scholarly journals RUN-UP OF PERIODIC WAVES ON BEACHES OF NON-UNIFORM SLOPE

1984 ◽  
Vol 1 (19) ◽  
pp. 23 ◽  
Author(s):  
Yoshinobu Ogawa ◽  
Nobuo Shuto
Keyword(s):  
Experimental Data ◽  
Wave Theory ◽  
Breaking Waves ◽  
Lagrangian Description ◽  
Periodic Waves ◽  
Swash Zone ◽  
Slope Method ◽  
Long Wave ◽  
Run Up ◽  
Better Than

Run-up of periodic waves on gentle or non-uniform slopes is discussed. Breaking condition and run-up height of non-breaking waves are derived "by the use of the linear long wave theory in the Lagrangian description. As to the breaking waves, the width of swash zone and the run-up height are-obtained for relatively gentle slopes (less than 1/30), on dividing the transformation of waves into dissipation and swash processes. The formula obtained here agrees with experimental data better than Hunt's formula does. The same procedure is applied to non-uniform slopes and is found to give better results than Saville's composite slope method.

The bifurcation of steady gravity water waves in (R, S) parameter space

1995 ◽  
Vol 302 ◽  
pp. 287-305 ◽  
Author(s):  
S. H. Doole ◽  
J. Norbury
Keyword(s):  
Parameter Space ◽  
Water Waves ◽  
Pressure Head ◽  
Wave Theory ◽  
Periodic Waves ◽  
Long Wave ◽  
S Parameter ◽  
Stokes Waves ◽  
Wave Region ◽  
Constant Period

The bifurcation of steady periodic waves from irrotational inviscid streamflows is considered. Normalizing the flux Q to unity leaves two other natural quantities R (pressure head) and S (flowforce) to parameterize the wavetrain. In a well-known paper, Benjamin & Lighthill (1954) presented calculations within a cnoidal-wave theory which suggested that the corresponding values of R and S lie inside the cusped locus traced by the sub- and supercritical streamflows. This rule has been applied since to many other flow scenarios. In this paper, regular expansions for the streamfunction and profile are constructed for a wave forming on a subcritical stream and thence values for R and S are calculated. These describe, locally, how wave brances in (R, S) parameter space point inside the streamflow cusp. Accurate numerics using a boundry-integral solver show how these constant-period branches extend globally and map out parameter space. The main result is to show that the large-amplitude branches for all steady Stokes’ waves lie surprisingly close to the subcritical stream branch, This has important consequences for the feasibility of undular bores (as opposed to hydraulic jumps) in obstructed flow. Moreover, the transition from the ‘long-wave region’ towards the ‘deep-water limit’ is char-acterized by an extreme geometry, bith of the wave branches and how they sit inside each other. It is also shown that a single (Q, R, S) trriple may represent more than one wave since the global branches can overlap in (R, S) parameter space. This non-uniqueness is not that associated with the known premature maxima of wave propertties as functions of wave amplitude near waves of greatest height.

The swash of solitary waves on a plane beach: flow evolution, bed shear stress and run-up

2015 ◽  
Vol 779 ◽  
pp. 556-597 ◽  
Author(s):  
Nimish Pujara ◽  
Philip L.-F. Liu ◽  
Harry Yeh
Keyword(s):  
Shear Stress ◽  
Solitary Waves ◽  
Large Scale ◽  
Breaking Waves ◽  
Shear Stresses ◽  
Bed Shear Stress ◽  
Swash Zone ◽  
Flow Evolution ◽  
Run Up ◽  
Bed Shear Stresses

The swash of solitary waves on a plane beach is studied using large-scale experiments. Ten wave cases are examined which range from non-breaking waves to plunging breakers. The focus of this study is on the influence of breaker type on flow evolution, spatiotemporal variations of bed shear stresses and run-up. Measurements are made of the local water depths, flow velocities and bed shear stresses (using a shear plate sensor) at various locations in the swash zone. The bed shear stress is significant near the tip of the swash during uprush and in the shallow flow during the later stages of downrush. In between, the flow evolution is dominated by gravity and follows an explicit solution to the nonlinear shallow water equations, i.e. the flow due to a dam break on a slope. The controlling scale of the flow evolution is the initial velocity of the shoreline immediately following waveform collapse, which can be predicted by measurements of wave height prior to breaking, but also shows an additional dependence on breaker type. The maximum onshore-directed bed shear stress increases significantly onshore of the stillwater shoreline for non-breaking waves and onshore of the waveform collapse point for breaking waves. A new normalization for the bed shear stress which uses the initial shoreline velocity is presented. Under this normalization, the variation of the maximum magnitudes of the bed shear stress with distance along the beach, which is normalized using the run-up, follows the same trend for different breaker types. For the uprush, the maximum dimensionless bed shear stress is approximately 0.01, whereas for the downrush, it is approximately 0.002.

scholarly journals Probabilistic characteristics of narrow-band long wave run-up onshore

2019 ◽  
Author(s):  
Sergey Gurbatov ◽  
Efim Pelinovsky
Keyword(s):  
Incident Wave ◽  
Narrow Band ◽  
Linear Equations ◽  
Breaking Waves ◽  
Wave Characteristics ◽  
Long Wave ◽  
Nonlinear Shallow Water Theory ◽  
Run Up ◽  
Non Gaussian ◽  
Two Stages

Abstract. The run-up of random long wave ensemble (swell, storm surge and tsunami) on the constant-slope beach is studied in the framework of the nonlinear shallow-water theory in the approximation of non-breaking waves. If the incident wave approaches the shore from deepest water, runup characteristics can be found in two stages: at the first stage, linear equations are solved and the wave characteristics at the fixed (undisturbed) shoreline are found, and, at the second stage, the nonlinear dynamics of the moving shoreline is studied by means of the Riemann (nonlinear) transformation of linear solutions. In the paper, detail results are obtained for quasi-harmonic (narrow-band) waves with random amplitude and phase. It is shown that the probabilistic characteristics of the runup extremes can be found from the linear theory, while the same ones of the moving shoreline – from the nonlinear theory. The role of wave breaking due to large-amplitude outliers is discussed, so that it becomes necessary to consider wave ensembles with non-Gaussian statistics within the framework of the analytical theory of non-breaking waves. The basic formulas for calculating the probabilistic characteristics of the moving shoreline and its velocity through the incident wave characteristics are given. They can be used for estimates of the flooding zone characteristics in marine natural hazards.

scholarly journals Probabilistic characteristics of narrow-band long-wave run-up onshore

2019 ◽  
Vol 19 (9) ◽  
pp. 1925-1935 ◽  
Author(s):  
Sergey Gurbatov ◽  
Efim Pelinovsky
Keyword(s):  
Incident Wave ◽  
Narrow Band ◽  
Linear Equations ◽  
Breaking Waves ◽  
Wave Characteristics ◽  
Long Wave ◽  
Nonlinear Shallow Water Theory ◽  
Run Up ◽  
Non Gaussian ◽  
Two Stages

Abstract. The run-up of random long-wave ensemble (swell, storm surge, and tsunami) on the constant-slope beach is studied in the framework of the nonlinear shallow-water theory in the approximation of non-breaking waves. If the incident wave approaches the shore from the deepest water, run-up characteristics can be found in two stages: in the first stage, linear equations are solved and the wave characteristics at the fixed (undisturbed) shoreline are found, and in the second stage the nonlinear dynamics of the moving shoreline is studied by means of the Riemann (nonlinear) transformation of linear solutions. In this paper, detailed results are obtained for quasi-harmonic (narrow-band) waves with random amplitude and phase. It is shown that the probabilistic characteristics of the run-up extremes can be found from the linear theory, while the same ones of the moving shoreline are from the nonlinear theory. The role of wave-breaking due to large-amplitude outliers is discussed, so that it becomes necessary to consider wave ensembles with non-Gaussian statistics within the framework of the analytical theory of non-breaking waves. The basic formulas for calculating the probabilistic characteristics of the moving shoreline and its velocity through the incident wave characteristics are given. They can be used for estimates of the flooding zone characteristics in marine natural hazards.

Runup of long waves on composite coastal slopes: numerical simulations and experiment

2020 ◽  
Author(s):  
Ira Didenkulova ◽  
Andrey Kurkin ◽  
Artem Rodin ◽  
Ahmed Abdalazeez ◽  
Denys Dutykh
Keyword(s):  
Experimental Data ◽  
Shallow Water ◽  
Numerical Study ◽  
Breaking Waves ◽  
Shallow Water Theory ◽  
Wave Runup ◽  
Coastal Slope ◽  
Long Wave ◽  
Nonlinear Shallow Water Theory ◽  
Runup Height

<p>The goal of this study is to investigate the effect of the bottom shape on wave runup. The obtained results have been confronted with available analytical predictions and a dedicated numerical simulation campaign has been carried out by the team. We study long wave runup on composite coastal profiles. Two types of beach profiles are considered. The Coastal Slope 1 consists of two merged plane beaches with lengths 1.2 m and 5 m and beach slopes tan α = 1:10 and tan β = 1:15 respectively. The Coastal Slope 2 also consists of two sections: plane beach with length 1.2 m and a beach slope α, which is merged with a convex (non-reflecting) beach. The latter is constructed in the way, that its total height and length remain the same as for the Coastal Slope 1.</p><p>The study is conducted with numerical (in silico) and experimental approaches.</p><p>Experiments have been conducted in the hydrodynamic flume of the Nizhny Novgorod State Technical University n.a. R.E. Alekseev. Both composite beach profiles were constructed in 2019. The Coastal Slope 1 consists of three parts made of aluminum. The plain beach part of the Coastal Slope 2 is also made of aluminum, and the convex profile consists of two parts made of curved PLEXIGLAS organic glass. The water surface oscillations are measured using capacitive and resistive wave gauges with recording frequencies of up to 80 Hz and 100 Hz respectively. Wave runup is measured by a capacitive string sensor installed along the slope.</p><p>A series of experiments on the generation and runup of regular wave trains with a period of 1s, 2s, 3s and 4s were carried out. The water level was kept constant for all experiments and was equal to 0.3 meters. Up to now, 21 experiments have been carried out (10 and 11 experiments for each Coastal Slope respectively).</p><p>A comparative numerical study is carried out in the framework of the nonlinear shallow water theory and the dispersive theory in the Boussinesq approximation.</p><p>As a result, we compare the long wave dynamics on these two bottom profiles and discuss the influence of nonlinearity and dispersion on the characteristics of wave runup. It is shown numerically that, in the framework of the nonlinear shallow water theory, the runup height on the Coastal Slope 2 tends to exceed the corresponding runup height on the Coastal Slope 1, that also agrees with our previous results (Didenkulova et al. 2009; Didenkulova et al. 2018). Taking dispersion into account leads to an increase in the spread in values of the wave runup height. As a consequence, individual cases when the runup height on the Coastal Slope 1 is higher than on the Coastal Slope 2 have been observed. In experimental data, such cases occur more often, so that the advantage of one slope over another is no longer obvious. Note also that the most nonlinear breaking waves with a period of 1s have a greater runup height on Coastal Slope 2 for both models and most experimental data.</p>

scholarly journals WAVE RUN-UP ON A NATURAL BEACH

1988 ◽  
Vol 1 (21) ◽  
pp. 10
Author(s):  
Mitsuo Takezawa ◽  
Masaru Mizuguchi ◽  
Shintaro Hotta ◽  
Susumu Kubota
Keyword(s):  
Surf Zone ◽  
Wave Theory ◽  
Transformation Model ◽  
Wave Transformation ◽  
Electromagnetic Current ◽  
Swash Zone ◽  
Reflected Waves ◽  
Wave Heights ◽  
Run Up ◽  
Incident Waves

The swash oscillation, waves and water particle velocity in the surf zone were measured by using 16 mm memo-motion cameras and electromagnetic current meters. It was inferred that incident waves form two-dimensional standing waves with the anti-node in the swash slope. Separation of the incident waves and reflected waves was attempted with good results using small amplitude long wave theory. Reflection coefficient of individual waves ranged between 0.3 and 1.0. The joint distribution of wave heights and periods in the swash oscillation exhibited different distribution from that in and outside the surf zone. This indicates that simple application of wave to wave transformation model fails in the swash zone.

Estimating ink mileage of dry toners in electrophotography

TAPPI Journal ◽  
2013 ◽  
Vol 12 (3) ◽  
pp. 9-14
Author(s):  
RENMEI XU ◽  
CELESTE M. CALKINS
Keyword(s):  
Experimental Data ◽  
Curve Fitting ◽  
Graphite Furnace ◽  
Atomic Absorption Spectrometer ◽  
Density Region ◽  
Coated Papers ◽  
Graphite Furnace Atomic Absorption ◽  
S Model ◽  
Better Than ◽  
Film Weight

This work investigates the ink mileage of dry toners in electrophotography (EP). Four different substrates were printed on a dry-toner color production Xerox iGen3 EP press. The print layout contained patches with different cyan, magenta, yellow, and black tonal values from 10% to 100%. Toner amounts on cyan patches were measured using an analytical method. Printed patches and unprinted paper samples, as well as dry toners, were dissolved in concentrated nitric acid. The copper concentrations in the dissolved solutions were analyzed by a Zeeman graphite furnace atomic absorption spectrometer. Analytical results were calculated to determine the toner amounts on paper for different tonal values. Their corresponding reflection densities were also measured. All data were plotted with OriginPro® 8 software, and four mathematical models were used for curve fitting. It was found that the C-S model fitted the experimental data of the two uncoated papers better than the other three models. None of the four models fitted the experimental data of the two coated papers, while the linear model was found to fit the data well. Linear fitting was the best in the practical density region for the two coated papers. Ink mileage curves obtained from curve fitting were used to estimate how much ink was required to achieve a target density for each paper; hence, the ink mileage was calculated. The highest ink mileage was 3.39 times the lowest ink mileage. The rougher the paper surface, the higher the requirement for ink film weight, and the lower ink mileage. No correlation was found between ink mileage and paper porosity.

scholarly journals Assessment of Numerical Methods for Plunging Breaking Wave Predictions

2021 ◽  
Vol 9 (3) ◽  
pp. 264
Author(s):  
Shanti Bhushan ◽  
Oumnia El Fajri ◽  
Graham Hubbard ◽  
Bradley Chambers ◽  
Christopher Kees
Keyword(s):  
Solitary Wave ◽  
Wave Breaking ◽  
Large Scale ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Wave Crest ◽  
Breaking Wave ◽  
Rans Turbulence Models ◽  
Run Up ◽  
Better Than

This study evaluates the capability of Navier–Stokes solvers in predicting forward and backward plunging breaking, including assessment of the effect of grid resolution, turbulence model, and VoF, CLSVoF interface models on predictions. For this purpose, 2D simulations are performed for four test cases: dam break, solitary wave run up on a slope, flow over a submerged bump, and solitary wave over a submerged rectangular obstacle. Plunging wave breaking involves high wave crest, plunger formation, and splash up, followed by second plunger, and chaotic water motions. Coarser grids reasonably predict the wave breaking features, but finer grids are required for accurate prediction of the splash up events. However, instabilities are triggered at the air–water interface (primarily for the air flow) on very fine grids, which induces surface peel-off or kinks and roll-up of the plunger tips. Reynolds averaged Navier–Stokes (RANS) turbulence models result in high eddy-viscosity in the air–water region which decays the fluid momentum and adversely affects the predictions. Both VoF and CLSVoF methods predict the large-scale plunging breaking characteristics well; however, they vary in the prediction of the finer details. The CLSVoF solver predicts the splash-up event and secondary plunger better than the VoF solver; however, the latter predicts the plunger shape better than the former for the solitary wave run-up on a slope case.

A Second Order Lagrangian Model for Irregular Ocean Waves

2005 ◽  
Vol 128 (3) ◽  
pp. 177-183 ◽  
Author(s):  
Sébastien Fouques ◽  
Harald E. Krogstad ◽  
Dag Myrhaug
Keyword(s):  
Specular Reflection ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Wave Theory ◽  
Ocean Waves ◽  
Second Order ◽  
Lagrangian Model ◽  
Lagrangian Description ◽  
Linear Wave ◽  
Irregular Solution

Synthetic aperture radar (SAR) imaging of ocean waves involves both the geometry and the kinematics of the sea surface. However, the traditional linear wave theory fails to describe steep waves, which are likely to bring about specular reflection of the radar beam, and it may overestimate the surface fluid velocity that causes the so-called velocity bunching effect. Recently, the interest for a Lagrangian description of ocean gravity waves has increased. Such an approach considers the motion of individual labeled fluid particles and the free surface elevation is derived from the surface particles positions. The first order regular solution to the Lagrangian equations of motion for an inviscid and incompressible fluid is the so-called Gerstner wave. It shows realistic features such as sharper crests and broader troughs as the wave steepness increases. This paper proposes a second order irregular solution to these equations. The general features of the first and second order waves are described, and some statistical properties of various surface parameters such as the orbital velocity, slope, and mean curvature are studied.

Numerical Investigation of Wave Period Influence on Long Wave Run-Up on Slope With Rigid Vegetation

2016 ◽  
Author(s):  
Jun Tang ◽  
Yongming Shen
Keyword(s):  
Shallow Water Equations ◽  
Water Wave ◽  
Wave Period ◽  
Coastal Vegetation ◽  
Coastal Structures ◽  
Rigid Vegetation ◽  
Comparison With Experiment ◽  
Long Wave ◽  
Nonlinear Shallow Water Equations ◽  
Run Up

Coastal vegetation can not only provide shade to coastal structures but also reduce wave run-up. Study of long water wave climb on vegetation beach is fundamental to understanding that how wave run-up may be reduced by planted vegetation along coastline. The present study investigates wave period influence on long wave run-up on a partially-vegetated plane slope via numerical simulation. The numerical model is based on an implementation of Morison’s formulation for rigid structures induced inertia and drag stresses in the nonlinear shallow water equations. The numerical scheme is validated by comparison with experiment results. The model is then applied to investigate long wave with diverse periods propagating and run-up on a partially-vegetated 1:20 plane slope, and the sensitivity of run-up to wave period is investigated based on the numerical results.

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