Shoaling Wave Shape Estimates from Field Observations and Derived Bedload Sediment Rates

Tarandeep S Kalra,Steve E Suttles,Alfredo L Aretxabaleta,Gibson R Leavitt,John C Warner,Christopher R Sherwood

doi:10.3390/jmse10020223

Tarandeep S Kalra, Steve E Suttles + Show 4 more

Open Access

https://doi.org/10.3390/jmse10020223

Copy DOI

Abstract

The shoaling transformation from generally linear deep-water waves to asymmetric shallow-water waves modifies wave shapes and causes near-bed orbital velocities to become asymmetrical, contributing to net sediment transport. In this work, we used two methods to estimate the asymmetric wave shape from data at three sites. The first method converted wave measurements made at the surface to idealized near-bottom wave-orbital velocities using a set of empirical equations: the “parameterized” waveforms. The second method involved direct measurements of velocities and pressure made near the seabed: the “direct” waveforms. Estimates from the two methods were well correlated at all three sites (Pearson’s correlation coefficient greater than 0.85). Both methods were used to drive bedload-transport calculations that accounted for asymmetric waves, and the results were compared with a traditional excess-stress formulation and field estimates of bedload transport derived from ripple migration rates based on sonar imagery. The cumulative bedload transport from the parameterized waveform was 25% greater than the direct waveform, mainly because the parameterized waveform did not account for negative skewness. Calculated transport rates were comparable to rates estimated from ripple migration except during the largest event, when calculated rates were as much as 100 times greater, which occurred during high period waves.

Highlights

Waves propagating towards the coast undergo transformations from their sinusoidal wave shape in deep water to non-linear wave shape in shallow water
The use of skewed waveforms in sediment-transport calculations represents an advance in computing bedload transport that accounts for wave-driven processes in morphodynamic models
The present work compares parameterizations of skewed waveforms from bulk surface-wave statistics with waveforms obtained from direct measurements near the seafloor, using observations from three different sites under relatively calm conditions

Summary

Introduction

Waves propagating towards the coast undergo transformations from their sinusoidal wave shape in deep water to non-linear wave shape in shallow water. “Skewed”, as used here, describes wave shapes, bottom-orbital velocities, and sediment transport generated by waves that cannot be adequately represented by linear (Airy) wave theory (e.g., [1]). As waves shoal and steepen, this assumption no longer holds, and non-linear equations are needed to accurately represent the waves [1]. This shoaling transformation causes the near-bottom wave orbital velocity to differ between the wave crest and trough cycles, referred to as velocity skewness [2]. As waves propagate further into the surf zone, the differential duration in crest and trough half cycles can lead to a differential acceleration in each half cycle, referred to as acceleration asymmetry [3]

Methods

Discussion

Conclusion