Marissa L. Yates

Field evidence of beach profile evolution toward equilibrium

An equilibrium framework is used to describe the evolution of the cross-shore profile of five beaches (medium grain size sand) in southern California. Elevations were observed quarterly on cross-shore transects extending from the back beach to 8 m depth, for 3–10 years. Transects spaced 100 m in the alongshore direction are alongshore averaged into nineteen 700–900 m long sections. Consistent with previous observations, changes about the time average profile in many sections are captured by the first mode empirical orthogonal function (EOF). The first EOF poorly describes sections with hard substrate (less than roughly 80% sandy bottom) and also fails near the head of a submarine canyon and adjacent to an inlet. At the 12 well-described sections, the time-varying amplitude of the first EOF, the beach state A, describes the well-known seasonal sand exchange between the shoreline and offshore (roughly between 4 and 7 m depth). We show that the beach state change rate dA/dt depends on the disequilibrium between the present state A and wave conditions, consistent with the equilibrium concepts of Wright and Short (1984) and Wright et al. (1985). Empirically determined, optimal model coefficients using the framework of Yates et al. (2009a, 2011) vary between sections, but a single set of globally optimized values performs almost as well. The model implements equilibrium concepts using ad hoc assumptions and empirical parameter values. The similarity with observed profile change at five southern California beaches supports the underlying model equilibrium hypotheses, but for unknown reasons the model fails at Duck, NC.

Equilibrium modeling of the beach profile on a macrotidal embayed low tide terrace beach

Eleven-year long time series of monthly beach profile surveys and hourly incident wave conditions are analyzed for a macrotidal Low Tide Terrace beach. The lower intertidal zone of the beach has a pluriannual cycle, whereas the upper beach profile has a predominantly seasonal cycle. An equilibrium model is applied to study the variation of the contour elevation positions in the intertidal zone as a function of the wave energy, wave power, and water level. When forcing the model with wave energy, the predictive ability of the equilibrium model is around 60% in the upper intertidal zone but decreases to 40% in the lower intertidal zone. Using wave power increases the predictive ability up to 70% in both the upper and lower intertidal zones. However, changes around the inflection point are not well predicted. The equilibrium model is then extended to take into account the effects of the tide level. The initial results do not show an increase in the predictive capacity of the model, but do allow the model free parameters to represent more accurately the values expected in a macrotidal environment. This allows comparing the empirical model calibration in different tidal environment. The interpretation of the model free parameter variation across the intertidal zone highlights the behavior of the different zones along the intertidal beach profile. This contributes to a global interpretation of the four model parameters for beaches with different tidal ranges, and therefore to a global model applicable at a wide variety sites.

Développement d'un modèle numérique non-linéaire et dispersif pour la propagation des vagues en zone côtière

Les effets non-lineaires et dispersifs etant particulierement importants pour les vagues en zone cotiere, nous etudions et developpons un modele potentiel completement non-lineaire et dispersif resolvant les equations d’Euler-Zakharov qui regissent l’evolution temporelle de la position et du potentiel des vitesses a la surface libre. La formulation mathematique ainsi que sa mise en œuvre numerique sont exposees, avec la presentation de la methode d’extension du domaine d’une a deux dimensions d’espace horizontales. Les capacites non-lineaires et dispersives de la version 1DH du modele sont demontrees a travers l’application a deux cas tests : d’abord, la generation et la propagation des harmoniques libres et liees associees aux vagues regulieres creees par un generateur de vagues de type piston sur un fond plat d’apres les experiences de CHAPALAIN et al. (1992), puis la propagation de vagues irregulieres au-dessus d’une barre sous-marine d’apres les experiences de BECQ-GIRARD et al. (1999). La bonne representation des transferts d’energie entre les differentes composantes harmoniques montre la capacite et la precision du modele a representer les effets dispersifs et non-lineaires d’ordres eleves. Le developpement d’une version 2DH du modele a ete teste pour simuler la propagation de vagues regulieres sur une marche immergee semi-circulaire agissant comme une lentille convergente, afin de reproduire deux des experiences de WHALIN (1971). Les premiers resultats obtenus utilisant des fonctions de base radiales pour calculer les derivees dans le plan horizontal montrent la capacite du modele de simuler des cas de bathymetries variables en 2DH. Cette methode semble prometteuse en vue de l’application a des cas realistes. Development of a nonlinear and dispersive numerical model of wave propagation in the coastal zone Abstract: Nonlinear and dispersive effects are significant for nearshore waves, leading to the study and development of a fully nonlinear and dispersive potential-flow model solving the Euler-Zakharov equations, which determine the temporal evolution of the free surface elevation and velocity potential. The mathematical model and its numerical implementation are presented, as well as the approach chosen to extend the model to two horizontal dimensions. The nonlinear and dispersive capabilities of the 1DH version of the model are demonstrated by applying the model to two test cases: (1) the generation of regular waves created by a piston-like wave maker and the propagation of the associated free and bound harmonics over a flat bottom, following the experiments of CHAPALAIN et al. (1992), and (2) the propagation of irregular waves over a barred beach profile, following the experiments of BECQ-GIRARD et al. (1999). The accuracy of the model in representing high-order nonlinear and dispersive effects is demonstrated by the reproduction of the energy transfers between different harmonic components. Then, the development of the 2DH version of the model is tested simulating the propagation of regular waves over a semi-circular step acting as a converging lens, reproducing two experiments of WHALIN (1971). The initial results obtained using Radial Basis Functions to estimate the horizontal derivatives demonstrate the ability of the model to simulate wave propagation over variable 2DH bathymetries. These results indicate the potential of applying the model to simulate realistic cases. Keywords: Nonlinear waves; Coastal hydrodynamics; Water wave simulation; Numerical modeling; Wave models; Radial Basis Functions.