scholarly journals On the Study of Second-Order Wave Theory and Its Convergence for a Two-Fluid System

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Chi-Min Liu ◽  
Hwung-Hweng Hwung ◽  
Ray-Yeng Yang
Keyword(s):  
Transfer Functions ◽  
Perturbation Technique ◽  
Wave Theory ◽  
Order Theory ◽  
Second Order ◽  
Stokes Wave ◽  
Order Effects ◽  
Fluid System ◽  
Two Fluids ◽  
Two Fluid

Second-order solutions of internal and surface waves in a two-fluid system are theoretically analyzed in this study. Using the perturbation technique, the derivation of second-order solutions for internal waves is revisited, and the results are expressed in one-by-one forms instead of a matrix form. Second-order solutions arising from the interactions of two arbitrary linear waves of different frequencies contain the sum-frequency (superharmonic) and the difference-frequency (subharmonic) components, which are separately examined. Internal Stokes wave being a special case of present solutions is firstly investigated. Next, the convergence of second-order theory and the second-order effects on wave profiles are analyzed. For general cases, the effects of the thickness ratio of two fluids and the ratio of wavenumbers of two first-order waves on second-order wave characteristics, which include transfer functions and particle velocities, are also examined. Moreover, most existing theories for the one-fluid and two-fluid systems can be deduced from present solutions.

scholarly journals SECOND ORDER THEORY OF MANOMETER WAVE MEASUREMENT

1982 ◽  
Vol 1 (18) ◽  
pp. 8
Author(s):  
F. Biesel
Keyword(s):  
Gravity Wave ◽  
Wave Theory ◽  
Order Theory ◽  
Second Order ◽  
Order Effects ◽  
Mean Values ◽  
Surface Level ◽  
First Order ◽  
Wave Measurements ◽  
Wave Measurement

The paper refers to pressure gage wave measurements . First order transformation of the pressure spectrum into a surface level spectrum leads to hitherto unexplained discrepancies with prototype simultaneous pressure and level measurements . Use of second order gravity wave theory allows to draw the following conclusions » Second order effects appear to give a reasonable explanation of the observed discrepancies . A complete check would require specially made wave measurements and analyses . Second order corrections do not significantly affect mean values, such as significant height, if the manometer depth is not unduly large.

Global Buckling of Frames with Laced Compression Members

2016 ◽  
Vol 837 ◽  
pp. 103-108 ◽  
Author(s):  
Michal Kovac ◽  
Zsuzsanna Vanik
Keyword(s):  
Order Theory ◽  
Second Order ◽  
Order Effects ◽  
Engineering Practice ◽  
Buckling Mode ◽  
Column Method ◽  
Global Buckling ◽  
Second Order Effects ◽  
Buckling Length ◽  
Simplified Procedure

The planar frames whose members consist of a laced built-up members are often used in civil engineering practice. For chords of these structures the 1st order theory internal forces and the assessment by equivalent column method are mostly used. In the equivalent column method the buckling length according to the global buckling mode of the structures should be used. If the distance between neighboring nodes is used as the buckling length of the chord, which is the common case, the second order effects with only the bow imperfections between nodes are taken into account in the equivalent column method. For frames sensitive to buckling in a sway mode the second order effects on structures with initial sway imperfection should be taken into account. Therefore, also in frames with the laced compression columns, where the effects of additional sway deformation cause additional normal forces in the chords, the sway imperfection should be applied and the second order in frame analysis should be performed to check these additive forces. This paper deals with the simplified procedure how to evaluate additive forces due to second order effects on the structure with the global sway imperfection.

Linear Evolution of a Narrow-Banded Surface Gravity Wavepacket Over an Infinite Step

2019 ◽  
Author(s):  
Yan Li ◽  
Thomas A. A. Adcock ◽  
Ton S. van den Bremer
Keyword(s):  
Water Depth ◽  
Evolution Equations ◽  
Multiple Scales ◽  
Fundamental Problem ◽  
Wave Theory ◽  
Second Order ◽  
Order Effects ◽  
Linear Evolution ◽  
Finite Water Depth ◽  
Higher Order Effects

Abstract This paper focuses on the classical and fundamental problem of waves propagating over an infinite step in finite water depth. Specifically, this paper aims to extend classical narrow-banded wave theory for constant water depth which uses a multiple-scales expansion to the case of an abrupt change in the water depth, known as an infinite step. This paper derives the linear evolution equations and is the first step towards the calculation of second-order and higher-order effects for wavepackets travelling over a step using commonly employed envelope-type evolution equations, in particular the bound sub- and super-harmonics at second order.

Slenderness Influence on the Behavior of Composite Columns

2016 ◽  
Vol 691 ◽  
pp. 40-50
Author(s):  
Štefan Gramblička ◽  
Andrea Hrusovska
Keyword(s):  
Cross Sections ◽  
Design Method ◽  
Tall Buildings ◽  
Concrete Columns ◽  
Order Theory ◽  
Second Order ◽  
Order Effects ◽  
Composite Columns ◽  
Steel Members ◽  
Composite Steel

Composite steel and concrete columns have been used in the tall buildings due theirs high-resistance and the possibility to reduce cross sections when we compered composite columns with reinforced concrete columns. There are a lot of types of composite columns. We are concerned with columns, which are completely or partially concrete-encased steel members. In practice, a lot of composite columns are relatively slender and in design the second - order effects will usually need to be included. A partially concrete encased steel cross-section was selected for laboratory tests of composite columns. According to the results of the experiments (total of 18 columns were tested in two series), we analyzed the effects of the second - order theory. The experimental results were compared with theoretical results obtained from the model developed in the non-linear software. The evaluation of the results is also shown in comparison with the general design method according to Eurocode 4, Design of composite steel and concrete structures - Part 1.1 General rules and rules for buildings.

An Experimental Study of Deviations from the Linear Transfer Function

1974 ◽  
Vol 32 ◽  
pp. 400-401
Author(s):  
William A. Voter ◽  
Harold P. Erickson
Keyword(s):  
Experimental Study ◽  
Image Formation ◽  
Order Theory ◽  
Second Order ◽  
Diffraction Spot ◽  
Order Effects ◽  
First Order ◽  
First Order Theory ◽  
Second Order Effects ◽  
The Fourier Transform

In a previous experimental study of image formation using a thin (20 nm) negatively stained catalase crystal, it was found that a linear or first order theory of image formation would explain almost entirely the changes in the Fourier transform of the image as a function of defocus. In this case it was concluded that the image is a valid picture of the object density. For thicker, higher contrast objects the first order theory may not be valid. Second order effects could generate false diffraction spots which would lead to spurious and artifactual image details. These second order effects would appear as deviations of the diffraction spot amplitudes from the first order theory. Small deviations were in fact noted in the study of the thin crystals, but there was insufficient data for a quantitative analysis.

The Consistent Second-Order Wave Theory and Its Application to a Submerged Spheroid

1970 ◽  
Vol 14 (01) ◽  
pp. 23-50
Author(s):  
Young H. Chey
Keyword(s):  
Free Surface ◽  
Solid Wall ◽  
Three Dimensional ◽  
Wave Theory ◽  
Order Theory ◽  
Wave Resistance ◽  
Second Order ◽  
Surface Phenomena ◽  
First Order ◽  
Theoretical Results

Because of the recognized inadequacy of first-order linearized surface-wave theory, the author has developed, for a three-dimensional body, a new second-order theory which provides a better description of free-surface phenomena. The new theory more accurately satisfies the kinematic boundary condition on the solid wall, and takes into account the nonlinearity of the condition at the free surface. The author applies the new theory to a submerged spheroid, to calculate wave resistance. Experiments were conducted to verify the theory, and their results are compared with the theoretical results. The comparison indicates that the use of the new theory leads to more accurate prediction of wave resistance.

scholarly journals Wave-Generated Current: A Second-Order Formulation

2020 ◽  
Vol 8 (6) ◽  
pp. 418
Author(s):  
Anne Katrine Bratland
Keyword(s):  
Wave Theory ◽  
Second Order ◽  
Stokes Drift ◽  
Wave Number ◽  
Stokes Wave ◽  
Wave Loads ◽  
Third Order ◽  
The Third ◽  
Computational Fluid Dynamics Cfd ◽  
The Mean

In Stokes’ wave theory, wave numbers are corrected in the third order solution. A change in wave number is also associated with a change in current velocity. Here, it will be argued that the current is the reason for the wave number correction, and that wave-generated current at the mean free surface in infinite depth equals half the Stokes drift. To demonstrate the validity of this second-order formulation, comparisons to computational fluid dynamics (CFD) results are shown; to indicate its effect on wave loads on structures, model tests and analyses are compared.

On higher-order wave theory for submerged two-dimensional bodies

1969 ◽  
Vol 38 (2) ◽  
pp. 415-432 ◽  
Author(s):  
Nils Salvesen
Keyword(s):  
Free Surface ◽  
Wave Theory ◽  
Order Theory ◽  
Wave Drag ◽  
Higher Order ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
Free Surface Waves ◽  
Body Shapes

The importance of non-linear free-surface effects on potential flow past two-dimensional submerged bodies is investigated by the use of higher-order perturbation theory. A consistent second-order solution for general body shapes is derived. A comparison between experimental data and theory is presented for the free-surface waves and for the wave resistance of a foil-shaped body. The agreement is good in general for the second-order theory, while the linear theory is shown to be inadequate for predicting the wave drag at the relatively small submergence treated here. It is also shown, by including the third-order freesurface effects, how the solution to the general wave theory breaks down at low speeds.

scholarly journals COUPLING STOKES AND CNOIDAL WAVE THEORIES IN A NONLINEAR REFRACTION MODEL

1988 ◽  
Vol 1 (21) ◽  
pp. 42
Author(s):  
Thomas A. Hardy ◽  
Nicholas C. Kraus
Keyword(s):  
Nonlinear Refraction ◽  
Wave Model ◽  
Wave Theory ◽  
Quantitative Agreement ◽  
Wave Mode ◽  
Finite Amplitude ◽  
Second Order ◽  
Stokes Wave ◽  
Linear Wave ◽  
Cnoidal Wave

An efficient numerical model is presented for calculating the refraction and shoaling of finite-amplitude waves over an irregular sea bottom. The model uses third-order Stokes wave theory in relatively deep water and second-order cnoidal wave theory in relatively shallow water. It can also be run using combinations of lower-order wave theories, including a pure linear wave mode. The problem of the connection of Stokes and cnoidal theories is investigated, and it is found that the use of second-order rather than first-order cnoidal theory greatly reduces the connection discontinuity. Calculations are compared with physical model measurements of the height and direction of waves passing over an elliptical shoal. The finite-amplitude wave model gives better qualitative and quantitative agreement with the measurements than the linear model.

Wave Statistics for Intermediate Depth Water—NewWaves and Symmetry

2004 ◽  
Vol 126 (1) ◽  
pp. 54-59 ◽  
Author(s):  
P. H. Taylor ◽  
B. A. Williams
Keyword(s):  
Linear Part ◽  
Nonlinear Behavior ◽  
Wave Theory ◽  
Order Theory ◽  
Small Degree ◽  
Second Order ◽  
Linear Wave ◽  
Intermediate Water ◽  
Wave Statistics ◽  
The Hilbert Transform

A study has been made into the average shape of large crests and troughs during several storms using wave elevation data from the WACSIS measurement program. The analysis techniques adopted were data-driven at all times, in order to test whether second-order wave theory could reproduce important features in the field data. The sea surface displayed obvious nonlinear behavior, reflected in the fact that the shapes of crests were always sharper and larger than their trough equivalents. Assuming that the dominant nonlinear correction is second order in the wave steepness (but without a knowledge of the detailed form of second-order theory), the average shapes of maxima in the underlying linear wave components were shown to match NewWave. This NewWave is the scaled auto-correlation function for a linear random process with the same power spectrum as the measured waves. Thus, NewWave was shown to be an acceptable model for the linear part of large waves on intermediate water depth (here ∼17 m). Assuming that NewWave is a good model for the linear part of large crests and troughs, a value for the second-order coefficient required to estimate crest elevation statistics was derived from the measured data for several storms. This coefficient was in good agreement with the results of the second-order random simulations of Forristall and Prevosto [1]. As well as studying vertical asymmetry, required for crest and trough statistics, horizontal asymmetry was examined using the Hilbert transform. Compared to a large amount of vertical asymmetry, the analysis showed that there was virtually no horizontal asymmetry for the bulk of the waves in the records. However, there is a very small degree of horizontal asymmetry exhibited in the largest waves in the records. Thus, given a surface elevation record, it is difficult to distinguish the direction of the time axis, again consistent with most of the nonlinearity being due to simple second-order bound waves.

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