Nicholas Dodd

A 2D numerical model of wave run-up and overtopping

A two-dimensional (2D) numerical model of wave run-up and overtopping is presented. The model (called OTT-2D) is based on the 2D nonlinear shallow water (NLSW) equations on a sloping bed, including bed shear stress. These equations are solved using an upwind finite volume technique and a hierarchical Cartesian Adaptive Mesh Refinement (AMR) algorithm. The 2D nature of the model means that it can be used to simulate wave transformation, run-up, overtopping and regeneration by obliquely incident and multi-directional waves over alongshore-inhomogeneous sea walls and complex, submerged or surface-piercing features. The numerical technique used includes accurate shock modeling, and uses no special shoreline-tracking algorithm or shoreline coordinate transformation, which means that noncontiguous flows and multiple shorelines can easily be simulated. The adaptivity of the model ensures that only those parts of the flow that require higher resolution (such as the region of the moving shoreline) receive it, resulting in a model with a high level of efficiency. The model is shown to accurately reproduce analytical and benchmark numerical solutions. Existing wave flume and wave basin datasets are used to test the ability of the model to approximate 1D and 2D wave transformation, run-up and overtopping. Finally, we study a 2D dataset of overtopping of random waves at off-normal incidence to investigate overtopping of a sea wall by long-crested waves. The data set is interesting as it has not been studied in detail before and suggests that, in some instances, overtopping at an angle can lead to more flooding than at normal incidence.

Morphological development of rip channel systems: Normal and near-normal wave incidence

The process of formation of a rip channel/crescentic bar system on a straight, sandy coast is examined. A short review of earlier studies is presented. A morphodynamic stability model is then formulated. The resulting model includes a comprehensive treatment of shoaling and surf zone hydrodynamics, including wave refraction on depth and currents and waves. The sediment transport is modeled using a total load formula. This model is used to study the formation of rip currents and channels on a straight single-barred coast. It is found that this more comprehensive treatment of the dynamics reveals the basic rip cells predicted in earlier studies for normal incidence. Also as before, cell spacings (λ) scale with shore-to-bar crest distance (X b ), while growth rates decrease. The λ increases with offshore wave height (H) up to a saturation value; increasing H also increases instability. Experiments at off-normal wave incidence ( > 0) introduce obliquity into the evolving bed forms, as expected, and λ increases approximately linearly. the e-folding times also increase with . At normal incidence, λ increases weakly with wave period, but at oblique angles, λ decreases. Tests also reveal the presence of forced circulation cells nearer to the shoreline, which carve out bed forms there. The dynamics of these forced cells is illustrated and discussed along with the associated shoreline perturbation. Transverse bars are also discovered. Their dynamics are discussed. Model predictions are also compared with field observations. The relevance of the present approach to predictions of fully developed beach states is also discussed.

Morphodynamic modelling of rip channel growth

The morphological evolution of a rip channel system due to normally incident waves has been investigated using two different approaches. The first approach is a state-of-the-art commercial 2DH Coastal Area model, whereas the second approach is a linear stability analysis. The results of the two different approaches have been compared and both models predict rip channel spacings and initial growth rates of similar magnitudes.

Modelling the formation and the long‐term behavior of rip channel systems from the deformation of a longshore bar

A nonlinear numerical model based on a wave- and depth-averaged shallow water equation solver with wave driver, sediment transport, and bed updating is used to investigate the long-term evolution of rip channel systems appearing from the deformation of a longshore bar. Linear and nonlinear regimes in the morphological evolution have been studied. In the linear regime, a crescentic bar system emerges as a free instability. In the nonlinear regime, merging/splitting in bars and saturation of the growth are obtained. In spite of excluding undertow and wave-asymmetry sediment transport, the initial crescentic bar system reorganizes to form a large-scale and shore-attached transverse or oblique bar system, which is found to be a dynamical equilibrium state of the beach system. Thus the basic morphological transitions “Longshore Bar and Trough” → “Rhythmic Bar and Beach” → “Transverse Bar and Rip” described by earlier conceptual models are here reproduced. The study of the physical mechanisms allows us to understand the role of the different transport modes: The advective part induces the formation of crescentic bars and megacusps, and the bedslope transport damps the instability. Both terms contribute to the attachment of the megacusps to the crescentic bars. Depending on the wave forcing, the bar wavelength ranges between 180 and 250 m (165 and 320 m) in the linear (nonlinear) regime.

Modeling of storm-induced coastal flooding for emergency management

This paper describes a model package that simulates coastal flooding resulting from storm surge and waves generated by tropical cyclones. The package consists of four component models implemented at three levels of nested geographic regions, namely, ocean, coastal, and nearshore. The operation is automated through a preprocessor that prepares the computational grids and input atmospheric conditions and manages the data transfer between components. The third generation spectral wave model WAM and a nonlinear long-wave model calculate respectively the wave conditions and storm surge over the ocean region. The simulation results define the water levels and boundary conditions for the model SWAN to transform the storm waves in coastal regions. The storm surge and local tides define the water level in each nearshore region, where a Boussinesq model uses the wave spectra output from SWAN to simulate the surf-zone processes and runup along the coastline. The package is applied to hindcast the coastal flooding caused by Hurricanes Iwa and Iniki, which hit the Hawaiian Island of Kauai in 1982 and 1992, respectively. The model results indicate good agreement with the storm-water levels and overwash debris lines recorded during and after the events, demonstrating the capability of the model package as a forecast tool for emergency management.

Shear Instabilities in the Longshore Current: A Comparison of Observation and Theory

Abstract Low-frequency (<0.01 Hz) oscillations in the surf zone longshore current with wavelengths too small (<300 m) to be surface gravity waves were observed during the 1986 SUPERDUCK experiment at Duck, North Carolina. The observations suggest that these oscillations are dynamically linked to the mean longshore current in the surf zone, leading Bowen and Holman to propose that the observed oscillations are manifestations of a shear instability in the longshore current. In this paper, field data from both the SUPERDUCK experiment (a barred beach) and the l980 NSTS experiment, at Leadbetter Beach, Santa Barbara, California (a plane beach), are used to compare quantitatively the model of Bowen and Holman (which is extended to include the effects of dissipation due to bottom friction) with observation. Observed frequency-cyclic wavenumber (f-K) spectra (constructed from alongshore arrays of velocity measurements made in about 1.5–2 m of water in the trough of the bar at SUPERDUCK, and in about 1 m at NSTS)...

On beach cusp formation

A system of shallow water equations and a bed evolution equation are used to examine the evolution of perturbations on an erodible, initially plane beach subject to normal wave incidence. Both a permeable (under Darcys law) and an impermeable beach are considered. It is found that alongshore-periodic morphological features reminiscent of swash beach cusps form after a number of incident wave periods on both beaches. On the permeable (impermeable) beach these patterns are accretional (erosional). In both cases flow is ‘horn divergent’. Spacings of the cusps are consistent with observations, and are close to those provided by a standing synchronous linear edge wave. An analysis of the processes leading to bed change is presented. Two physical mechanisms are identified: concentration gradient and flow divergence, which are dominant in the lower and upper swash respectively, and their difference over a wave cycle leads to erosion or deposition on an impermeable beach. Infiltration enters this balance in the upper swash. A bed wave of elevation is shown to advance up the beach at the tip of the uprush, with a smaller wave of depression on the backwash. It is found that cusp horns can grow by a positive feedback mechanism stemming from decreased (increased) backwash on positive (negative) bed perturbations.

On the destabilization of a longshore current on a plane beach: Bottom shear stress, critical conditions, and onset of instability

The effect on the stability of a wave-driven longshore current of varying the bottom shear stress is investigated. The shear stress is assumed to be quadratic and parameterized (as usual) through a bottom friction coefficient (cd). The bottom shear stress affects both the mean longshore current (which it opposes) and the onset (or otherwise) of a shear instability in the longshore current through its aforementioned effect on the mean current (and therefore the current shear) and by damping instabilities directly. Reducing cd can destabilize the longshore current by increasing its strength, thereby increasing the current shear so as to overcome the damping of bottom friction and thus leading to the development of instabilities. At the same time, this decrease in cd directly reduces the damping experienced by the instabilities that develop. It is also shown that while the primary effect of bottom friction is to damp instabilities, there are other effects, notably linked to the flow curvature, which act to destabilize the flow. Both the weak- and the strong-longshore-current approximations are examined. For the weak-current approximation it is shown that curvature effects are particularly important in providing a destabilizing mechanism. It is also shown that for both approximations a “global” cutoff frequency is likely to exist, below which no linear instability will develop. Critical conditions are identified for each approximation (and therefore for two different longshore current profiles), beyond which instabilities will start to develop. Results suggest that a critical shear will exist for any plane beach and that for Leadbetter Beach, Santa Barbara (examined in the 1980 Nearshore Sediment Transport Study (NSTS)), the current will not become unstable until an offshore shear of about 0.03 s−1 is reached. This was apparently not achieved during NSTS.

Beach-face evolution in the swash zone

We investigate swash on an erodible beach using the one-dimensional shallow-water equations fully coupled to a bed-evolution (Exner) equation. In particular, the dam-break/bore-collapse initial condition of Shen & Meyer ( J. Fluid Mech. , vol. 16, 1963, pp. 113–125) and Peregrine & Williams ( J. Fluid Mech. , vol. 440, 2001, pp. 391–399) is investigated using a numerical model based on the method of characteristics. A sediment-transport formula (cubic in velocity u : Au 3 ) is used here; this belongs to a family of sediment-transport formulae for which Pritchard & Hogg ( Coastal Engng , vol. 52, 2005, pp. 1–23) showed that net sediment transport under the Shen & Meyer (1963) bore collapse is offshore throughout the swash zone when a non-erodible bed is considered. It is found that full coupling with the beach, although still resulting in the net offshore transport of sediment throughout the swash zone, leads to a large reduction in the net offshore transport of sediment from the beach face. This is particularly true for the upper third of the swash zone. Moreover, in contradistinction to swash flows over non-erodible beds, flows over erodible beaches are unique to the bed mobility and porosity under consideration; this has very important implications for run-up predictions. The conclusion is that it is essential to consider full coupling of water and bed motions (i.e. full morphodynamics) in order to understand and predict sediment transport in the swash, regardless of other physical effects (e.g. turbulence, infiltration, pre-suspended sediment, etc.).

Physics of nearshore bed pattern formation under regular or random waves

We present an investigation into the growth of nearshore, rhythmic patterns. A comprehensive linear stability model of the surf and shoaling zones is used to examine which type of pattern, transverse or crescentic bar, is likely to form under different wave conditions. In contrast to earlier studies we examine normal and near-normal incidence on a plane beach. In doing so we reproduce results of earlier, more restricted studies and thereby identify the physical mechanisms leading to the growth of different patterns. This paper also focuses on the role of random wave height distribution compared with regular waves and identifies conditions likely to lead to pattern growth. To this end, an amended wave height dissipation function is presented, which allows us to move between random and regular regimes. It is found that a sharply defined surf breakpoint leads to larger growth rates and crescentic-bar-type features. In contrast, a large spread in breaking gives rise to transverse bar patterns with reduced growth rates. Transverse bar alongshore spacing is typically about 1/4 to 1/2 the width of the surf zone, while crescentic bar spacing is larger, up to twice this width. It is also shown that pattern types are influenced by the wave height to depth ratio in the surf zone. This indicates that sites with substantial inner surf zone wave energy and thus greater energy available to move sediment will give rise to transverse bar patterns. A new, propagating mode is identified in such cases, which exists for normal wave incidence. Finally, the role of wave shoaling and wave refraction, either on the bed or on the currents is examined. Crescentic bars seem to be a very robust feature as they stem from the model even if those three effects are ignored. Thus the only essential feedback for their formation is the coupling between depth-controlled breaking and the evolving bathymetry. In contrast, transverse bar formation is very sensitive to wave refraction being enhanced by refraction over the bed and weakened by refraction over the current.