Run-up Process Research Articles

Spectral Sampling Method for Uncertainty Propagation in Long-Wave Runup Modeling

This paper presents a stochastic approach to model input uncertainty with a general statistical distribution and its propagation through the nonlinear long-wave equations. A Godunov-type scheme mimics breaking waves as bores for accurate description of the energy dissipation in the runup process. The polynomial chaos method expands the flow parameters into series of orthogonal modes, which contain the statistical properties in stochastic space. A spectral projection technique determines the orthogonal modes from ensemble averages of systematically sampled events through the long-wave model. This spectral sampling method generates an output statistical distribution using a much smaller sample of events comparing to the Monte Carlo method. Numerical examples of long-wave transformation over a plane beach and a conical island demonstrate the efficacy of the present approach in describing uncertainty propagation through nonlinear and discontinuous processes for flood-hazard mapping.

Infragravity Wave Motions and Runup over Shallow Fringing Reefs

This paper presents the results of a combined laboratory and numerical investigation into the role of infragravity motions in the wave runup process over fringing coral reefs. Laboratory experiments were performed with a reef profile typical of fringing reef systems along the southeast coast of Guam. Spectral analysis of the measured time histories of surface elevation over the reef face and flats show significant changes to the wave energy spectrum shoreward of the break point. Most of the wave energy in the incident wave frequency band is dissipated within a few wavelengths of the reef face with the wave motions over the reef flat and shoreline dominated by oscillations at infragravity periods [O(100s) prototype]. The infragravity wave energy is minimum at the reef crest and increases as waves propagate shoreward over the reef flat and also with increasing water level on the reef. The dominant infragravity mode is the first reef oscillation mode with a wavelength approximately equal to four times the wi...

The Order Tracking Study of Variant Speed Process of Aeroengine Vibration Signal

Order tracking is an important method to analyze the response characteristics of rotating machinery for fault diagnosis and condition monitoring in rotating machinery. Order tracking method overcomes the shortcomings of traditional resampling and FFT method. A new use based on the order tracking analysis is proposed in this paper, the computed order tracking method is applied to analyse the dynamic vibration signals during aeroengine start-stop process.In the aeroengine test, the fault characteristic of rotating shafts is related to the rotating speed,vibration will be more complicated and diversified with the increasing speed during run-up process, and has characteristics of periodicity and multiple frequency. It is of vital critical to extract characteristic information from exterior measurement vibration signal and get interior fault information. Applying the order tracking in the analysis of aeroengine signals shows that it can extract the fault characteristics and realize the state monitoring.

Variability in spatial patterns of long nonlinear waves from fast ferries in Tallinn Bay

Abstract. High-speed ferries are known to generate wakes with unusually long periods, and occasionally large amplitudes which may serve as a qualitatively new forcing factor in coastal regions that are not exposed to a sea swell. An intrinsic feature of such wakes is their large spatial variation. We analyze the variability of wake conditions for the coasts of Tallinn Bay, the Baltic Sea, a sea area with very intense fast ferry traffic. The modelled ship wave properties for several GPS-recorded ship tracks reasonably match the measured waves in terms of both wave heights and periods. It is shown that the spatial extent of the wake patterns is very sensitive to small variations in sailing conditions. This feature leads to large variations of ship wave loads at different coastal sections with several locations regularly receiving high ship wave energy. The runup of the largest ship wakes on the beach increases significantly with an increase in wave height whereas shorter (period <2–5 s) waves merge into longer waves in the shoaling and runup process.

Seasonal variations in wave characteristics around a coral reef island, South Maalhosmadulu atoll, Maldives

Synchronous measurements of waves were made at six locations around a small reef platform island in the Maldives during both westerly and northeast monsoon conditions. Summary statistics of wave records indicated similar Hs values propagating onto windward and leeward reef surfaces and a distinct growth in wave height as waves shoal toward island shorelines. Waves up to 0.78 m were recorded impacting the island shoreline. Wave energy on the reef platform was strongly modulated by seasonal winds with wave energy during the westerly monsoon an order of magnitude larger than wave conditions in the northeast monsoon. Spectral analysis of wave records highlighted spatial differences in wave energy around the island. Windward reefs and shorelines are dominated by waves at wind and swell frequencies, whereas wind-wave energy is absent from leeward shorelines. Consequently, windward shorelines have up to twice the gross energy input than leeward shorelines. Results have significant implications for geomorphic processes. Longer duration and greater incident wave energy during the westerly monsoon has promoted higher growth of the western reef flat (+ 0.2 m) and more energetic shoreline runup processes have produced markedly higher western island ridges (+ 0.7 m). Incident shoreline wave processes are sufficient to entrain beach sediments during both monsoon periods although periods of active sediment mobilisation are constrained to mid- to high-tide stages. The windward–leeward gradient in shoreline wave energy is likely to drive littoral sediment flux. Seasonal modulation of the shoreline wave energy gradients account for observed oscillations in beach position around island shorelines. Large differences in incident wave energy between monsoons is considered to affect the rate of beach change around island shorelines rather than the total volumetric movement of island beaches.

Comparison Between Moving Paddle and Mass Source Methods for Solitary Wave Generation and Propagation Over a Steep Sloping Beach

Two methods for generating nonlinear solitary waves on constant water depth in order to study their further runup over a steep sloping beach are presented. The first method is based on a prescribed wave paddle motion inducing a desired free surface profile. The second generation procedure is based on an appropriate mass source term added to the mass conservation equation in an internal source line. These two wave generation methods are implemented in the industrial Computational Fluid Dynamics code (CFD): PHOENICS (Parabolic Hyperbolic Or Elliptic Numerical Integration Code Series). The generated solitary wave’s profile and their non-breaking runup over an impermeable steep beach are in good agreement with experimental data of Lin, Chang and Liu (1999). No appreciable discrepancies are observed between experimental and simulated velocities during the runup and rundown processes except for the horizontal velocity component at the final stage of the second runup. The moving paddle and mass source methods performed equally well on reproducing non-breaking runup despite the difference in their wave generation procedures.

Propagation and run-up of nearshore tsunamis with HLLC approximate Riemann solver

A numerical model describing the propagation and run-up process of nearshore tsunamis in the vicinity of shorelines is developed based on an approximate Riemann solver. The governing equations of the model are the nonlinear shallow-water equations. The governing equations are discretized explicitly by using a finite volume method. The nonlinear terms in the momentum equations are solved with the Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver. The developed model is first applied to prediction of water motions in a parabolic basin, and propagation and subsequent run-up process of nearshore tsunamis around a circular island. Computed results are then compared with available analytical solutions and laboratory measurements. Very reasonable agreements are observed.

Survey Results of the Indian Ocean Tsunami in the Maldives

The Indian Ocean Tsunami occurred on 26 December 2004, causing serious damage in the Maldives, which is 2,000 km distant from the epicenter. A post-tsunami survey was carried out from 31 January to 4 February 2005. Tsunami height distribution, tsunami behavior in atoll and characteristics of tsunami disaster in atoll island were discussed through survey results. The height of tsunami traces in the Maldives ranged from 0.6 to 3.4 m. The trace height was not small even where there was a developed reef and even at island inside an atoll. The tsunami behavior appeared to be complex in an atoll. Several minutes were necessary for tsunami inflow to an atoll. Inertial force was small in the run-up process in some islands, but was not so in some islands. Because the Maldives consists of low-lying islands, a solid structure and artificial ground is required to improve the safety level of the Maldives.

HLLC Approximate Riemann Solver를 이용한 천수방정식 해석

본 연구에서는 수치모형을 이용하여 근해지진해일의 처오름 현상과 전파양상을 이용하여 해석하였다. 모의에 사용된 수치모형은 지진해일 거동의 해석에 적합한 비선형 천수방정식을 지배방정식으로 채택하였으며, 유한체적법을 이용하여 해석영역을 이산화 하였고 Riemann 문제를 해석하기 위하여 HLLC approximate Riemann solver와 Weighted Averaged Flux 기법을 이용하였다. 수치모형의 검증을 위하여 마찰 없는 수조에서의 수면진동문제와 원형섬 주위에서 고립파의 진행과 처오름에 대한 문제에 적용하여 각각 해석해 및 실험결과와 비교하였다. 수치모형에 의한 결과는 해석해와 수리모형실험 관측자료와 잘 일치하였다. The propagation and associated run-up process of nearshore tsunamis in the vicinity of shorelines have been analyzed by using a two-dimensional numerical model. The governing equations of the model are the nonlinear shallow-water equations. They are discretized explicitly by using a finite volume method and the numerical fluxes are reconstructed with a HLLC approximate Riemann solver and weighted averaged flux method. The model is applied to two problems; The first problem deals with water surface oscillations, while the second one simulates the propagation and subsequent run-up process of nearshore tsunamis. Predicted results have been compared to available analytical solutions and laboratory measurements. A very good agreement has been observed.

Visualization Analysis of Runup and Mixing of Internal Waves on an Upper Slope

Laboratory experiments were conducted in a 2D wave tank, where a Plexiglas plate was installed in order to understand the runup and breaking of internal waves over a sloping boundary. During the experiments, a fluid consisting of fresh water and salt water was prepared to imitate the density-stratified ocean. An image processing technique was used to reveal the profile of internal waves and the mixture of the upper-layer and lower-layer water. The measured wave profiles were compared with the calculated results by the method of characteristics. The major feature of the runup processes was well reproduced by the theoretical solution, except for the upper slope region. Calculation using the k-e model was carried out, and the predicted density variation due to mixing was compared with a set of luminance data analyzed by the image processing technique.

임원에서의 1983년 동해 중부 지진해일 수치모의: 2. 임원항에서의 범람

동해에서 발생한 1983년 지진해일의 동해안에서 처오름 과정을 수치해석하였다. 비선형 천수방정식에 근거한 유한차분 수치모형을 이용하였으며, 임원에서 최대 처오름높이를 예측하였다. 예측된 결과는 현장 관측자료와 비교적 잘 일치하였다. 지진해일 범람 위험을 강조하기 위해 처오름높이를 근거한 시험적인 최대범람도를 제작하였다. The run-up process of the 1983 Central East Sea Tsunami along the Eastern Coast is numerically investigated in this study. A finite difference numerical model based on the nonlinear shallow-water equations is employed. The maximum run-up height at Imwon is predicted and compared to field observation. A good agreement is observed. A maximum inundation map is made based on the maximum run-up heights to accentuate hazards of tsunami flooding.

Non-breaking and breaking solitary wave run-up

The run-up of non-breaking and breaking solitary waves on a uniform plane beach connected to a constant-depth wave tank was investigated experimentally and numerically. If only the general characteristics of the run-up process and the maximum run-up are of interest, for the case of a breaking wave the post-breaking condition can be simplified and represented as a propagating bore. A numerical model using this bore structure to treat the process of wave breaking and subsequent shoreward propagation was developed. The nonlinear shallow water equations (NLSW) were solved using the weighted essentially non-oscillatory (WENO) shock capturing scheme employed in gas dynamics. Wave breaking and post-breaking propagation are handled automatically by this scheme and ad hoc terms are not required. A computational domain mapping technique was used to model the shoreline movement. This numerical scheme was found to provide a relatively simple and reasonably good prediction of various aspects of the run-up process. The energy dissipation associated with wave breaking of solitary wave run-up (excluding the effects of bottom friction) was also estimated using the results from the numerical model.

Solitary Wave Runup on Plane Slopes

This study deals with the runup of solitary waves on a uniform plane beach connected to an open ocean of constant depth. The waves are nonbreaking during the runup process. A nonlinear solution to the classical shallow water equation, that describes the wave characteristics on the beach, is obtained analytically by using a hodograph transformation. It was found that the nonlinear theory agreed well with experimental results. The maximum runup predicted by the nonlinear theory is larger than that predicted earlier and the correction is on the order of the offshore relative wave height for a given slope. This correction for nonbreaking waves on beaches decreases as the beach slope steepens.

NUMERICAL SIMULATION OF WAVE BREAKING AND SWASH ON PERMEABLE UNIFORM SLOPE

The MPS method, generally called the Particle Method, which is the Lagrangian concept to solve the Navier-Stokes equation, is applied to the plunging breaker on a uniform slope. The MPS method has a superiority in the accurate calculation of the complicated behavior of water surface. In other word, it is less affected by the numerical diffusion due to the convection term than the Eulerian methods. The characteristics of splash due to the collision of a wave with a slope and the transition of the mode from the breaking to the runup via the bore are investigated based on the detailed numerical information of the velocity field on a slope.By introducing the additional drag term, which represents the existence of the permeable layer, into the governing equation, the wave breaking and runup on the permeable slope is also simulated. The effect of the permeability of the slope on the wave runup process is also discussed.

Dispersive mudslide-induced tsunamis

Abstract. A nonlinear nested model for mudslide-induced tsunamis is proposed in which three phases of the life of the wave, i.e. the generation, far-field propagation and costal run-up are described by means of different mathematical models, that are coupled through appropriate matching procedures. The generation and run-up dynamics are simulated through a nonlinear shallow-water model with movable lateral boundaries: in the generation region two active layers are present, the lower one describing the slide descending on a sloping topography. For the intermediate phase, representing wave propagation far from the generation region, the hydrostatic assumption is not assumed as appropriate in general and, therefore, a nonlinear model allowing for weak phase dispersion, namely a Kadomtsev-Petviashvili equation, is used. This choice is made in order to assess the relevance of dispersive features such as solitary waves and dispersive tails. It is shown that in some realistic circumstances dispersive mudslide-induced tsunami waves can be produced over relatively short, distances. In such cases the use of a hydrostatic model throughout the whole tsunami history turns out to give erroneous results. In particular, when solitary waves are generated during the tsunami propagation in the open sea, the resulting run-up process yields peculiar wave forms leading to amplified coastal inundations with respect to a mere hydrostatic context.

Tsunami sedimentation associated with the 1923 Kamchatka earthquake

The Kuril-Kamchatka region is notorious for the occurrence of earthquake tsunamis, and historical documents show that they have caused repeatedly considerable damage since the 1750s. The great tsunami generated in April 1923 around the northern Kamchatka Trench flooded the coast of Ust'-Kamchatsk, depositing a thin sand layer which is traceable up to 3 km or more inland beyond the present coastline. Local government documents indicate that the 1923 tsunami flooded low-lying coastal areas covered by thick snow. The unusual process of tsunami run-up without loss of tractive load is interpreted to have resulted from the smoothing of fields by the ice-covered surface. We conclude that the tsunami flooded snowfields and deposited an extensive sheet of sand. A mixture of snow and seawater flooded over the area and caused damage to vegetation.

Geomorphological effects of tsunami run-up and backwash

Geomorphological processes associated with tsunami run-up and backwash are highly complex. To date, most studies have considered the sedimentology of palaeo-tsunamis while almost no detailed studies have been undertaken in areas known to have been affected by tsunamis in recent times. Research on contemporary tsunamis show that coastal landscapes may be greatly altered not only by direct tsunami run-up orthogonal to the shoreline, but also by episodes of vigorous backwash and by water flow sub-parallel to the coastline. The combined effect of these processes produces hitherto unrecognised coastal landforms that are dominated by the effects of high-magnitude erosion and deposition. Deposition of large boulders is also associated with severe tsunamis, while in adjacent areas run-up processes often result in the deposition of continuous and discontinuous sediment sheets. In many instances the upper limit of sediment deposition lies well below the upper limit of wave run-up which is frequently marked by a well-defined zone of stripped vegetation and soil. The processes described have considerable implications for models of coastal evolution. It may even be the case that the evolution of particular stretches of coastline are dominated by such high-magnitude low-frequency events.

A shearing-wave generator for operation in deep bore holes

An oscillation generator is developed for the German geological research project KTB (continental deep drilling). The purpose is to explore the structure of the lithosphere by shearing waves. Some technical demands are similar to the requirements of industrial servo drives: true running without cogging torques, run-up without rotor position sensor, and torque detection from the cable terminals. Supplying the machine and measuring the data through a thin and long cable impose additional problems that must be solved. The investigations show that a permanent-magnet synchronous machine is appropriate for producing shearing waves at the bottom of a deep bore hole. The restricted transmittable power makes a separate run-up motor necessary operating at a fifth of the generator frequency. The operation program, the sensorless run-up process, and the torque determination from the cable terminals are controlled by a microprocessor.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Report on the International Workshop on Long-Wave Run-up

A workshop reviewing the current research on long-wave run-up was held in the Marine Science Center of the University of Southern California at Catalina Island, California, in August 1990. The workshop covered theoretical, experimental, and field studies of run-up phenomena. The primary application of the research results discussed was in tsunami run-up and flooding and in tsunami run-up hazard mitigation. Certain other applications of long-wave run-up related to wind waves were also discussed. This report summarizes the twenty-six papers presented and it provides one particular view of the current understanding of this run-up process.

Nonlinear Modeling of Wave Runup on Sloping Beach

A new method of identifying nonlinear systems has been developed and applied to the wave runup process. The new method consists of estimating the parameters of the nonlinear system through the known relation between the correlation functions of the input and output records. The unknown function representing the nonlinear system is expanded into a series of Hermite polynomials. The output autocovariances are expressed in terms of the input autocorrelations and the unknown system function. This provides as many equations as there are autocovariance estimates. From these equations the parameters of the function representing the nonlinear system are estimated. The autocorrelations and spectral density have been computed by using the nonlinear model and compared with the actual autocorrelation and spectral density of the measured output. The predictions are reasonably close to the observations. Results presented indicate the possibility of representing the surf zone as a nonlinear system.