Concepts in gravel beach dynamics

The paper introduces a complete set of Boussinesq-type equations suitable for water waves and wave-induced nearshore circulation over an inhomogeneous, permeable bottom. The derivation starts with the conventional expansion of the fluid particle velocity as a polynomial of the vertical coordinate z followed by the depth integration of the vertical components of the Euler equations for the fluid layer and the volume-averaged equations for the porous layer to obtain the pressure field. Inserting the kinematics and pressure field into the Euler and volume-averaged equations on the horizontal plane results in a set of Boussinesq-type momentum equations with vertical vorticity and z -dependent terms. A new approach to eliminating the z dependency in the Boussinesq-type equations is introduced. It allows for the existence and advection of the vertical vorticity in the flow field with the accuracy consistent with the level of approximation in the Boussinesq-type equations for the pure wave motion. Examination of...

Fully Nonlinear Boussinesq-Type Equations for Waves and Currents over Porous Beds

Measurements and modelling of beach groundwater flow in the swash-zone: a review

Modelling gravel barrier profile response to combined waves and tides using XBeach: Laboratory and field results

Groundwater responses to swash motions were observed on a natural gravel beach at Slapton Sands, UK. Detailed hydrodynamic measurements of swash depth, flow velocity and groundwater elevation were made using a cross-shore array of pressure transducers and current metres. The groundwater-level remained closely linked to the tidal elevation throughout the flood and ebb stages of the tide and prevented the formation of an elevated seepage face. The swash and groundwater spectra were dominated by a broad band of incident-frequency energy, but both displayed an increasing contribution of low-frequency energy moving landwards. A behavioural divergence was identified across the swash zone as groundwater motions were observed when no swash is overhead on the beach face. Fourier analysis and cross-correlations assisted to identify the role of two distinct pathways in the transferral of fluid from the swash to the groundwater. One that causes instantaneous swash-frequency groundwater-level rises via an energy flux through the saturated lower beachface. A second pathway, lagged by up to 4 s, was caused by vertical infiltration from large swashes across the unsaturated upper beachface. Infiltration across the upper-swash zone causes the backwash discharge to be weakened by 50% compared to the uprush discharge, severely limiting the ability of the backwash to transport sediment. The lack of tidal-scale groundwater-level asymmetry ensures that the upper beachface remains unsaturated throughout the whole tidal cycle and allows continued infiltration. It is concluded that this persistent infiltration has important consequences for the morphological changes commonly observed on gravel beaches by allowing accretion in the upper-swash at all stages of the tide.

Swash–groundwater interaction on a steep gravel beach

The development of a numerical model for the simulation of water flow in and above a porous beach is described. The model, OTTP-1D, is based on a previous hydrodynamic model of the swash zone, OTT-1D, and builds on the numerical methods developed in the earlier model by the addition of a permeable layer representing a gravel beach. The porewater flow equations used in the present model are described along with the boundary layer approach used to determine the bed shear stress when the effects of exchange between the free-flow and porewater flow regions of the model are taken into consideration. These equations are transformed so as to make them amenable to solution by an upwind finite volume method in the same way as the earlier model. The model is verified against a simple analytical case of Darcy flow and an estimate of lower limit of applicable grain size made thereby. Validation against observed water depths and free-flow velocities recorded on a gravel beach at Slapton, U.K. in 2001 is also undertaken. The model accurately predicts both measured instantaneous water depths and velocities. DOI: 10.1061/~ASCE!0733-950X~2004!130:5~223! CE Database subject headings: Porous media; Porous flow; Numerical models; Validation; Beaches.

Suzanne Clarke

Papers

Modeling Flow In and Above a Porous Beach