Run-up Pattern Research Articles

Analysis of the tsunami amplification effect by resonance in Yeongil Bay

Predicting tsunami hazards based on the tsunami source, propagation, runup patterns is critical to protect humans and property. Potential tsunami zone, as well as the historical tsunamis in 1983 and 1993, can be a threat to the east coast of South Korea. The Korea Meteorological Administration established a tsunami forecast warning system to reduce damage from tsunamis, but it does not consider tsunami amplification in the bay due to resonance. In this study, the Numerical model, Cornell Multi-grid Coupled Tsunami model, was used to investigate natural frequency in the bay due to coastal geometry. The study area is Yeongill bay in Pohang, southeast of South Korea, because this area is a natural bay and includes three harbors where resonance significantly occurs. This study generated a Gaussian-shaped tsunami, propagated it into the Yeongill bay, and compared numerical modeling results with data from tide gauge located in Yeongill bay during several storms through spectral analysis. It was found that both energies of tsunamis and storms were amplified at the same frequencies, and maximum tsunami wave height was amplified about 3.12 times. The results in this study can contribute to quantifying the amplification of tsunami heights in the bay.

WAVE RUNUP ON AN ARRAY OF STRUCTURES DUE TO A SOLITARY WAVE INTERACTING WITH STEADY CURRENTS

The present study investigates the runup patterns formed during the interactions of a solitary wave with an array of idealized structures in the presence of following and opposing steady current flows. A series of experiments were performed at Coastal and Hydraulic Engineering Research Laboratory (CHERL) of Stony Brook University. A solitary wave of 0.1 m high was considered to interact with an array of idealized buildings on a beach berm. The wave was generated in the flume in the absence and presence of steady currents. Two different steady current velocities, one weaker and the other stronger, were generated using the flume flow recirculation system.

Interaction of a solitary wave with an array of macro-roughness elements in the presence of steady currents

The present study focuses on the effects of following and opposing steady currents on the interactions of a solitary wave with an array of macro-roughness elements, placed on a berm beach. A series of laboratory experiments and high-fidelity numerical simulations are conducted. The large eddy simulations are carried out using the open source computational fluid dynamics package, OpenFOAM. Wave breaking conditions on the berm are found to be controlled by the intensity of the currents. The opposing currents influence the layer of water rushing up the macro-roughness elements, leading to asymmetric runup patterns. Furthermore, the vortices forming around the elements' sharp edges, resulting from the interactions of the wave with the elements, are modified to a large extent due to the combined wave and current effect. The elliptical vortex tubes become up to ~20% wider under the effect of the following current flow, whereas their size is reduced by up to ~90% when the opposing currents are present. The following currents enhance the bed shear velocity, leading to intensified bed shear stress zones throughout the macro-roughness environment. On the other hand, the intensification of the bed shear velocity and corresponding stress occurs on the seaside in the presence of opposing currents. Overall, the results indicate that the currents entirely change the hydrodynamics of the interactions between the solitary wave and macro-roughness environment.

Characterization of beach run-up patterns in Bagnoli bay during ABBACO project

ABSTRACT This paper reports the results of an integrated atmospheric and wave run-up forecasting system, validated with in situ measured data, for the coastal site of Bagnoli, inside the Gulf of Pozzuoli, in the Thyrrenian Sea. A modelling chain consisting of Weather Research and Forecasting model, Wave Watch 3 model and a run-up calculator was used to obtain the levels on the beach of Bagnoli, in the framework of the rehabilitation project of the industrial site. Hindcasted waves were validated with observed ones in intermediate depth, while run-up excursions were validated using video-monitoring system located on the beach. The run-up observations were obtained by time stack images analysed using video-monitoring system. An error compensation algorithm was implemented for the correction of the systematic deviations from the DGPS more precise measurements. Among the different schemes chosen for wave run-up prediction, the one of Stockdon et al. [Empirical parameterization of setup, swash, and runup. Coast Eng. 2006;53(7):573–588] was found to be outperforming in matching with the observed run-up levels. This result was expected because of the structure of this formula, which takes into account both the set-up and swash run-up contributions.

The 2014 Lake Askja rockslide‐induced tsunami: Optimization of numerical tsunami model using observed data

AbstractA large rockslide was released from the inner Askja caldera into Lake Askja, Iceland, on 21 July 2014. Upon entering the lake, it caused a large tsunami that traveled about ∼3 km across the lake and inundated the shore with vertical runup measuring up to 60–80 m. Following the event, comprehensive field data were collected, including GPS measurements of the inundation and multibeam echo soundings of the lake bathymetry. Using this exhaustive data set, numerical modeling of the tsunami has been conducted using both a nonlinear shallow water model and a Boussinesq‐type model that includes frequency dispersion. To constrain unknown landslide parameters, a global optimization algorithm, Differential Evolution, was employed, resulting in a parameter set that minimized the deviation from measured inundation. The tsunami model of Lake Askja is the first example where we have been able to utilize field data to show that frequency dispersion is needed to explain the tsunami wave radiation pattern and that shallow water theory falls short. We were able to fit the trend in tsunami runup observations around the entire lake using the Boussinesq model. In contrast, the shallow water model gave a different runup pattern and produced pronounced offsets in certain areas. The well‐documented Lake Askja tsunami thus provided a unique opportunity to explore and capture the essential physics of landslide tsunami generation and propagation through numerical modeling. Moreover, the study of the event is important because this dispersive nature is likely to occur for other subaerial impact tsunamis.

The role of a vertical reference point in changing gait regulation in cricket run-ups

The need to identify information sources which facilitate a functional coupling of perception and action in representative practice contexts is an important challenge for sport scientists and coaches. The current study investigated the role of visual information in regulating athlete gait behaviours during a locomotor pointing task in cricket. Integration of experiential knowledge of elite coaches and theoretical understanding from previous empirical research led us to investigate whether the presence of an umpire would act as a vertical informational constraint that could constrain the emergent coordination tendencies of cricket bowlers’ run-up patterns. To test this idea, umpire presence was manipulated during run-ups of 10 elite medium-fast bowlers. As hypothesised, removal of the umpire from the performance environment did not result in an inability to regulate gait to intercept a target, however, the absence of this informational constraint resulted in the emergence of different movement patterns in participant run-ups. Significantly lower standard deviation values of heel-to-crease distances were observed in the umpire condition at multiple steps, compared to performance in the no-umpire condition. Manipulation of this informational constraint altered gait regulation of participants, offering a mechanism to understand how perception–action couplings can be varied during performance in locomotor pointing tasks in sport.

Numerical Modeling of the Influence of the Beach Profile on Wave Run-Up

AbstractAn analysis of the run-up over different beach profiles is performed to evaluate the influence of the seabed shape on shore flooding. The analysis was carried out on the basis of numerical solutions of the nonlinear shallow water equations. The chosen solver was shown to provide reliable (both quantitatively and qualitatively) run-up results by comparing numerical solutions (of both solitary and regular waves) with the only available analytical solution forced by a localized topographic change. The run-up patterns on both a natural beach profile and three simpler and schematic profiles derived from it were evaluated. Different wave conditions (both random and groups) were used for a total amount of 96 different cases of inundation. Results are expressed in terms of both maximum (Zmax) and steady-state (Zsteady) run-up. It is found that both types of run-up depend on the offshore variable H0L0, as suggested by several available studies, and that, for all tested cases, random waves induce the larges...

A note on trapped Gerstner waves

The progressive Gerstner wave is studied theoretically in a rotating inviscid ocean when the bottom has a constant slope. Exact solutions are found in Lagrangian coordinates without applying the hydrostatic assumption for the pressure. For waves propagating with the coast to the right in the Northern Hemisphere, trapped Gerstner wave solutions are found for slope angles β with respect to the horizontal in the range 0 < β ≤ π/2. In particular, the Stokes edge wave transforms into the deep‐water coastal Kelvin wave in the vertical wall limit β = π/2. It is shown that standing waves obtained by superposition of oppositely traveling Gerstner wave trains in the nonrotating case are not exact solutions of the Lagrangian equations. This is discussed in relation to observed beach features and runup patterns.

A selection of nonlinear problems in water waves, analysed by perturbation-parameter techniques

The methods of analysis based on asymptotic expansions, with a small parameter, are briefly outlined. These techniques are then applied to three examples in the theory of water waves, the aim being to demonstrate the effectiveness of this approach. Throughout, we relate this procedure to more rigorous methods. The classical problem of water waves is formulated, and then various parameter choices are incorporated. The first problem examines the properties of small-amplitude, periodic waves over constant vorticity and, invoking the ideas of breakdown, scaling and matching, the possibility of stagnation is investigated. In the second case, a Camassa-Holm equation is derived; this is found to be relevant only for the horizontal velocity component in the flow at a specific depth. However, this special, integrable equation requires the retention of a number of terms of different asymptotic order--which is the least satisfactory way to use these methods. The final example, which shows how some new aspects of a familiar problem can be obtained by these methods, develops an asymptotic description of edge waves. This leads to a single equation that captures all aspects of the run-up pattern at a shoreline.

Observations of nonlinear runup patterns on plane and rhythmic beach morphology

Application of nonlinear forecasting and bispectral analysis to video observations of runup over cuspate topography shows that these alongshore patterns in the morphology are accompanied by changes to the fundamental behavior of the runup time series. Nonlinear forecasting indicates that at beach cusp horns, the behavior of swash flow is more predictable and global (meaning that characteristics of individual swash events are well represented by the behavior of the time series as a whole). Conversely, at beach cusp bays, the behavior of swash flow is less predictable and more local (meaning that the characteristics of individual swash events are best represented by the behavior of a small fraction of the time series). Bispectral analysis indicates that there is a nonlinear transfer of energy from the incident wave frequency f to the infragravity frequency ∼f/2 which only occurs in the bay, suggesting that the local behavior is caused by interactions between successive swash cycles which are magnified by channeling caused by the beach cusp geometry. The local behavior and the bispectral signatures are not present in offshore measurements, and they are not present in runup time series collected when the beach was planar. These results provide evidence that interactions between successive runups 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.

Neural network for tsunami and runup forecast

This paper examines the use of neural network to model nonlinear tsunami processes for forecasting of coastal waveforms and runup. The three‐layer network utilizes a radial basis function in the hidden, middle layer for nonlinear transformation of input waveforms near the tsunami source. Events based on the 2006 Kuril Islands tsunami demonstrate the implementation and capability of the network. Division of the Kamchatka‐Kuril subduction zone into a number of subfaults facilitates development of a representative tsunami dataset using a nonlinear long‐wave model. The computed waveforms near the tsunami source serve as the input and the far‐field waveforms and runup provide the target output for training of the network through a back‐propagation algorithm. The trained network reproduces the resonance of tsunami waves and the topography‐dominated runup patterns at Hawaii's coastlines from input water‐level data off the Aleutian Islands.

Some approaches to local modelling of tsunami wave runup on a coast

This paper presents a method for the calculation of the tsunami wave runup on an actual coast. This method consists in preliminary study of peculiarities of wave patterns near the coast for a series of simplified model water areas inheriting the basic characteristics of the considered fragment of the coastal zone and the use of the obtained results for the interpretation of the complicated runup pattern for a real coast. The results presented here are related to modelling tsunami waves runup on a part of the coast of the Bay of Bengal.

Water Waves near a Shoreline in a Flow with Vorticity: Two Classical Examples

The equations that describe the classical problem of water waves-inviscid, no surface tension and constant pressure at the surface - are non-dimensionalised and scaled appropriately, and the two examples: traditional gravity waves and edge waves, are introduced. In addition each type of wave is allowed to propagate over an existing flow field that is rotational and also admits a shoreline; some examples of such background flows are presented. Then, for each problem, a suitable asymptotic solution is constructed; for gravity waves, this is chosen to be that which gives a balance between nonlinearity and dispersion far from the shore (so that a soliton-type problem is recovered there), and then the behaviour of this solution is examined as the shoreline is approached. Sufficiently close to the shore, the asymptotic expansion is not valid, resulting in the formulation of a new, scaled problem. It is then shown - not surprisingly - that the wave, close inshore, is dominated by nonlineaity, with the amplitude of the wave growing according to Green’s law. The problem of edge waves is formulated in a similar fashion, although the relevant scales are different; in particular, the background flow must be roughly of the same size as the edge wave itself, for a self-consistent asymptotic theory of the type presented here. The development follows closely that used in the absence of a background flow, but with the background flow now appearing in the solution to leading order. This has the effect of distorting, for example, the run-up pattern of the edge waves at the shoreline, to the extent that, under certain conditions, the two solutions of the earlier theory can now be replaced by one (unique) solution.

Edge waves: theories past and present

The problem of edge waves as an example within classical water-wave theory is described by presenting an overview of some of the theories that have been offered for this phenomenon. The appropriate governing equations and boundary conditions are formulated, and then the important discoveries of Stokes and Ursell, concerning the travelling edge wave, are presented. (We do not address the corresponding problem of standing waves.) Thus, the linear problem and its spectrum are constructed; in addition, we also present the linear long-wave approximation to the problem, as well as Whitham's weakly nonlinear extension to Stokes' original theory. All these discussions are based on the same formulation of the problem, allowing an immediate comparison of the results, whether this be in terms of different approximations or whether the theory be for an irrotational flow or not. Gerstner's exact solution of the water-wave problem is then briefly described, together with a transformation that produces an exact solution of the full equations for the edge wave. The form of this solution is then used as the basis for a multiple-scale description of the edge wave over a slowly varying depth; this leads to a version of the shallow-water equations which has an exact solution that corresponds to the edge wave. Some examples of the theoretical predictions for the run-up pattern are presented. We conclude with three variants of nonlinear model equations that may prove useful in the study of edge waves and, particularly, the interaction of different modes.

Edge waves along a sloping beach

We construct a family of explicit rotational solutions to the nonlinear governing equations for water waves, describing edge waves propagating over a plane-sloping beach. A detailed analysis of the edge wave dynamics and of the run-up pattern is made possible by the use of the Lagrangian approach to the water motion. A graphical representation of the edge wave is also presented.

The Storegga tsunami along the Norwegian coast, its age and run up

The statigraphy in 25 coastal lakes shows that most of the Norwegian coastline was impacted by a large tsunami about 7200 14C BP. The methodology has been to core a staircase of lake basins above the contemporary sea level in several areas and to map the tsunami deposit to its maximum elevation. The tsunami was identified in the sedimentary record as an erosional unconformity overlain by graded or massive sand with shell fragments, followed by redeposited organic detritus. The greatest recorded runup along the coast (10–11 m above high tide) is found in areas most proximal to the Storegga slide scar on the Norwegian continental slope (Sunnmøre). To the north and south, runup is less, about 6–7 m at Bjugn (250 km north of Sunnmøre) and about 3–5 m in Austrheim (200 km to the south of Sunnmerre). This runup pattern supports the suggestion that the tsunami was generated by the Second Storegga Slide. The recorded runup heights are consistent within and between the investigated areas, and imply that the tsunami wave was not significantly influenced by the local topography, suggesting a very long wave length. The mapped runup estimates are in good agreement with a numerical model of the tsunami generated by the Second Storegga slide, and indicate that the slide was a single major event rather than a set of smaller slides.

TOPOGRAPHIC CONTROL OF RUN-UP VARIABILITY

This paper presents observations of currents recorded in the swash zones of a number of morphologically different types of beaches in order to demonstrate the large variability in run-up patterns that exists primarily because of variability in beach face and surf zone configuration. Run-up spectra are shown for steep and flat beaches under low (