scholarly journals FIFTH ORDER GRAVITY WAVE THEORY

2011 ◽  
Vol 1 (7) ◽  
pp. 10 ◽  
Author(s):  
Lars Skjelbreia ◽  
James Hendrickson
Keyword(s):  
Theoretical Calculations ◽  
Wave Length ◽  
Wave Theory ◽  
Order Theory ◽  
Wave Characteristics ◽  
Finite Height ◽  
Scientists And Engineers ◽  
Fifth Order ◽  
Horizontal Bottom ◽  
Made In

In dealing with problems connected with gravity waves, scientists and engineers frequently find it necessary to make lengthy theoretical calculations involving such wave characteristics as wave height, wave length, period, and water depth. Several approximate theoretical expressions have been derived relating the above parameters. Airy, for instance, contributed a very valuable and complete theory for waves traveling over a horizontal bottom in any depth of water. Due to the simplicity of the Airy theory, it is frequently used by engineers. This theory, however, was developed for waves of very small heights and is inaccurate for waves of finite height. Stokes presented a similar solution for waves of finite height by use of trigonometric series. Using five terms in the series, this solution will extend the range covered by the Airy theory to waves of greater steepness. No attempt has been made in this paper to specify the range where the theory is applicable. The coefficients in these series are very complicated and for a numerical problem, the calculations become very tedious. Because of this difficulty, this theory would be very little used by engineers unless the value of the coefficient is presented in tabular form. The purpose of this paper is to present the results of the fifth order theory and values of the various coefficients as a function of the parameter d/L.

scholarly journals Experimental Investigation on Characteristics of Sand Waves with Fine Sand under Waves and Currents

Water ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 612 ◽  
Author(s):  
Zhenlu Wang ◽  
Bingchen Liang ◽  
Guoxiang Wu
Keyword(s):  
Large Scale ◽  
Wave Length ◽  
Wave Theory ◽  
Fine Sand ◽  
Sand Wave ◽  
Wave Steepness ◽  
Sand Waves ◽  
Wave Characteristics ◽  
Waves And Currents ◽  
Wave Nonlinearity

A series of physical experiments was conducted to study the geometry characteristics and evolution of sand waves under waves and currents. Large scale bedforms denoted as sand waves and small bedforms represented by ripples were both formed under the experimental hydrodynamic conditions. Combining the experimental data with those from previous research, the characteristics of waves and currents and measured sand waves were listed. Small amplitude wave theory and Cnoidal wave theory were used to calculate the wave characteristics depending on different Ursell numbers, respectively. The results show good agreement between the dimensionless characteristics of sand waves and the dimensionless wave characteristics with a smaller wave steepness. When the wave steepness is large, the results seem rather scattered which may be affected by the wave nonlinearity. Sand wave steepness hardly changed with bed shear stress. A simple linear relationship can be found between sand wave length and wave steepness. It is easy to evaluate the sand wave characteristics from the measured wave data.

scholarly journals THE EFFECT OF BED SLOPE ON WAVE CHARACTERISTICS

1982 ◽  
Vol 1 (18) ◽  
pp. 36
Author(s):  
R.C. Nelson
Keyword(s):  
Sediment Transport ◽  
Velocity Field ◽  
Wave Theory ◽  
Bed Sediment ◽  
Wave Shape ◽  
Wave Characteristics ◽  
Course Of Action ◽  
Bed Slope ◽  
Wave Induced ◽  
Made In

In all wave theories used in engineering applications it is assumed that the profile of the bed is horizontal which results in a symmetrical wave shape and velocity field, so that, strictly speaking, they can be applied only to this condition. Nearshore bottom profiles are, however, seldom horizontal, and a wave moving over a shoaling slope has an asymmetrical profile which is associated with an asymmetrical velocity field within the wave which, in turn, directly influences the movement of bed sediment. As a matter of necessity, but within reason, engineers have ignored the influence of bed slope on the wave theory used. This course of action was justifiable on many counts, not the least of which was that inaccuracies associated with the theories used were far greater than any inaccuracies introduced by ignoring bed slope parameters. However, wave theories developed in recent years have become increasingly accurate and reliable so that it may now be necessary to take account of bed slope parameters in applying these wave theories before further improvements can be made in the techniques used to predict wave-induced sediment transport.

scholarly journals Sonochemical and Sonoelectrochemical Production of Energy Materials

Catalysts ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 284
Author(s):  
Faranak Foroughi ◽  
Jacob J. Lamb ◽  
Odne S. Burheim ◽  
Bruno G. Pollet
Keyword(s):  
Reaction Rates ◽  
Surface Cleaning ◽  
Energy Materials ◽  
Fast Reaction ◽  
Ultrasound Frequency ◽  
Production Of Hydrogen ◽  
Scientists And Engineers ◽  
Electrocatalyst Materials ◽  
Made In ◽  
Semiconductor Photocatalyst

Sonoelectrochemistry is the combination of ultrasound and electrochemistry which provides many advantages in electrochemistry, such as fast reaction rates, surface cleaning and activation, and increased mass transport at an electrode. Due to the advantages, some efforts have been made in order to benefit sonoelectrochemistry in the field of energy and environmental engineering. This review paper highlights the developed progress of the application of sonoelectrochemistry in the production of hydrogen, electrocatalyst materials and electrodes for fuel cells and semiconductor photocatalyst materials. This review also provides the experimental methods that are utilized in several sonoelectrochemical techniques, such as different set-ups generally used for the synthesis of energy-related materials. Different key parameters in the operation of sonoelectrochemical synthesis including ultrasonication time, ultrasound frequency and operation current have been also discussed. There are not many research articles on the sonoelectrochemical production of materials for supercapacitors and water electrolyzers which play crucial roles in the renewable energy industry. Therefore, at the end of this review, some articles which have reported the use of ultrasound for the production of electrocatalysts for supercapacitors and electrolyzers have been reviewed. The current review might be helpful for scientists and engineers who are interested in and working on sonoelectrochemistry and electrocatalyst synthesis for energy storage and energy conversion.

The continuous absorption of light in alkali-metal vapours

1953 ◽  
Vol 219 (1136) ◽  
pp. 89-101 ◽  
Keyword(s):  
Cross Section ◽  
Alkali Metals ◽  
Theoretical Calculations ◽  
Wave Length ◽  
Energy Difference ◽  
Continuous Absorption ◽  
Absorption Of Light ◽  
Sodium Vapour ◽  
Good Agreement ◽  
Dipole Length

The first section of this paper is an account of some experiments on the absorption of light in sodium vapour from the series limit at 2412 Å to about 1600 Å (an energy difference of 2·6 eV). The absorption cross-section at the limit is 11·6 ± 1·2 x 10 -20 cm 2 . The cross-section decreases giving a minimum of 1·3 ± 0·6 x 10 -20 cm 2 at 1900 Å and then increases to 1600 Å. A theoretical calculation by Seaton based on the dipole-length formula gives good agreement with the experiments at the series limit and also correctly predicts the wave-length for the minimum, but it predicts a significantly lower absorption at the minimum. The experiments described in the first section of the paper conclude a series on the absorption of light in the alkali metals. The second section consists of a general discussion of the results of these experiments and of their relation to theoretical calculations. There is good agreement between theory and experiment except in regard to the magnitude of the absorption at the minimum.

scholarly journals BREAKWATER ARMOR DISPLACEMENT THRESHOLDS: A POSSIBLE CORRELATION WITH CUMULATIVE WAVE ENERGY

1984 ◽  
Vol 1 (19) ◽  
pp. 186
Author(s):  
Daniel L. Behnke ◽  
Frederic Raichlen
Keyword(s):  
Wave Energy ◽  
Wave Train ◽  
Wave Length ◽  
Simple Wave ◽  
Wave Theory ◽  
Irregular Waves ◽  
Reconstruction Technique ◽  
Regular Wave ◽  
Regular Waves ◽  
Three Dimensional Model

An extensive program of stability experiments in a highly detailed three-dimensional model has recently been completed to define a reconstruction technique for a damaged breakwater (Lillevang, Raichlen, Cox, and Behnke, 1984). Tests were conducted with both regular waves and irregular waves from various directions incident upon the breakwater. In comparison of the results of the regular wave tests to those of the irregular wave tests, a relation appeared to exist between breakwater damage and the accumulated energy to which the structure had been exposed. The energy delivered per wave is defined, as an approximation, as relating to the product of H2 and L, where H is the significant height of a train of irregular waves and L is the wave length at a selected depth, calculated according to small amplitude wave theory using a wave period corresponding to the peak energy of the spectrum. As applied in regular wave testing, H is the uniform wave height and L is that associated with the period of the simple wave train. The damage in the model due to regular waves and that caused by irregular waves has been related through the use of the cumulative wave energy contained in those waves which have an energy greater than a threshold value for the breakwater.

scholarly journals VI. Corrections to the computed lengths of waves of light published in the Philosophical Transactions of the year 1868

1872 ◽  
Vol 162 ◽  
pp. 89-109
Keyword(s):  
Spectral Line ◽  
Royal Society ◽  
Wave Length ◽  
Solar Spectrum ◽  
Spectral Lines ◽  
Fifth Order ◽  
Principal Lines ◽  
General Table

In a paper communicated to the Royal Society in the year 1867, and printed in the Philosophical Transactions for 1868, I attempted the computation of the Lengths of Waves of Light for all the lines which Kirchhoff had observed in the Solar Spectrum, by adopting an algebraical formula of the fifth order, and substituting in it for every spectral line the value of Kirchhoff’s measure for that line, the numerical bases of the formula being derived from Fraunhofer’s and Ditscheiner’s measures of the wave-lengths for six principal lines. Subsequently I obtained the means of comparing many of my computed results with measures of wave-lengths by Ångstrȍm and Ditscheiner, and l found that the discordances were far larger than I had anticipated. I remarked, however, “By means of the comparison........ there is no difficulty in computing for any other line the correction that ought to be applied to the wave-length in the principal Tables, in order to exhibit the true wave-lengths on Ditscheiner’s scale, without appreciable error.” Want of leisure long prevented me from entering upon the examination necessary for preparing, in a form easy for applications, the correction which my numbers required. Lately, however, I have taken it up; and I have constructed a Table of corrections to the numbers of my Table generally, and I have applied them, both to the general Table of wave-lengths and to the values of wave-lengths for the spectral lines of the atmosphere and several metals (the accurate exhibition of which was, in fact, the first object of my computations). I now offer these corrections and corrected numbers for the acceptance of the Royal Society.

Effect of Shallow Water on a Mathematical Hull at High Subcritical and Supercritical Speeds

1986 ◽  
Vol 30 (02) ◽  
pp. 85-93
Author(s):  
A. Millward ◽  
M. G. Bevan
Keyword(s):  
Shallow Water ◽  
Wave Theory ◽  
Hull Form ◽  
Towing Tank ◽  
Resistance Peak ◽  
Good Agreement ◽  
Made In

Experiments have been made in a towing tank to measure the resistance of a mathematical hull form in deepwater and in shallow water at high subcritical and supercritical speeds. The data have been compared with calculations using linearized wave theory for the same hull shape. The results have shown fairly good agreement, with the greatest differences occurring near the subcritical resistance peak.

scholarly journals IMPROVEMENT OF MACHINE SAFETY DEVICES

2018 ◽  
Vol 58 (1) ◽  
pp. 17 ◽  
Author(s):  
Bohdan Matviiovych Hevko ◽  
Roman Bohdanovych Hevko ◽  
Oleksandra Mykolaivna Klendii ◽  
Mykola Vasyliovych Buriak ◽  
Yurii Volodymyrovych Dzyadykevych ◽  
...  
Keyword(s):  
Optimum Design ◽  
Test Bench ◽  
Theoretical Calculations ◽  
Experimental Investigations ◽  
Dynamic Parameters ◽  
Safety Devices ◽  
Basic Parameters ◽  
Machine Safety ◽  
Made In ◽  
New Machine

The article presents a development of new machine safety devices, which provide protection of operating elements from overload. Theoretical calculations have been made in order to determine the optimum design, kinematic and dynamic parameters of safety devices. A test bench has been developed and experimental investigations have been conducted in order to determine basic parameters of overload clutches.

The Button Head Bullet Effects on the Incident Pulse of Split Hopkinson Press Bar

2015 ◽  
Vol 782 ◽  
pp. 311-315
Author(s):  
Jia Qu ◽  
Geng Chen ◽  
Guang Ping Zou
Keyword(s):  
Elastic Wave ◽  
Wave Length ◽  
Constant Strain Rate ◽  
Peak Stress ◽  
Wave Theory ◽  
Pulse Shaper ◽  
Lagrange Method ◽  
Stress Increase ◽  
Split Hopkinson ◽  
Peak Value

In order to make the specimen deformed under a constant strain rate and the stress in the specimen kept homogeneous, the wave shaper technology was adopted to modify the incidence waves of the normal Split Hopkinson Press Bar. A method of changing the shape of the bullet was suggested to be applied on the SHPB. Bullets with different length and different curvature have been researched in this paper. And the effection of the button head bullet about incidence pulse was simulated with Lagrange method by ANSYS/LS-DYNA. It is shown in the results that changing the curvature of the bullet impact the rising edge of incidence waves, and the peak stress increase with the speed of the bullet increase, the peak stress and length of incidence waves increased with the length of the button head bullet, when the peak stress reached a certain strength, increasing the bullet length could make the stress peak value lasted longer. Due to the reason that the button head bullet was based on the elastic wave theory, the wave length and the max stress of the shaped wave would be controlled conveniently and avoid the shortcoming that the analogue specimens could not be recycled in the normal pulse shaper technology.

scholarly journals Wave length and celerity downstream from a hydraulic jump

RBRH ◽  
2019 ◽  
Vol 24 ◽  
Author(s):  
Ana Paula Gomes ◽  
Eduardo Pivatto Marzec ◽  
Luiz Augusto Magalhães Endres
Keyword(s):  
Dispersion Equation ◽  
Hydraulic Jump ◽  
Wave Length ◽  
Vortex Formation ◽  
Wave Period ◽  
Time Interval ◽  
Significant Wave ◽  
Wave Characteristics ◽  
Wave Celerity

ABSTRACT The wave period, i. e., the time interval which corresponds to a complete oscillation, is an important parameter of wave characterization. It allows the estimation of other important wave characteristics such as the length and celerity. This study aims at describing the results of a relationship among the significant, mean, and peak periods of waves generated downstream from a hydraulic jump. The frequency of vortex formation in the roller region within the hydraulic jump was used. Besides those relationships, wave lengths were also determined by the dispersion equation by considering the wave-current overlapping effect in order to identify the wave celerity. Estimated results of wave celerity were compared to their experimental results. Our findings allowed us to identify that the significant wave period was the most representative period for the characterization of a wave downstream from a hydraulic jump.

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