A new physical concept of relaxation time is introduced in this research as the time required for the beach to dissipate its initial perturbation. This concept is investigated using a simple beach-evolution model of shoreline rotation at pocket beaches, based on the assumption that the instantaneous change of the shoreline plan-view shape depends on the long-term equilibrium plan-view shape. The expression of relaxation time is developed function of the energy conditions and the physical characteristics of the beach; it increases at longer beaches having coarse sediments and experiencing low-energy conditions. The relaxation time, calculated by the developed model, is validated by the shoreline observations extracted from video images at two artificially embayed beaches of Barcelona (NW Mediterranean) suffering from perturbations of sand movement and a nourishment project. This finding is promising to estimate the shoreline response and useful to improve our understanding of the dynamic of pocket beaches and their stability.
This research is carried out in the framework of the program Surface Water and Ocean Topography (SWOT) which is a partnership between NASA and CNES. Here, a new hybrid model is implemented for filling gaps and forecasting the hourly sea level variability by combining classical harmonic analyses to high statistical methods to reproduce the deterministic and stochastic processes, respectively. After simulating the mean trend sea level and astronomical tides, the nontidal residual surges are investigated using an autoregressive moving average (ARMA) methods by two ways: (1) applying a purely statistical approach and (2) introducing the SLP in ARMA as a main physical process driving the residual sea level. The new hybrid model is applied to the western Atlantic sea and the eastern English Channel. Using ARMA model and considering the SLP, results show that the hourly sea level observations of gauges with are well reproduced with a root mean square error (RMSE) ranging between 4.5 and 7 cm for 1 to 30 days of gaps and an explained variance more than 80 %. For larger gaps of months, the RMSE reaches 9 cm. The negative and the positive extreme values of sea levels are also well reproduced with a mean explained variance between 70 and 85 %. The statistical behavior of 1-year modeled residual components shows good agreements with observations. The frequency analysis using the discrete wavelet transform illustrate strong correlations between observed and modeled energy spectrum and the bands of variability. Accordingly, the proposed model presents a coherent, simple, and easy tool to estimate the total sea level at timescales from days to months. The ARMA model seems to be more promising for filling gaps and estimating the sea level at larger scales of years by introducing more physical processes driving its stochastic variability.
The occurrence and characteristics of transverse finger bars at Surfers Paradise (Gold Coast, Australia) have been quantified with 4 years of time-exposure video images. These bars are attached to the inner terrace and have an oblique orientation with respect to the coastline. They are observed during 24 % of the study period, in patches up to 15 bars, with an average lifetime of 5 days and a mean wavelength of 32 m. The bars are observed during obliquely incident waves of intermediate heights. Bar crests typically point toward the incoming wave direction, i.e., they are up-current oriented. The most frequent beach state when bars are present (43 % of the time) is a rhythmic low-tide terrace and an undulating outer bar. A morphodynamic model, which describes the feedback between waves, currents, and bed evolution, has been applied to study the mechanisms for finger bar formation. Realistic positive feedback leading to the formation of the observed bars only occurs if the sediment resuspension due to roller-induced turbulence is included. This causes the depth-averaged sediment concentration to decrease in the seaward direction, enhancing the convergence of sediment transport in the offshore-directed flow perturbations that occur over the up-current bars. The longshore current strength also plays an important role; the offshore root-mean-square wave height and angle must be larger than some critical values (0.5 m and 20(a similar to), respectively, at 18-m depth). Model-data comparison indicates that the modeled bar shape characteristics (up-current orientation) and the wave conditions leading to the bar formation agree with data, while the modeled wavelengths and migration rates are larger than the observed ones. The discrepancies might be because in the model we neglect the influence of the large-scale beach configuration.
Shoreface-connected sand ridges are rhythmic bedforms that occur on many storm-dominated inner shelves. The ridges span several kilometers, are a few meters high, and they evolve on a timescale of centuries. A process-based model is used to gain a fundamental insight into the response of these ridges to extraction of sand. Different scenarios of sand extraction (depth, location, and geometry of the extraction area; multiple sand extractions) are imposed. For each scenario, the response timescale as well as the characteristics of the new equilibrium state are determined. Results show that ridges partially restore after extraction, i.e., the disturbed bathymetry recovers on decadal timescales. However, in the end, the ridge original sand volume is not recovered. Initially, most sand that accomplishes the infill of the pit originates from the area upstream of the extraction, as well as from the areas surrounding the pit. The contribution of the latter strongly decreases in the subsequent time period. Depending on the location of the pit, additional sand sources contribute: First, if the pit is located close to the downstream trough, the pit gains sand by reduction of sand transport from the ridge to this trough. Second, if the pit is located close to the adjacent outer shelf, the ridge recovery is stronger due to an import of sand from that area. Furthermore, pits that are located close to the nearshore zone have a weak recovery, deeper pits have longer recovery timescales, wide and shallow pits recover most sand, while multiple sand pits slow down the recovery process.
The influence of wave–bedform feedbacks on both the initial formation of shoreface-connected sand ridges (sfcr) and on grain size sorting over these ridges on micro-tidal inner shelves is studied. Also, the effect of sediment sorting on the growth and the migration of sfcr is investigated. This is done by applying a linear stability analysis to an idealized process-based morphodynamic model, which simulates the initial growth of sfcr due to the positive coupling between waves, currents, and an erodible bed. The sediment consists of sand grains with two different sizes. New elements with respect to earlier studies on grain sorting over sfcr are that wave-topography interactions are explicitly accounted for, entrainment of sediment depends on bottom roughness, and transport of suspended sediment involves settling lag effects. The results of the model indicate that sediment sorting causes a reduction of the growth rate and migration speed of sfcr, whereas the wavelength is only slightly affected. In the case where the entrainment of suspended sediment depends on bottom roughness, the coarsest sediment is found in the troughs; otherwise, the finest sediment occurs in the troughs. Compared to previous work, modeled maximum variations in the mean grain size over the topography are in better agreement with field observations. Settling lag effects are important for the damping of high-wavenumber mode instabilities such that a preferred wavelength of the bedforms is obtained.
A model was developed and analyzed to quantify the effect of graded sediment on the formation of tidal sand ridges. Field data reveal coarse (fine) sediment at the crests (in the troughs), but often phase shifts between the mean grain-size distribution and the bottom topography occur. Following earlier work, this study is based on a linear stability analysis of a basic state with respect to small bottom perturbations. The basic state describes an alongshore tidal current on a coastal shelf. Sediment is transported as bed load and dynamic hiding effects are accounted for. A one-layer model for the bed evolution is used and two grain size classes (fine and coarse sand) are considered. Results indicate an increase in growth and migration rates of tidal sand ridges for a bimodal mixture, whilst the wavelength of the ridges remains unchanged. A symmetrical externally forced tidal current results in a grain-size distribution which is in phase with the ridges. Incorporation of an additional external M4 tidal constituent or a steady current results in a phase shift between the grain-size distribution and ridge topography. These results show a general agreement with observations. The physical mechanism responsible for the observed grain-size distribution over the ridges is also discussed.
A non-linear morphodynamic model of a microtidal coastal shelf is used to study the response of shoreface-connected sand ridges and the net sand balance of the shelf to large-scale interventions. The model describes the interaction between storm-driven currents and the erodible bottom. The transport of sediment comprises both bedload and suspended load contributions and is due to the joint action of waves (stirring of sediment from the bed) and net currents (causing transport). Three basic types of interventions are studied: extracting sand from ridges, nourishing sand at the shelf and constructing navigation channels. The model results indicate that for all interventions studied a relatively fast local recovery (time scale of decades to centuries) of the disturbed bathymetry to its original pattern takes place. Readjustment of the global system to its original equilibrium state (the saturation process) occurs on a longer time scale (several centuries). During the adjustment stage, significant net sand exchanges between inner shelf and adjacent outer shelf and near-shore zone occur. The results further suggest that extraction of sand from the shelf and dredging of navigation channels have negative implications for the stability of the beach (its sand volume decreases).