Surf Zone Model Research Articles

A Coupled Hydrodynamic-Equilibrium Type Beach Profile Evolution Model

An equilibrium beach profile model is developed and coupled with a parametric hydrodynamic model to provide feedback between the evolving morphology and the hydrodynamics. The model is compared to laboratory beach profiles evolving toward equilibrium conditions under constant forcing. The equilibrium model follows the classical approach but uses the bulk sediment transport as the governing model parameter. This approach is coupled with empirically derived and normalised sediment transport functions and a parametric surf zone wave transformation model. The dissipation predicted by the surf zone model controls the cross-shore position of the maxima in the sediment transport functions and hence the cross-shore evolution of the beach profile. Realistic beach profile shapes are generated for both erosive (barred) and accretive (bermed) beach profiles, and predictions of bar and berm position are satisfactory. With more complex normalised sediment transport functions, the model can be applied to conditions with a cyclical wave climate. However, the model concept is better associated with erosive wave conditions and further work is required to improve the link between the modelled dissipation and local transport for accretive conditions.

A new offshore transport mechanism for shoreline‐released tracer induced by transient rip currents and stratification

AbstractOffshore transport from the shoreline across the inner shelf of early‐stage larvae and pathogens is poorly understood yet is critical for understanding larval fate and dilution of polluted shoreline water. With a novel coupling of a transient rip current (TRC) generating surf zone model and an ocean circulation model, we show that transient rip currents ejected onto a stratified inner shelf induce a new, previously unconsidered offshore transport pathway. For incident waves and stratification typical for Southern California in the fall, this mechanism subducts surf zone‐origin tracers and transports them at least 800 m offshore at 1.2 km/d analogous to subduction at ocean fronts. This mechanism requires both TRCs and stratification. As TRCs are ubiquitous and the inner shelf is often stratified, this mechanism may have an important role in exporting early‐stage larvae, pathogens, or other tracers onto the shelf.

Rotational surf zone modeling for [formula omitted] Boussinesq–Green–Naghdi systems

A surf zone model is developed and tested based on the O(μ4) Boussinesq–Green–Naghdi system of Zhang et al. (2013). Because the model is fundamentally rotational, it uses fewer ad hoc assumptions than are found in many Boussinesq breaking wave systems. Eddy viscosity is used to describe both breaking dissipation and bottom friction, with breaking viscosities derived from the turbulent kinetic energy equation coupled with an O(μ4) rotational wave model. In contrast, bottom friction is included by imposing the frictional coefficient-derived boundary stress as an equivalent eddy viscosity. Numerical tests for one horizontal dimension show good agreement with regular and irregular wave breaking tests, and for solitary wave runup. Surface elevation decay, setup, runup, interior orbital velocities, and depth-varying undertow velocities can all be modeled reasonably. Comparison with an O(μ2) system shows similar performance for water surface elevations in the surf zone, demonstrating that the dissipation model is the major controlling factor. However, the O(μ4) model shows significantly improved representations of the velocity profile in the surf zone, as expected.

A mode split, Godunov‐type model for nonhydrostatic, free surface flow

SUMMARYA previously developed model for nonhydrostatic, free surface flow is redesigned to improve computational efficiency without sacrificing accuracy. Both models solve the Reynolds averaged Navier–Stokes equations in a fractional step manner with the pressure split into hydrostatic and nonhydrostatic components. The hydrostatic equations are first solved with an approximate Riemann solver. The hydrostatic solution is then corrected by including the nonhydrostatic pressure and requiring the velocity field to obey the incompressibility constraint.The original model requires the solution of a Riemann problem at every cell face for each vertical layer of cells, which is computationally expensive. The redesigned model instead solves the shallow water (long wave) equations for the hydrostatic solution. Vertical shear is computed by subtracting the shallow water equations from the full three dimensional equations, which removes the hydrostatic thrust terms. Therefore, the required fluxes may be more efficiently computed with velocity based upwind differencing rather than solving a Riemann problem in each vertical layer of cells. This approach is termed mode splitting and has been used in hydrostatic coastal and ocean circulation models, but not surf zone models. Numerical predictions are compared with analytical solutions and experimental data to show that the mode split model is as accurate as the original model, but requires significantly less computational effort especially for large numbers of cell layers. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.

Ensemble prediction of coastal flood risk arising from overtopping by linking meteorological, ocean, coastal and surf zone models

AbstractThis paper presents an integrated ‘Clouds‐to‐Coast’ ensemble modelling framework of coastal flood risk due to wave overtopping. The modelling framework consists of four key components: meteorological forecasts, wave–tide–surge predictions, nearshore wave models and surf zone models. This type of ensemble prediction approach allows us to estimate the probabilities of various outcomes and so improve our understanding of the reliability of results. It also provides a measure of the uncertainty associated with predictions, which can be particularly large for extreme storms, and allows us to assess how the uncertainty propagates from meteorological forecasts to overtopping and subsequent coastal flood risk predictions. Copyright © 2013 Royal Meteorological Society

Boussinesq–Green–Naghdi rotational water wave theory

Using Boussinesq scaling for water waves while imposing no constraints on rotationality, we derive and test model equations for nonlinear water wave transformation over varying depth. These use polynomial basis functions to create velocity profiles which are inserted into the basic equations of motion keeping terms up to the desired Boussinesq scaling order, and solved in a weighted residual sense. The models show rapid convergence to exact solutions for linear dispersion, shoaling, and orbital velocities; however, properties may be substantially improved for a given order of approximation using asymptotic rearrangements. This improvement is accomplished using the large numbers of degrees of freedom inherent in the definitions of the polynomial basis functions either to match additional terms in a Taylor series, or to minimize errors over a range. Explicit coefficients are given at O(μ2) and O(μ4), while more generalized basis functions are given at higher order. Nonlinear performance is somewhat more limited as, for reasons of complexity, we only provide explicitly lower order nonlinear terms. Still, second order harmonics may remain good to kh≈10 for O(μ4) equations. Numerical tests for wave transformation over a shoal show good agreement with experiments. Future work will harness the full rotational performance of these systems by incorporating turbulent and viscous stresses into the equations, making them into surf zone models.

Improving the efficiency and accuracy of a nonhydrostatic surf zone model

A previously developed model for simulating breaking surf zone waves is improved to yield more accurate and computationally efficient predictions. The model employs a sigma coordinate transformation in the vertical direction and solves the Reynolds averaged Navier–Stokes equations in a fractional step manner with the pressure split into hydrostatic and nonhydrostatic components. The hydrostatic equations are first solved with an approximate Riemann solver and the velocity field is then corrected to be divergence free by including the nonhydrostatic pressure. The previous model required a cumbersome modification to accurately predict surf zone wave heights. In this paper, a simpler alteration is presented that is shown to also yield accurate surf zone wave height predictions. In addition, other opportunities for improving model accuracy, robustness, and computational efficiency are also investigated including the discretization of advection terms and the selective neglect of potentially insignificant lateral viscous terms in the governing equations.

The influence of wave direction on the morphological response of a double sandbar system

Nearshore sandbars are often characterized by three-dimensional bed patterns. To analyze the influence of wave direction on the morphological response of a double sandbar system, this paper uses the 2DH nonlinear surf zone model MORFO55. Depending on wave direction, different morphologies emerge as free instabilities. These morphological responses differ in terms of geometry (shape of the alongshore rhythmic patterns) and temporal evolution. Nearly shore-normal waves favor the emergence of crescentic patterns along both the inner and outer bars. These instabilities arise from “bedsurf” coupling, which is the positive feedback between the bed perturbations and the wave-breaking patterns resulting in rip-cell circulations. The system is stable for intermediate wave incidence angles because the longshore current shifts the circulation cells alongshore, inhibiting the growth of initial perturbations. For larger angles, the system is again unstable. Two types of oblique bars emerge. The first type forms between the crest of the inner bar and the shoreline and is oriented down-current. The second type is superimposed on the two bars and is oriented up-current. Although previous studies attribute the formation of oblique bars to the deflection of the longshore current (that is a cross-shore process), we show here that this mechanism contributes to the bar formation but the growth rate is mainly governed by a longshore process. Specifically, it is the positive feedback between the bathymetry and the longshore gradient of the sediment concentration. Finally, interactions between the patterns in the two shore-parallel bars are analyzed. In the observed configurations, the influence is always one way as the inner-bar dynamics never influence those of the outer bar. The outer-bar instabilities cause undulations in the inner bar when the outer-bar instabilities grow faster than those of the inner bar.

Modeling surf zone tracer plumes: 2. Transport and dispersion

Five surf zone dye tracer releases from the HB06 experiment are simulated with a tracer advection diffusion model coupled to a Boussinesq surf zone model (funwaveC). Model tracer is transported and stirred by currents and eddies and diffused with a breaking wave eddy diffusivity, set equal to the breaking wave eddy viscosity, and a small (0.01 m2 s−1) background diffusivity. Observed and modeled alongshore parallel tracer plumes, transported by the wave driven alongshore current, have qualitatively similar cross‐shore structures. Although the model skill for mean tracer concentration is variable (from negative to 0.73) depending upon release, cross‐shore integrated tracer moments (normalized by the cross‐shore tracer integral) have consistently high skills (≈0.9). Modeled and observed bulk surf zone cross‐shore diffusivity estimates are also similar, with 0.72 squared correlation and skill of 0.4. Similar to the observations, the model bulk (absolute) cross‐shore diffusivity is consistent with a mixing length parameterization based on low‐frequency (0.001–0.03 Hz) eddies. The model absolute cross‐shore dispersion is dominated by stirring from surf zone eddies and does not depend upon the presence of the breaking wave eddy diffusivity. Given only the bathymetry and incident wave field, the coupled Boussinesq‐tracer model qualitatively reproduces the observed cross‐shore absolute tracer dispersion, suggesting that the model can be used to study surf zone tracer dispersion mechanisms.

Effects of wave averaging on estimates of fluid mixing in the surf zone

[1] Irrotational surface gravity waves approach the beach and break at a relatively high frequency, while vorticity generated by each new wave breaking event strongly interacts with the existing vorticity distribution at relatively low frequencies, leading to a surf zone that is energetic over a wide range of temporal scales. This poses a challenge to any surf zone model to accurately resolve all relevant scales. One approach to sidestep this issue is to use a short-wave-averaged model, where fast-scale wave effects are included as forcing terms for the mean current. This is in contrast to Boussinesq wave-resolving models, where each individual wave is resolved along with any ambient current. In general, these two models will predict different current fields for the same wave and bathymetric input and therefore predict different mixing behavior of the flow. Using Lagrangian methods, we compare wave-averaged and wave-resolving model results to data from the RCEX experiment, which mapped the rip current circulation over a rip-channeled bathymetry using nearshore surface drifters. Absolute and pair dispersion estimates, including the finite size Lyapunov exponent, based on virtual trajectories are shown to be consistent with field observations, except for scales less than 5 m, where field drifters predict greater pair dispersion than both models because of either unresolved subgrid processes or GPS error. A simple Lagrangian stochastic model is able to reproduce some of this short time and length scale diffusivity found in the observational data.

Data assimilation and bathymetric inversion in a two‐dimensional horizontal surf zone model

A methodology is described for assimilating observations in a steady state two‐dimensional horizontal (2‐DH) model of nearshore hydrodynamics (waves and currents), using an ensemble‐based statistical estimator. In this application, we treat bathymetry as a model parameter, which is subject to a specified prior uncertainty. The statistical estimator uses state augmentation to produce posterior (inverse, updated) estimates of bathymetry, wave height, and currents, as well as their posterior uncertainties. A case study is presented, using data from a 2‐D array of in situ sensors on a natural beach (Duck, NC). The prior bathymetry is obtained by interpolation from recent bathymetric surveys; however, the resulting prior circulation is not in agreement with measurements. After assimilating data (significant wave height and alongshore current), the accuracy of modeled fields is improved, and this is quantified by comparing with observations (both assimilated and unassimilated). Hence, for the present data, 2‐DH bathymetric uncertainty is an important source of error in the model and can be quantified and corrected using data assimilation. Here the bathymetric uncertainty is ascribed to inadequate temporal sampling; bathymetric surveys were conducted on a daily basis, but bathymetric change occurred on hourly timescales during storms, such that hydrodynamic model skill was significantly degraded. Further tests are performed to analyze the model sensitivities used in the assimilation and to determine the influence of different observation types and sampling schemes.

The variation of the velocity and turbulent kinetic energy field in the wave in the vicinity of the breaking point

The paper describes experimental investigation of the flow and turbulent kinetic energy under the weakly plunging breaking wave in the outer surf zone. Experiments for the present study were carried out on a surf zone model with a constant slope of 1:17 in the vicinity of the wave breaking point. Experimental results show that the kinetic energy is largest under the wave crest and decreases rapidly after the wave crest has passed. Visualization of the flow proved that the velocity profile during backflow phases resembles the steady open channel flow, but during the onflow phases the velocity profile is unlike any other flow situation.

A note on wave energy dissipation over steep beaches

This paper revisits the derivation of the parametric surf zone model proposed by Baldock et al. [Baldock, T. E., Holmes, P., Bunker, S. & Van Weert, P. 1998 Cross-shore hydrodynamics within an unsaturated surf zone. Coast. Eng. 34, 173–196.]. We show that a consistent use of the proposed Rayleigh distribution for surf zone wave heights results in modification of the expressions for the bulk dissipation rate and enhanced dissipation levels on steep beaches and over-saturated surf zone conditions. As a consequence, the modification proposed herein renders the model robust even on steep beaches where it could otherwise develop a shoreline singularity.

Surf zone transformation of wave height to water depth ratios

A solid body of data exists on which to base engineering decisions regarding the maximum wave heights that can be achieved in shallow water at the point of incipient breaking. Effort is now being directed towards the study of how wave height varies as waves propagate through the surf zone and what parameters control this process. Early surf zone models assumed a constant value of C while later models incorporate a decay function for H h due to turbulence in the breaking wave. A few more recent studies have recognised a second process by which H h can decay through the surf zone where there is a strong underlying infragravity wave motion. The work presented here investigates the characteristics of this latter decay process on a natural exposed dissipative beach, including its magnitude and dual dependence on local mean water depth and distance from the breaker line. Some comparisons are then made with the decay characteristics of the former process.

TOWARD A SIMPLE MODEL OF THE WAVE BREAKING TRANSITION REGION IN SURF ZONES

Breaking waves undergo a transition from oscillatory, irrotational motion, to highly rotational (turbulent) motion with some particle translation. On plane or monotonically decreasing beach profiles, this physically takes place in such a way that the mean water level remains essentially constant within the transition region. Further shoreward a rapid set-up takes place within the inner, bore-like region. The new surf zone model of Svendsen (1984) begins at this transition point and the new wave there contains a trapped volume of water within the surface roller moving with the wave speed. This paper describes a simple model over the transition zone designed to match the Svendsen (1984) model at the end of the transition region. It uses a simple, linear growth model for the surface roller area development and semi-empirical model for the variation of the wave shape factor. Breaking wave type can vary from spilling through plunging as given by a surf similarity parameter. The model calculates the wave height decrease and width of the transition region for all breaker types on plane or monotonically depth decreasing beaches.

Sediment transport and morphology at the surf zone of Presque Isle, Lake Erie, Pennsylvania

A four-year investigation of surf zone sedimentation at Presque Isle, Pennsylvania, was undertaken in preparation for the design of a segmented breakwater system. Sediment transport calculations were based on hind-cast annual wave power statistics and “calibrated” by known accretion rates at the downdrift spit terminus. 30,000 m 3 of sediment reaches the peninsula annually from updrift beaches. The transport volume increases downdrift due to shoreface erosion and retreat of the peninsular neck. At the most exposed point on Presque Isle (the lighthouse) the annual transport is 209,000 m 3. East of the lighthouse is a zone of net shoreface accretion as the longshore transport rate progressively decreases. The downdrift variation in sediment supply, combined with increasing refraction and attenuation of the dominant westerly storm waves produce a systematic change in prevailing surf zone morphology. Storms produce a major longshore bar and trough along the exposed peninsular neck. The wave energy during non-storm periods is too low to significantly alter the bar which consequently becomes a permanent feature. The broad shoreface and reduced wave energy level east of the lighthouse produce a morphology characterized by large crescentic outer bars, transverse bars, and megacusps along the beach. At the sheltered and rapidly prograding eastern spit terminus the prevalent beach morphology is that of a ridge and runnel system in front of a megacuspate shore. The morphodynamic surf zone model developed for oceanic beaches in Australia is used as a basis for interpretation of shoreface morphologic variability at Presque Isle. In spite of interference by major shoreline stabilization structures, and differences between oceanic and lake wave spectra, the nearshore bar field at Presque Isle does closely correspond to the Australian model.