scholarly journals WAVES GENERATED BY A PISTON-TYPE WAVEMAKER

1970 ◽  
Vol 1 (12) ◽  
pp. 36 ◽  
Author(s):  
Ole Secher Madsen
Keyword(s):  
Mathematical Model ◽  
Finite Number ◽  
Wave Height ◽  
Finite Amplitude ◽  
Governing Equations ◽  
Approximate Evaluation ◽  
Large Wave ◽  
Wave Heights ◽  
The Waves ◽  
Theoretical Results

When a wavemaker generates a finite number of waves, it has been found that one of the first and one of the last waves in such a burst is considerably larger than the average A mathematical model, based on the linearized governing equations, is used for the particular problem of the waves generated by a sinusoidally moving piston-type wavemaker starting from rest Theoretical results for the magnitude of the large wave relative to the average agree fairly well with experiments, however, the actual wave height is smaller in the experiments than predicted by theory It is shown, by extending the classical wavemaker theory to second order, that finite amplitude effects do not offer an explanation However, pistons rarely fit the tank dimensions exactly, and an approximate evaluation indicates that the discrepancy between predicted and observed wave heights can be attributed to the effects of leakage around the piston.

scholarly journals MACH-REFLECTION AS A DIFFRACTION PROBLEM

1976 ◽  
Vol 1 (15) ◽  
pp. 45 ◽  
Author(s):  
Udo Berger ◽  
Soren Kohlhase
Keyword(s):  
Wave Height ◽  
Incident Wave ◽  
Water Waves ◽  
Gas Dynamics ◽  
Mach Reflection ◽  
Diffraction Problem ◽  
Vertical Wall ◽  
Oblique Wave ◽  
Wave Heights ◽  
The Waves

As under oblique wave approach water waves are reflected by a vertical wall, a wave branching effect (stem) develops normal to the reflecting wall. The waves progressing along the wall will steep up. The wave heights increase up to more than twice the incident wave height. The £jtudy has pointed out that this effect, which is usually called MACH-REFLECTION, is not to be taken as an analogy to gas dynamics, but should be interpreted as a diffraction problem.

LARGE SCALE EXPERIMENTS ON EVOLUTION AND RUN-UP OF BREAKING SOLITARY WAVES

2007 ◽  
Vol 01 (03) ◽  
pp. 257-272 ◽  
Author(s):  
KAO-SHU HWANG ◽  
YU-HSUAN CHANG ◽  
HWUNG-HWENG HWUNG ◽  
YI-SYUAN LI
Keyword(s):  
Solitary Wave ◽  
Wave Height ◽  
Solitary Waves ◽  
Water Depth ◽  
Large Scale ◽  
Scale Effects ◽  
Wave Heights ◽  
Run Up ◽  
Hydraulics Laboratory ◽  
The Waves

The evolution and run-up of breaking solitary waves on plane beaches are investigated in this paper. A series of large-scale experiments were conducted in the SUPER TANK of Tainan Hydraulics Laboratory with three plane beaches of slope 0.05, 0.025 and 0.017 (1:20, 1:40 and 1:60). Solitary waves of which relative wave heights, H/h0, ranged from 0.03 to 0.31 were generated by two types of wave-board displacement trajectory: the ramp-trajectory and the solitary-wave trajectory proposed by Goring (1979). Experimental results show that under the same relative wave height, the waveforms produced by the two generation procedures becomes noticeably different as the waves propagate prior to the breaking point. Meanwhile, under the same relative wave height, the larger the constant water depth is, the larger the dimensionless run-up heights would be. Scale effects associated with the breaking process are discussed.

Forced Wave Motion of Liquid Partially Filling a High-Speed Rotor

1985 ◽  
Vol 107 (4) ◽  
pp. 446-452
Author(s):  
J. Inoue ◽  
Y. Jinnouchi ◽  
Y. Araki
Keyword(s):  
High Speed ◽  
Wave Motion ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Rotor Vibration ◽  
Liquid Motion ◽  
Large Wave ◽  
Main Emphasis ◽  
Two Dimensional Flow ◽  
Theoretical Results

Wave motion of a liquid in a partially filled hollow cylindrical rotor, which rotates at a high speed and is forced to vibrate, is theoretically and experimentally investigated. Main emphasis is placed on the analysis of a large wave motion in the liquid which may cause self-excited vibrations of the rotor. Assuming a thin liquid layer, simplified equations of motion are derived by integration of the governing equations for a two-dimensional flow. Nonlinearity and viscosity are taken into account in the analysis. A large wave motion with a broken wavecrest is analyzed by applying a theory of hydraulic jump. Illustrating typical examples of the theoretical results together with the experimental ones, the dynamic behavior of the liquid motion and the basic relations between the liquid force and the rotor vibration are discussed.

scholarly journals WAVE INVESTIGATIONS IN SHALLOW WATER

1970 ◽  
Vol 1 (12) ◽  
pp. 10 ◽  
Author(s):  
Winfried Siefert
Keyword(s):  
Shallow Water ◽  
Wave Height ◽  
Wind Direction ◽  
Tidal Flat ◽  
Propagation Direction ◽  
Elbe Estuary ◽  
Zero Crossing ◽  
Wave Heights ◽  
The Mean ◽  
The Waves

Examination of the significant heights of zero-crossing waves in the Elbe Estuary has yielded two noteworthy results: 1 In the deeper water of the estuary, the value of the quotient relating the significant and the mean wave heights is larger than on the bordering tidal flat. 2. The value of this function is dependent on the height of the waves; on the tidal flat this dependency is considerably more sensitive than in deeper water. With increasing wave height the value of significant wave height divided by mean height becomes smaller The propagation direction of waves moving onto the tidal flat is contingent upon the position of intertidal channels Such channels sharply reduce the possible propagation directions The waves nearly always move up-channel regardless of the wind direction It is possible to derive special wave period and wave height distributions representing the conditions m very shallow water.

Forced small-amplitude water waves: a comparison of theory and experiment

1960 ◽  
Vol 7 (1) ◽  
pp. 33-52 ◽  
Author(s):  
F. Ursell ◽  
R. G. Dean ◽  
Y. S. Yu
Keyword(s):  
Wave Height ◽  
Water Waves ◽  
Small Amplitude ◽  
Experimental Error ◽  
Wave Motion ◽  
Wave Theory ◽  
Finite Amplitude ◽  
Uniform Density ◽  
Wave Channel ◽  
Wave Heights

This paper describes an attempt to verify experimentally the wavemaker theory for a piston-type wavemaker. The theory is based upon the usual assumptions of classical hydrodynamics, i.e. that the fluid is inviscid, of uniform density, that motion starts from rest, and that non-linear terms are neglected. If the water depth, wavelength, wave period, and wavemaker stroke (of a harmonically oscillating wavemaker) are known, then the wavemaker theory predicts the wave motion everywhere, and in particular the wave height a few depths away from the wavemaker.The experiments were conducted in a 100 ft. wave channel, and the wave-height envelope was measured with a combination hook-and-point gauge. A plane beach (sloping 1:15) to absorb the wave energy was located at the far end of the channel. The amplitude-reflexion coefficient was usually less than 10%. Unless this reflexion effect is corrected for, it imposes one of the most serious limitations upon experimental accuracy. In the analysis of the present set of measurements, the reflexion effect is taken into account.The first series of tests was concerned with verifying the wavemaker theory for waves of small steepness (0.002 ≤ H/L ≤ 0.03). For this range of wave steepnesses, the measured wave heights were found to be on the average 3.4% below the height predicted by theory. The experimental error, as measured by the scatter about aline 3.4% below the theory, was of the order of 3%. The systematic deviation of 3.4% is believed to be partly due to finite-amplitude effects and possibly to imperfections in the wavemaker motion.The second series of tests was concerned with determining the effects of finite amplitude. For therange of wave steepnesses 0.045 ≤ H/L ≤ 0.048, themeasured wave heights were found to be on the average 10% below the heightspredictedfrom the small-amplitude theory. The experimental error was again of the order of 3%.It is considered that these measurements confirm the validity of the small-amplitude wave theory. No confirmation of this accuracy has hitherto been given for forced motions.

scholarly journals Numerical Simulation of Large Wave Heights from Super Typhoon Nepartak (2016) in the Eastern Waters of Taiwan

2020 ◽  
Vol 8 (3) ◽  
pp. 217 ◽  
Author(s):  
Shih-Chun Hsiao ◽  
Hongey Chen ◽  
Han-Lun Wu ◽  
Wei-Bo Chen ◽  
Chih-Hsin Chang ◽  
...  
Keyword(s):  
Wave Height ◽  
Wind Field ◽  
Outer Region ◽  
Circulation Model ◽  
Large Wave ◽  
Significant Wave ◽  
Hybrid Techniques ◽  
Super Typhoon ◽  
Storm Wave ◽  
Wave Heights

Super Typhoon Nepartak (2016) was used for this case study because it is the most intense typhoon that made landfall in Taiwan in the past decade. Winds extracted from the Climate Forecast System version 2 (CFSV2) and ERA5 datasets and merged with a parametric typhoon model using two hybrid techniques served as the meteorological conditions for driving a coupled wave-circulation model. The computed significant wave heights were compared with the observations recorded at three wave buoys in the eastern waters of Taiwan. Model performance in terms of significant wave height was also investigated by employing the CFSV2 winds under varying spatial and temporal resolutions. The results of the numerical experiments reveal that the simulated storm wave heights tended to decrease significantly due to the lower spatial resolution of the hourly winds from the CFSV2 dataset; however, the variations in the storm wave height simulations were less sensitive to the temporal resolution of the wind field. Introducing the combination of the CFSV2 and the parametric typhoon winds greatly improved the storm wave simulations, and similar phenomena can be found in the exploitation of the ERA5 dataset blended into the parametric wind field. The overall performance of the hybrid winds derived from ERA5 was better than that from the CFSV2, especially in the outer region of Super Typhoon Nepartak (2016).

scholarly journals EXPERIMENTAL DATA ON THE OVERTOPPING OF SEAWALLS BY WAVES

2011 ◽  
Vol 1 (7) ◽  
pp. 36
Author(s):  
A. Paape
Keyword(s):  
Wave Height ◽  
Know How ◽  
The Past ◽  
Maximum Value ◽  
Wave Heights ◽  
Run Up ◽  
Materials Used ◽  
The Stability ◽  
The Waves ◽  
Made In

In the past it has been found that serious damage and breaching of seawalls is most frequently caused by overtopping. Hence for the design of seawalls data must be available about the overtopping by waves of the different profiles that might be possible. Naturally the conditions under which damage is caused to the seawall also depend on the type of construction and the materials used, for example: the stability of grass covered dikes can be endangered seriously by water flowing over the inner slope. In many designs the necessary height of a seawall has been defined such that not more than 2% of the waves overtop the crest, under chosen design conditions. This criterion has been determined on the assumption that the overtopping must remain very small. Some overtopping has to be accepted because no maximum value for wave height and wave run-up can be given, unless of course the wave height is limited by fore-shore conditions. Unfortunately this criterion gives no information about the volume and concentration of water overtopping the crest in each instance. Moreover it is of interest to know how this overtopping varies with other conditions, such as changes in the significant wave height. Information about the overtopping by waves was obtained from model investigations on simple plane slopes w^th inclinations varying from 1 : 8 to 1 : 2. The experiments were made in a windflume where wind generated waves as well as regular waves were employed. Using wind generated waves, conditions from nature regarding the distribution of wave heights could be reproduced. It appeared that the overtopping depends on the irregularity of the waves and that the same effects cannot be reproduced using regular paddle generated waves. In this paper a description of the model and the results of these tests are given. Investigations are m progress on composite slopes, including the reproduction of conditions for a seawall which suffered much overtopping but remained practically undamaged during the flood of 1953.

Comparison of Distributions of Wave Heights From Nonlinear Schröedinger Equation Simulations and Laboratory Experiments

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Huidong Zhang ◽  
Zhivelina Cherneva ◽  
Carlos Guedes Soares ◽  
Miguel Onorato
Keyword(s):  
Numerical Simulations ◽  
Wave Height ◽  
Laboratory Experiments ◽  
Height Distribution ◽  
Sea State ◽  
Large Wave ◽  
Wave Height Distribution ◽  
Wave Basin ◽  
Free Surface Displacement ◽  
Wave Heights

Numerical simulations of the nonlinear Schrödinger (NLS) equation are performed by imposing randomly synthesized free surface displacement at the wave maker characterized by the Joint North Sea Wave Project (JONSWAP) spectrum and compared with four different sea states generated in the deepwater wave basin of Marintek. The comparisons show that the numerical simulations have a high degree of agreement with the laboratory experiments although a little overestimation can be observed, especially in the severe sea state. Thus, the simulations still catch the main characteristics of extreme waves and provide an important physical insight into their generation. The coefficient of kurtosis λ40 presents a similar spatial evolution trend with the abnormal wave density, and the nonlinear Gram–Charlier (GC) model is used to predict the wave height distribution. It is demonstrated again that the theoretical approximation based on the GC expansion can describe large wave heights reasonably well in most cases. However, if the sea state is severe, wave breaking can significantly decrease the actual tail of wave height distribution, and discrepancy occurs when comparing with the numerical simulation. Moreover, the number of waves also plays an important role on the prediction of extreme wave height.

scholarly journals MODELING AND PRODUCTIVITY PREDICTION OF THE COMPANIES-INTERNAL CROWDSOURCING-BASED IDEATION

2021 ◽  
Vol 1 ◽  
pp. 2147-2156
Author(s):  
Pavel Livotov
Keyword(s):  
Mathematical Model ◽  
Finite Number ◽  
Research Question ◽  
Performance Function ◽  
Non Linear ◽  
Series Of Experiments ◽  
Productivity Prediction ◽  
A Company

AbstractThe internal crowdsourcing-based ideation within a company can be defined as an involvement of its staff, specialists, managers, and other employees, to propose solution ideas for a pre-defined problem. This paper addresses a question, how many participants of the company-internal ideation process are required to nearly reach the ideation limit for the problems with a finite number of workable solutions. To answer the research question, the author proposes a set of metrics and a non-linear ideation performance function with a positive decreasing slope and ideation limit for the closed-ended problems. Three series of experiments helped to explore relationships between the metric attributes and resulted in a mathematical model which allows companies to predict the productivity metrics of their crowdsourcing ideation activities such as quantity of different ideas and ideation limit as a function of the number of contributors, their average personal creativity and ideation efficiency of a contributors’ group.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

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