Recent theoretical work by Birchfield & Galvin (in press) and Guza & Davis (1974) has attempted to show how normally incident waves reflected from the beach may be unstable to longshore perturbations. Guza & Davis show that non-linear shallow water wave theory can be used to estimate the strength of a resonant interaction between the totally reflected, standing wave component of the incident waves and a pair of free edge wave modes, whereby the edge wave modes can grow through energy transfer from the incident waves. Their theory applies only to the generation of edge waves of longer periods than the incident waves, and cannot therefore explain the existence of the important edge waves at the incident wave frequency itself. Nevertheless, they show that the zero-order subharmonic (frequency a/2) edge wave tends to grow most rapidly, in general agreement with the observations of Bowen & Inman (I 969). 501 4"0 3-0 3"0- 2-0 n=l 2-0- n-2 (x) v (x) 1"0 X) 1.0~ 1 ___ I i J 0-50 0"75 1.00 0.25 0-50 0-75 1.00 -1.o°1 ) -1.0- x/L x/L FIG. I. Offshore dependence of the onshore u(x) and longshore v(x) currents for standing edge waves of modes n = I and n = 2. The amplitudes are normalized to v(x) = x atx =o. 150.0- BEACH PROFILE h =ho (1-e -(xx) 1 o~ ho=7"O5m / 100-0- FIG. 2 Edge wave dispersion curves n= 3 for modes n = 0-6 on ~ 50-0- Slapton Beach. 0 ! ~ I I ] 5"0 1 .0 15-0 20"0 25.0 T Secs Downloaded from http://pubs.geoscienceworld.org/jgs/article-pdf/131/1/69/4896796/gsjgs.131.1.0069.pdf by guest on 28 September 2021 72 D. A. Huntley & A. J. Bowen Edge wave and near shorefeatures Edge wave motion provides a semi-quantitative explanation for many nearshore features which exhibit rhythmical longshore patterns. Both cuspate and crescentic features of nearshore sediment topography have been studied in relation to edge wave motion. Bowen & Inman (1971) showed that the existence of submerged crescentic bars can be explained by the pattern of drift velocities at the bottom boundary layer of a standing edge wave. Here, incident waves were assumed to be of small amplitude, contributing only to the threshold velocity required to set the beach material in motion.