Observations of nonlinear run-up patterns on plane and rhythmic beach morphology

Application of non-linear forecasting and bispectral analysis to video observations of run-up over cuspate topography shows that these alongshore patterns in the morphology are accompanied by changes to the fundamental behaviour of the run-up timeseries. Nonlinear forecasting indicates that at beach cusp horns, the behaviour of swash flow is more predictable and global (meaning that characteristics of individual swash events are well represented by the behaviour of the timeseries as a whole). Conversely, at beach cusp bays, the behaviour of swash flow is less predictable and more local (meaning that the characteristics of individual swash events are best represented by the behaviour of a small fraction of the timeseries). Bispectral analysis indicates that there is a nonlinear transfer of energy from the incident wave frequency f to infragravity frequency ~f/2 which only occurs in the bay, suggesting that the local behaviour is caused by interactions between successive swash cycles which are magnified by channelling caused by the beach cusp geometry. The local behaviour and the bispectral signatures are not present in offshore measurements, and are not present in runup timeseries collected when the beach was planar. These results provide evidence that interactions between successive run-ups are a fundamental characteristic of beach cusp bays. Ultimately, these interactions could lead to the growth of an infragravity wave with an alongshore wavelength forced by the presence of beach cusps

Mechanisms for the Formation of Rhythmic Topography in the Nearshore Region

The possibility that the periodic features observed in the nearshore region are the result of self-organisational processes is investigated in this work. The behaviour of two numerical models, based on different techniques, has been analysed in order to describe the formation of periodic features in the surf and swash zone respectively. The appearance of periodic patterns in the nearshore region has been traditionally linked to the presence of standing edge waves with the topographic changes passively driven by the flow patterns. A more recent approach indicates the possibility that periodic patterns appear because of feedback processes between beach morphology and flow. In the first model, the coupling between topographic irregularities and wave driven mean water motion in the surf zone is examined. This coupling occurs due to the fact that the topographic perturbations produce excess gradients in the wave radiation stress that cause a steady circulation. To investigate this mechanism, the linearised stability problem in the case of an originally plane sloping beach and normal wave incidence is solved. It is shown that the basic topography can be unstable with respect to two different modes: a giant cusp pattern with shore attached transverse bars that extend across the whole surf zone and a crescentic pattern with alternate shoals and pools at both sides of the breaking line showing a mirroring effect. For the swash zone, the formation of beach cusps has been investigated. The several theories proposed in the past have been analysed and all the field and laboratory measurements available in the literature collected in order to test such theories. It is suggested that, with the available measurements it is not possible to distinguish between the standing edge wave model and the self-organisation approach. A numerical model based on self-organisation has been here developed and tested in order to understand the processes occurring during beach cusp formation and development, to evaluate the sensitivity towards the parameters used and to look at how the model might relate to field observations. Results obtained confirm the validity of the self-organisation approach and its capacity to predict beach cusp spacing with values in fair agreement with the available field measurements and with most of the input parameters primarily affecting the rate of the process rather than the final spacing. However, changes in the random seed and runs for large numbers of swash cycles reveal a dynamical system with significant unpredictable behaviour. A qualitative comparison between the model results and field measurements collected by Masselink et al. (1997) during beach cusp formation and development has also been performed on the basis of a non-linear fractal technique. Results indicate beach locations and time-scales where non-linearities are more important and self-organisation can play a fundamental role

Shifting sands

The article presents the proposed changes to the New Zealand Draft Curriculum on the Nature of Science. In July 2006, the draft was released to school and the wider educational community for consultation on the national curriculum policy. It asserts to help science teachers to develop their understanding on nature of scientific knowledge and on how the community can effectively teach such aspects of the curriculum in the classroom setting

The use of video imagery to analyse groundwater and shoreline dynamics on a dissipative beach

Groundwater seepage is known to influence beach erosion and accretion processes. However, field measurements of the variation of the groundwater seepage line (GWSL) and the vertical elevation difference between the GWSL and the shoreline are limited. We developed a methodology to extract the temporal variability of the shoreline and the wet-dry boundary using video imagery, with the overarching aim to examine elevation differences between the wet-dry boundary and the shoreline position in relation to rainfall and wave characteristics, during a tidal cycle. The wet-dry boundary was detected from 10-minute time-averaged images collected at Ngaranui Beach, Raglan, New Zealand. An algorithm discriminated between the dry and wet cells using a threshold related to the maximum of the red, green and blue intensities in Hue-Saturation-Value. Field measurements showed this corresponded to the location where the watertable was within 2 cm of the beachface surface. Timestacks, time series of pixels extracted from cross-shore transects in the video imagery, were used to determine the location of the shoreline by manually digitizing the maximum run-up and minimum run-down location for each swash cycle, and averaging the result. In our test data set of 14 days covering a range of wave and rainfall conditions, we found 6 days when the elevation difference between the wet-dry boundary and the shoreline remained approximately constant during the tidal cycle. For these days, the wet-dry boundary corresponded to the upper limit of the swash zone. On the other 8 days, the wet-dry boundary and the shoreline decoupled with falling tide, leading to elevation differences of up to 2.5 m at low tide. Elevation differences between the GWSL and the shoreline at low-tide were particularly large when the cumulative rainfall in the preceding month was greater than 200 mm. This research shows that the wet-dry boundary (such as often used in video shoreline-finding algorithms) is related to groundwater seepage on low-sloped, medium to fine sand beaches such as Ngaranui Beach (mean grain size~0.27 mm, beach slope ~1:70) and may not be a good indicator of the position of the shoreline

The effects of tides on swash statistics on an intermediate beach

Swash hydrodynamics were investigated on an intermediate beach using runup data obtained from video images. Under mild, near-constant, offshore wave conditions, the presence of a sandbar and the tidally controlled water depth over its crest determined whether most of the incoming waves broke before reaching the shoreline. This forced a change in the pattern of wave energy dissipation across the surf zone between low and high tide, which was reflected by changes to swash on time scales of a few hours. Significant runup height (Rs, defined as 4 times the standard deviation of the waterline time series), was found to vary by a factor of 2 between low tide, when most of the waves were breaking over the sandbar (Rs/Hs ≈ 1.5, where Hs is the offshore significant wave height) and high tide, when the waves were barely breaking (Rs/Hs ≈ 2.7). The increase in wave energy dissipation during low tide was also associated with changes in swash maxima distribution, a decrease in mean swash period, and increasing energy at infragravity frequencies. Bispectral analysis suggested that this infragravity modulation might have been connected with the presence of secondary waves

A finite-difference ghost-point multigrid method for multi-scale modelling of sorption kinetics of a surfactant past an oscillating bubble

We propose a method for the numerical solution of a multiscale model describing sorption kinetics of a surfactant around an oscillating bubble. The evolution of the particles is governed by a convection-diffusion equation for the surfactant concentration $c$, with suitable boundary condition on the bubble surface, which models the action of the short range attractive-repulsive potential acting on them when they get sufficiently close to the surface \cite{multiscale_mod}. In the domain occupied by the fluid, the particles are transported by the fluid motion generated by the bubble oscillations. The method adopted to solve the equation for $c$ is based on a finite-difference scheme on a uniform Cartesian grid and implemented in 2D and 3D axisymmetric domains. We use a level-set function to define the region occupied by the bubble, while the boundary conditions are discretized by a ghost-point technique to guarantee second order accuracy at the curved boundary. The sparse linear system is finally solved with a geometric multigrid technique designed \textit{ad-hoc\/} for this specific problem. Several accuracy tests are provided to prove second order accuracy in space and time. The fluid dynamics generated by the oscillating bubble is governed by the Stokes equation solved with a second order accurate method based on a monolithic approach, where the momentum and continuity equations are solved simultaneously. Since the amplitude of the bubble oscillations are very small, a simplified model is presented where the computational bubble is actually steady and its oscillations are represented purely with time-dependent boundary conditions. A numerical comparison with the moving domain model confirms that this simplification is perfectly reasonable for the class of problems investigated in this paper

The use of imaging systems to monitor shoreline dynamics

The development of imaging systems is nowadays established as one of the most powerful and reliable tools for monitoring beach morphodynamics. Two different techniques for shoreline detection are presented here and, in one case, applied to the study of beach width oscillations on a sandy beach (Pauanui Beach, New Zealand). Results indicate that images can provide datasets whose length and sample interval are accurate enough to resolve inter-annual and seasonal oscillations, and long-term trends. Similarly, imaging systems can be extremely useful in determining the statistics of rip current occurrence. Further improvements in accuracy and reliability are expected with the recent introduction of digital systems