Encyclopedia of Coastal Science

Living Edition
| Editors: Charles W. Finkl, Christopher Makowski

Accretion and Erosion Waves on Beaches

  • Douglas L. Inman
  • Scott A. JenkinsEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-48657-4_1-2

An accretion/erosion wave is a local irregularity in beach form that moves along the shore in the direction of net littoral drift. The initial irregularity may be caused by a wide variety of events such as the bulge from an ephemeral stream delta, the material from the collapse of a sea cliff, erosion or accretion associated with convergence and divergence of wave energy over an offshore bar, erosion downdrift of a structure such as a groin, sudden loss of sand by slumping at the head of a submarine canyon, or rapid accretion due to beach nourishment as when dredge spoil is placed on a beach. Given the wide variety of causes leading to local beach irregularities, accretion/erosion waves are common transport modes along beaches.

The wave-like form of an accretion/erosion wave is related to the change in sediment transport rate along the beach (divergence of the drift). Specifically, an irregularity in beach topography along an otherwise straight beach produces wave refraction and diffraction that locally modifies the littoral drift system. Wave convergence at an accretionary bulge reduces the littoral drift passing the bulge, causing downcoast erosion. Consequently, the accretionary bulge moves downdrift with an erosional depression preceding it. An initial erosional depression in beach form, as in the lee of a groin, moves downdrift as a traveling sand deficit because the transport potential of the downdrift side of the depression is always greater.

Accretion and erosion waves are best observed from the air or by comparison of beach profiles with time and distance along the beach. The associated change may be several hundred meters in beach width, but more typically is about 10–20 m over a distance of about 1–2 km and may be masked locally by cusps and other small-scale beach features.


The concept of an accretion/erosion wave was developed to account for the downdrift movement of a sand delta deposited across the beach by an ephemeral stream (Inman and Bagnold 1963). It was observed that the downdrift movement occurred as an accretionary bulge preceded by an erosional depression (Fig. 1). The net littoral drift perturbs deltaic accretion through a series of spit extensions (t2). Over time, the cumulative spit extensions will progressively displace the accretionary bulge in the downdrift direction, while local wave refraction and refraction-induced divergence of the littoral drift cause erosion downdrift of the bulge (t3). The areas of accretion and erosion migrate downdrift together in a phase-locked arrangement referred to as an accretion/erosion wave. The movement of the accretion/erosion form was quantified by surveys of the flood delta of the San Lorenzo River in central California (Hicks and Inman 1987), and further evaluated from the sudden release of sand at the San Onofre power plant in southern California (Inman 1987).
Fig. 1

Formation of accretion/erosion wave downdrift from an episodically formed sand delta at time, where t < t2 ≪ t3. (Modified from Inman and Bagnold 1963)

The propagation rate of the accretion/erosion wave form is slow initially because the on–offshore dimensions and volume of sand to be moved are at a maximum, and a significant fraction of that volume remains outside the region of rapid transport by waves (Fig. 1; t1). Once the material enters the surf zone, the longshore transport rates are much higher and the entire accretion/erosion form moves faster, spreads out along the beach, and decreases in cross-shore amplitude. Measurements near the sand release at San Onofre, CA, showed that the form of the accretional wave initially traveled with a speed of about 0.6–1.1 km/year in the 1.8 km near the release point (nearfield) and much faster farther from the release (farfield). The delta from the Santa Cruz River floods of 1982/83 was large (800,000 m3) and extended offshore to depths of over 10 m, and that material moved about 0.5–1.5 km/year during the first year (Hicks and Inman 1987). Subsequently, the downdrift erosion and accretion waves from the delta moved with speeds of 2.2–2.8 km/year (Table 1).
Table 1

Propagation speeds of accretion/erosion waves


Net downdrift transport rate

Speed of accretion/erosion wave (km year−1)







Santa Cruz, CA

Accretion from San Lorenzo River Delta

Hicks and Inman (1987)




Santa Cruz, CA

Erosion and bypass accretion from Santa Cruz Harbor

Hicks and Inman (1987)




Santa Barbara, CA

Erosion from harbor and bypass accretion

Inman (1987)




San Onofre, CA

Accretion from sand release

Inman (1987)




Oceanside, CA

Erosion from harbor

Inman and Jenkins (1985)




Assateague Island, MD

Erosion from jetties at Ocean City Inlet

Leatherman et al. (1987)




Outer Banks, NC

Migration of Oregon Inlet

Inman and Dolan (1989)




Nile Delta, Egypt

Accretion wave from onshore migration of sand blanket

Inman et al. (1992)




aNearfield is within 1–2 lengths of the perturbing feature such as a sand delta

It has been observed that any structure that interrupts the littoral drift of sand along a beach results in an erosional chain reaction traveling downdrift from the structure (Inman and Brush 1973). The propagation rates of the downdrift erosion wave was evaluated from beach surveys following the construction of the harbor jetties at Santa Barbara, CA (Inman 1987), and the enlargement of the harbor at Oceanside, CA (Inman and Jenkins 1985). Once in the farfield of the structure, the erosion wave, followed by the accretion wave moved downdrift at 2.5–2.8 km/year at Santa Barbara and 2.2–4.0 km/year at Oceanside (Table 1).

Accretion/erosion waves also occur along beaches and barriers downdrift of tidal inlets (e.g., Inman and Dolan 1989). The erosion wave from the jetties at Ocean City, MD, is a well-known example. The inlet between Fenwick and Assateague barrier islands was stabilized by jetties in 1935. The jetties trapped the littoral drift and caused an erosion wave to travel downdrift along Assateague Island, resulting in a landward recession of the entire barrier island of 460 m in 20 years (Shepard and Wanless 1971).

The Nile Delta experiences accretion/erosion waves driven by the currents of the east Mediterranean gyre that sweep across the shallow shelf with speeds up to 1 m/s. Divergence of the current downdrift of the Rosetta and Burullus promontories entrains blankets of sand that episodically impinge on the beach. These sand blankets cause shoreline irregularities with average amplitudes of 100 m and wavelengths of about 8 km that travel along the shore at rates of 0.5–1 km/year as accretion/erosion waves (Inman et al. 1992) (see entry on Littoral Cells).

A related example of a traveling accretion/erosion feature occurs when the littoral drift impinges on an inlet causing it to migrate downdrift (Fig. 2). The migration proceeds as an accretion of the updrift bank in response to positive fluxes of sediment delivered by the net littoral drift Q, while the downdrift bank of the inlet erodes due to a negative divergence of drift across the inlet, ∂Q/∂ℓ < 0. The negative divergence of the drift across the inlet is caused by wave refraction over the ebb-tide bar and by a loss of a portion of the drift to flood-tide entrainment at the inlet, ΔQt. Also the offshore tidal bar, maintained by the ebb-tide flow, moves downdrift with the inlet migration. Although the migration rates of the up- and downdrift banks of the inlet and the tidal bar are phase-locked, they are out of phase with the local net sediment changes in the shorezone bordering the inlet. The inlet banks and channel form an accretion/erosion sequence that travels along the beach and surf zone while the ebb-tide bar forms an accretion wave that moves along the shore in deeper water. Their relative on/offshore positions depend on the inlet tidal velocities that are functions of the size of the inlet and the volume of tidal flow through it (Inman and Dolan 1989; Jenkins and Inman 1999).
Fig. 2

Schematic diagram of the divergence of drift (∂Ql/∂l) at a migrating tidal inlet with net tidal flux of sediment, Qt. (Modified from Inman and Dolan 1989)

Accretion/erosion waves associated with river deltas and migrating inlets are common site-specific cases that induce net changes in the littoral budget of sediment. However, it appears that accretion/erosion waves in some form are common along all beaches subject to longshore transport of sediment. This is because coastline curvature and bathymetric variability (e.g., shelf geometry and offshore bars) introduce local variability in the longshore transport rate.

Mechanics of Migration

An accretion/erosion wave is a wave- and current-generated movement of the shoreline in response to changing sources and sinks in the local balance of sediment flux along a beach. The downdrift propagation of the wave form is driven by advective and diffusive fluxes of sedimenb mass (Fig. 3a). For convenience, these processes are usually expressed in terms of the longshore flux of sediment volume Q into and out of a control cell (Qin, Qout; Fig. 3b). By convention, fluxes of sediment into the cell are positive and fluxes out are negative. The net change of the volume fluxes between the updrift and downdrift boundaries of the control cell (Qin − Qout = divergence of drift) will result in a net rate of change in the position of the shoreline ∂x/∂t. Shifts in shoreline position will in turn cause the beach profile within the control cell to adjust to new equilibrium positions (Fig. 3b). The new profile positions alter local wave refraction causing adjustments in the flux of sediment leaving the control cell (Qout). The variation in Qout will alternately accrete and erode the beach downdrift of the control cell. As a consequence, propagation of the accretion/erosion wave involves a chain reaction in the local sediment flux balances. The reaction is set off by a disturbance on the updrift side of the control cell that yields a shoreline response on the downdrift side.
Fig. 3

The balance of sediment for a propagating accretion/erosion wave. (Modified from Inman and Dolan 1989)

At a tidal inlet, these dynamics are impacted by additional fluxes of sediment into or out of a control cell centered at the inlet. When the tidal transport of sediment is ebb-dominated (ΔQt > 0), the sediment flux into the control cell builds the ebb-tide bar and increases the rate of sediment that passes over the bar to the downdrift side of the inlet (Fig. 2). This stabilizes the inlet position by decreasing deposition on the updrift side and erosion on the downdrift side. Flood-dominated tidal transport (ΔQt < 0) has the opposite effect and will cause the inlet to migrate faster (Jenkins and Inman 1999).



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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Center for Coastal Studies, Scripps Institution of OceanographyUniversity of California, San DiegoLa JollaUSA
  2. 2.Marine Physical LaboratoryScripps Institution of Oceanography, UC San DiegoLa JollaUSA