https://doi.org/10.1130/G47089.1

Manuscript received 9 October 2019 Revised manuscript received 24 December 2019 Manuscript accepted 23 January 2020

© 2020 Geological Society of America. For permission to copy, contact [email protected]. Published online 18 March 2020

Experimental quantification of under oscillatory flow James F. Bramante1,2, J. Taylor Perron2, Andrew D. Ashton1 and Jeffrey P. Donnelly1 1Department of & , Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, USA 2Department of , Atmospheric & Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

ABSTRACT geometry, bedrock strength, and char- Although wave-driven abrasion of submarine bedrock affects the evolution of rocky coasts acteristics (Sklar and Dietrich, 2006; Turowski and reefs globally, the dependence of the abrasion rate on wave forcing and sediment avail- et al., 2007; Lamb et al., 2008). ability remains poorly quantified. We performed experiments in which an artificial substrate The unsteadiness of flow and sediment mo- was abraded by varying amounts of coarse-grained sediment subjected to oscillatory flows. In tion under waves may cause rate laws for wave- these experiments, the bedrock incision rate scaled by the square of bedrock tensile strength (I, driven abrasion to deviate from those derived –1 2 –1 m yr MPa ) varied with mean root-mean-square (rms) velocity (, m s ) according to a for steady flow in . Theoretical and nu- 4.2 power law, I = 1.0 (angle brackets indicate time-averaging over an entire experiment). merical models suggest that, in steady flows, Additionally, the relationship between sediment load and bedrock incision rate demonstrates the abrasion rate is determined by shear stress tools and cover effects similar to abrasion in fluvial environments, such that incision is fastest and sediment characteristics (Sklar and Dietrich, at intermediate sediment loads. However, because oscillatory flows accumulate sediment into 2004; Lamb et al., 2008; Aubert et al., 2016). In bedforms, the increased bedrock exposure reduces the efficiency of the cover effect for high contrast, under oscillatory flows, shear stresses sediment loads relative to unidirectional flow. Our results provide an empirical model that can and flux vary over seconds-long time be used to predict bedrock incision rates in nearshore environments­ based on wave forcing. scales, the boundary layer is not fully developed, and normal stresses due to fluid acceleration can INTRODUCTION rocky platforms at the base of cliffs, ver- contribute to (Fredsoe and In many coastal environments, waves drive tical by abrasion of up to 0.02 m yr–1 Deigaard, 1992; and Calantoni, 2001). loose sediment over exposed bedrock, eroding has been measured (Robinson, 1977; Blanco- Also, bedforms develop under oscillatory flow the bed and driving geomorphological change. Chao et al., 2007). Robinson (1977) observed even when sediment sparsely covers the bed On rocky , wave-driven abrasion can con- that abrasion of the bedrock platform under (e.g., Pedocchi and Garcia, 2009). tribute to the downwearing of shore platforms beaches decreases with thickness of the over- Here, we present results from experiments (Blanco-Chao et al., 2007; Trenhaile, 2000). On lying sediment, but that study had insufficient in which we used an oscillatory flow to coral reefs, wave-driven abrasion of the reef sur- data to quantify the effect. quantify the abrasion rate of bedrock as a func- face reduces net accretion rates and can produce Abrasion by unidirectional flow in terrestrial tion of oscillation velocity and sediment load. spatially variable accretion (e.g., Grossman and bedrock channels is analogously important to We found that abrasion increases exponentially Fletcher, 2004). Additionally, field observations the evolution of landscapes. Laboratory with oscillation velocity and exhibits tools and (e.g., Cloud, 1954) and geostatistical analysis experiments have constrained rate laws gov- cover effects different from those observed in (Duce et al., 2016) suggest wave-driven abrasion erning riverbed abrasion as a function of sedi- unidirectional abrasion mill experiments. drives the formation of fore-reef grooves. Un- ment flux and bedrock tensile strength. Rotary derstanding the evolution of hard-bottom coastal abrasion mill experiments (Sklar and Dietrich, OSCILLATORY ABRASION environments requires knowledge of the rela- 2001; Scheingross et al., 2014) demonstrated the EXPERIMENTS tionships between abrasion rate and wave and existence of the tools and cover effects hypoth- To simulate wave-driven abrasion of subma- sediment characteristics. esized by Gilbert (1877): Sediment impacts on rine bedrock, we constructed a prototype oscil- Despite the prevalence of wave-driven the bed enhance abrasion, but as sediment load lating u-tube (POUT) that consisted of a 2.45-m- abrasion on reefs globally, and its potential increases, sediment covers the bed, reducing the long horizontal duct with rectangular cross importance for rocky shores, few studies have abrasion rate (Sklar and Dietrich, 2004). From section and two vertical reservoir pipes (Fig. 1A; measured the dependence of erosion on wave these results, models have been developed to Fig. DR1 in the GSA Data ­Repository1). Two characteristics and sediment availability. On predict bedrock incision as a function of thrusters and a control system generated and

1GSA Data Repository item 2020154, Figures DR1–DR4, Videos DR1–DR5 of bed forms, and Tables DR1 and DR2 (summarizing the videos and all experiments), is available online at http://www.geosociety.org/datarepository/2020/, or on request from [email protected].

CITATION: Bramante, J.F., Perron, J.T., Ashton, A.D., and Donnelly, J.P., 2020, Experimental quantification of bedrock abrasion under oscillatory flow: Geology, v. 48, p. 541–545, https://doi.org/10.1130/G47089.1

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Downloaded from http://pubs.geoscienceworld.org/gsa/geology/article-pdf/48/6/541/5051203/541.pdf by MBL WHOI Library user on 01 December 2020 2 square of the substrate tensile strength (σT ; Sk- A lar and Dietrich, 2001; Scheingross et al., 2014). (In situations where sediment instead slides on top of exposed bedrock, may be a more appropriate quantity for scaling abrasion rates.) The abrasion medium, subrounded silici-

clastic with sieve diameter D50 = 6.1 mm, was scattered uniformly across the duct floor and foam before initiation of each experiment. We re- fer to the average volume of gravel per unit area of the duct floor as sediment load,S (cm3 cm–2). Upon initiation of oscillatory flow in each ex- periment, most of the sediment rapidly self-or- ganized into one or more bedforms, leaving most of the duct floor covered only by scattered sedi- ment grains. The morphology of the bedforms varied with S. At low S (0.0075–0.015 cm3 cm–2), the bedforms consisted of mobile bands 1–2 grain diameters thick and 10–30 grain diameters wide that migrated over distances much greater than B their width (Fig. 1B; Videos DR1 and DR2). In experiments with high S (≥0.12 cm3 cm–2), the bedforms consisted of mounds several grain di- ameters high with appearance similar to rolling- grain ripples (Fig. 1B; Videos DR3 and DR4; Pedocchi and Garcia, 2009). Motion of these mounds differed between low (<0.75 m s–1) and –1 high (≥0.75 m s ) urms. In low-urms/moderate-S

and high-urms/high-S experiments, the mounds had a stationary core, and sediment saltated from the stoss face of a mound, over the mound crest, to the bare substrate on the lee side every half- oscillation (Fig. 1B; Videos DR3 and DR4). In

high-urms/moderate-S experiments, the mounds migrated back and forth in their entirety, pri- marily through (Fig. 1B; Video DR5). The isolated bedforms in our experiments with high-S resembled isolated ripples of - sized sediment observed in the field. For ex- ample, on the Ningaloo Australia fringing reef, large wave events expose bare substrate that is covered by coarse sand ripples (Rosenberger et al., 2019). On mixed sand-gravel beaches, iso- lated ripples form on otherwise immobile beds Figure 1. Experimental design and influence of bedforms. (A) Schematic drawing of the oscil- when flows are insufficiently strong to mobilize latory flow tunnel. PVC—polyvinyl chloride. (B) Video stills from two experiments illustrating gravel (Hay et al., 2014). a fully mobile sediment band (left column) and a partially static isolated ripple (right column). Blue boxes indicate two layers of sediment grains that remain stationary during the entire The number and spacing of bedforms in our wave period and cover the bed. Sediment had median (95% confidence interval) sieve diameter experiments tended to increase with increasing –3 of D50 = 6.1 (4.2–7.6) mm and density ρs = 2570 (2300–2840) kg m ; is mean oscillation S and decrease with increasing urms (Fig. DR2). velocity time-averaged over an entire experiment. When two to three bedforms formed, their spac-

ing scaled with do (range: 0.6do−1do) and was maintained sinusoidal water-level fluctuations which varied between experiments due to differ- consistent with field observations of orbital rip- in the vertical reservoirs. When the POUT was ences between foam batches from the manufactur- ple spacing in coarse sediment beds (Fig. DR3; filled, the water in the horizontal duct oscil- er, to simulate reef or bedrock substrate (Schein- Pedocchi and Garcia, 2009). Because these bed-

lated with a natural period of Ts ≈ 4.75 s and gross et al., 2014). The erosion rate was measured forms produced spatial variability in the abra-

with root-mean-square (rms) velocity (urms, m by weighing the foam and was normalized by sion rate, the foam was to the length of one –1 –1 s ) of up to 1 m s . Given a particular urms and the foam surface area and density to produce the full bed-form spacing (0.8do). Because only one

Ts, the distance a water parcel travels during incision rate. Because bedrock subjected to the bedform would be located on the foam, we nor- half of an oscillation is the orbital diameter, low-velocity impacts of rolling or saltating sedi- malized S in each experiment by the number of

duor= 2/msTs π. ment fails in tension (Sklar and Dietrich, 2001), bedforms, which we will refer to as normalized To generate detectable erosion during short and following previous experiments investigat- sediment load (S*, cm3 cm–2). experiments, we used closed-cell urethane foam ing the volumetric erosion rate of , concrete, We performed two sets of experiments us-

with low tensile strength (σT = 0.34–0.71 MPa), and foam, we multiplied the incision rate by the ing the POUT (Table DR2). In the first set,

542 www.gsapubs.org | Volume 48 | Number 6 | GEOLOGY | Geological Society of America

Downloaded from http://pubs.geoscienceworld.org/gsa/geology/article-pdf/48/6/541/5051203/541.pdf by MBL WHOI Library user on 01 December 2020 3 –2 2 we held S constant at either 0.03 cm cm or where I is incision rate scaled by σT rate increased with increasing S* until reaching 3 –2 –1 2 7 –1 0.12 cm cm and varied urms in the range 0.4– (m ­yr MPa ); Ct = 3.15 × 10 s yr is a a maximum (tools effect) and then decreased –1 1.0 m s . In the second set, we held urms con- ­conversion factor for time; K is a constant with increasing S* (cover effect). The shape of stant at 0.5, 0.6, or 0.75 m s–1 and varied S over [s(n–1) m–(n–1) MPa2]; angle brackets (< >) indicate our inferred tools and cover effect was similar 0.0075–0.48 cm3 cm–2. time-averaging over an entire experiment; and n to that found in rotary mill experiments (Sklar is a dimensionless exponent. A nonlinear least- and Dietrich, 2001), but it had a slower decay CONTROLS ON BEDROCK INCISION squares fit provided estimates (95% confidence of incision rate, indicating a weaker cover ef-

Across all experiments, mean incision rate of interval) of n = 4.2 (3.6, 4.8) and CtK = 1.0 (0.7, fect. The tools and cover effects can be mod- 2 the bedrock simulant increased with urms (Fig. 2), 1.3), with R = 0.86. Thus, incision rate scales eled with a power function of sediment mass

which is described by a power law of the with urms raised to a power of ∼4. (T17; Turowski and Hodge, 2017). Applied to

form: For a given urms, the relationship between the the abrasion mill experiments, T17 collapses to incision rate and S was characterized by tools a special case in which additional sediment falls n I = (1) and cover effects (Fig. 3), where the incision equally on exposed and already covered bed- rock (Turowski et al., 2007). In our experiments, however, the best fit of T17 indicates that sedi- Figure 2. Relationship ment is preferentially sequestered in bedforms, 0 10 Substrate tensile between mean oscillation reducing the cover effect (Fig. 3). strength velocity and bedrock inci- The transition from the tools effect to the cov- σ = 0.34 MPa sion rate. Black line is the T nonlinear least-squares fit er effect can be observed in the spatial pattern σ = 0.39 MPa T of power law to all data. of abrasion. For low S, the incision rate reached σT = 0.46 MPa Gray shading indicates a maximum at the center of the range of bed-

) 95% confidence interval 2 σT = 0.71 MPa form motion (Fig. 4A), because the entire bed- of fit. Vertical error bars form was mobilized during each flow oscillation.

MPa represent ±1 standard -1 Total sediment load deviation in mean inci- However, for high S, a portion of the bedform (cm3cm-2) 10-1 sion rate as estimated remained immobile, and incision rates were low- S = 0.48 from Monte Carlo uncer- est under the center of the bedform and highest S = 0.24 tainty analysis in which at the bed-form edges, where sediment saltated S = 0.12 measurement uncertainty S = 0.09 and variability in material vigorously (Fig. 4A). For a constant, high S, a S = 0.06 properties (foam weight, large portion of the bed under the bedform was S = 0.03 foam density, and foam Incision rate, I (myr covered at low urms, whereas the same region S = 0.015 tensile strength) were experienced maximum incision rates at higher S = 0.0075 propagated through the u as the bedform was fully mobile (Fig. 4B). incision rate calculation rms 4.2 2 I = 1.0 (R = 0.86) 10,000 times for each 10-2 experiment. Horizontal DISCUSSION 0.4 0.5 0.6 0.70.8 0.9 1.0 bars indicate interquar- Sediment Controls on Wave-Driven Mean oscillation velocity, (ms-1) tile range of oscillation rms Abrasion and Reef Morphology velocity during each experiment. Incision rate Our experiments demonstrate that the abrasion

was calculated as I = (mpre – mpost)/(Asub × ρsub × texp), where mpost is post-experimental weight rate under oscillatory flow increases exponentially after foam was dried in an oven at 100 °C for 8 h, mpre is pre-experiment weight, texp is experi- with orbital velocity and that S provides a sec- ment duration, Asub is the foam’s exposed surface area, and ρsub is foam density. ondary control through tools and cover effects. The transition of bedforms from fully mobile to partially static appears to mark the transition in Figure 3. Influence of Abrasion dominance from the tools to the cover effect. The POUT mill sediment availability on = 0.76 ± 0.015 m s-1 power-law dependence of abrasion rate on oscil- 0.5 rms bedrock incision rate. Ver- = 0.60 ± 0.015 m s-1 tical error bars represent lation velocity implies a strong feedback between

) rms 2 -1 ±1 standard deviation of water depth and abrasion rate, because the orbital = 0.51 ± 0.015 m s 0.4 the mean incision rate as velocity under waves decreases rapidly with in- MPa estimated in Monte Carlo -1 uncertainty analysis. creasing depth (Fig. DR4). Thus, as a surface low- 0.3 Symbol definitions are as ers through wave-driven abrasion, the abrasion in Figure 2; is mean rate will decrease rapidly, a negative feedback oscillation velocity time- relationship that likely influences the temporal 0.2 averaged over an entire experiment. Lines are evolution and equilibrium state of landforms such as shore platforms and fore-reef grooves. 0.1 nonlinear least squares fits of I = k1S*[1 – (1 – The magnitude of the incision rates observed Incision rate, I (m yr k2)k3S*]^[1/(1–k2)] (T17; in our experiments also demonstrates the poten- 0 Turowski and Hodge, 2017, tial importance of abrasion for the evolution of 0 0.03 0.06 0.12 0.24 their equation 9) to data in 3 -2 nearshore environments. For example, the ten- Normalized sediment load, S* (cm cm ) the figure, wherek 1 is free parameter accounting for sile strength of reef-building corals is typically sediment characteristics; k2 modulates the probability (P) that additional sediment falls on 1.0–3.2 MPa, while the reef substrate on which exposed or covered bedrock; and k3 accounts for maximum instantaneous bed-load flux at a the corals grow has lower tensile strength, typi- given velocity. Single values of k and k were optimized for all data in the figure, whilek was 1 2 3 cally 0.2–0.8 MPa (Madin, 2005; Madin et al., allowed to vary for each of three orbital velocities. For the dashed line, k2 was set constant at 0.999, equivalent to abrasion mill case (Turowski et al., 2007). For the solid line, k2 = 1.46 was 2013). Typical trade wind–driven waves in optimized from all data. POUT—prototype oscillating u-tube. the central North Pacific (Hs = 1.5 m, Tp = 8 s;

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Downloaded from http://pubs.geoscienceworld.org/gsa/geology/article-pdf/48/6/541/5051203/541.pdf by MBL WHOI Library user on 01 December 2020 A ­relationship between oscillation velocity and in- Figure 4. Variability in cision rate that predicts coastal bedrock abrasion abrasion rate with position rates from typical wave characteristics. relative to bedforms. Inci- sion rate was measured ACKNOWLEDGMENTS along the length of foam We thank the Massachusetts Institute of Technol- substrate demonstrating ogy (MIT) Makerworkshop for material assistance. the influence of bedforms This study was supported by the U.S. Department of in three experiments: (A) Defense Strategic Environmental Research and Devel- with mean oscillation opment Program through award SERDP RC-2336, velocity time-averaged by the Woods Hole Oceanographic Institution Ocean over an entire experiment Venture Fund, and by the MIT Department of Earth, = 0.75 m s–1, includ- rms Atmospheric and Planetary Sciences Student Research ing those in Figure 1B, Fund. We also thank Jens Turowski and an anony- and (B) with sediment B mous reviewer for their insightful comments on our load S* = 0.12 cm3 cm–2. manuscript. Incision rates were nor- malized by the maximum incision rate in each REFERENCES CITED profile. 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