A Note on the Evaluation of the Wave Resistance of Two-Dimensional Bodies from Measurements of the Downstream Wave Profile

1983 ◽  
Vol 27 (02) ◽  
pp. 90-92
Author(s):  
James H. Duncan
Keyword(s):  
Wave Train ◽  
Wave Theory ◽  
Stokes Wave ◽  
Two Dimensional ◽  
Third Order ◽  
The Subject ◽  
Lord Kelvin ◽  
The Waves ◽  
The Vertical Distribution

As a body moves horizontally at constant speed in the proximity of a free surface it experiences a resistance due to the generation of waves. In two-dimensional cases the determination of this resistance from properties of the wave train has been the subject of several investigations. The linear theory was first presented by Lord Kelvin [1] 2 and later by Havelock [2] and Lamb [8]. Wehausen and Laitone [4] have derived an exact resistance formula in terms of the vertical distribution of velocity in the waves and the downstream surface height profile. This formula was later evaluated by Salvesen and von Kerczek [5] using third-order Stokes wave theory.

Nonlinear Aspects of Subcritical Shallow-Water Flow Past Two-Dimensional Obstructions

1978 ◽  
Vol 22 (04) ◽  
pp. 203-211
Author(s):  
Nils Salvesen ◽  
C. von Kerczek
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Flow Problem ◽  
Free Stream ◽  
The Body ◽  
Two Dimensional ◽  
Third Order ◽  
Submerged Body ◽  
The Mean ◽  
The Waves

Some nonlinear aspects of the two-dimensional problem of a submerged body moving with constant speed in otherwise undisturbed water of uniform depth are considered. It is shown that a theory of Benjamin which predicts a uniform rise of the free surface ahead of the body and the lowering of the mean level of the waves behind it agrees well with experimental data. The local steady-flow problem is solved by a numerical method which satisfies the exact free-surface conditions. Third-order perturbation formulas for the downstream free waves are also presented. It is found that in sufficiently shallow water, the wavelength increases with increasing disturbance strength for fixed values of the free-stream-Froude number. This is opposite to the deepwater case where the wavelength decreases with increasing disturbance strength.

The two-dimensional laminar jet in parallel streaming flow

1967 ◽  
Vol 27 (3) ◽  
pp. 431-443 ◽  
Author(s):  
I. Wygnanski
Keyword(s):  
Order Term ◽  
Asymptotic Series ◽  
Maximum Error ◽  
Approximate Determination ◽  
Two Dimensional ◽  
Direct Expansion ◽  
Third Order ◽  
Laminar Jet ◽  
External Stream

Solutions to the problem of a two-dimensional, laminar jet of incompressible fluid issuing into a uniform stream in the direction of the main flow are considered. Two co-ordinate-type expansions are developed. A direct expansion, when suitably transformed, predicts approximately the velocity along the plane of symmetry of the jet for all values of the abscissa, with a maximum error of 7·6% far downstream from the origin. This error is established by comparison with a second, asymptotic expansion valid only at large values of the abscissa. The two expansions are subsequently joined, permitting an approximate determination of a constant which multiplies a third-order term in the asymptotic series and which initially remained unknown even after satisfying all boundary conditions imposed on these series.The decay of velocity excess along the plane of symmetry of the jet is accelerated by the presence of the external stream.

An experimental investigation of breaking waves produced by a towed hydrofoil

1981 ◽  
Vol 377 (1770) ◽  
pp. 331-348 ◽  
Keyword(s):  
Surface Profile ◽  
Phase Speed ◽  
Breaking Waves ◽  
Finite Amplitude ◽  
Stokes Wave ◽  
Two Dimensional ◽  
Vertical Thickness ◽  
Turbulent Momentum ◽  
The Vertical Distribution ◽  
Turbulent Water

This paper presents the results of experiments on breaking waves produced by towing a submerged, two-dimensional hydrofoil at constant depth and speed. The wave field consists of a breaker followed by a train of lower, non-breaking waves. The breaker has a small zone of turbulent water riding its forward slope; this zone is called the breaking region. Measurements were made of surface height profiles, the vertical distribution of mean horizontal velocity in the wake of the wave, and the vertical thickness of the wake. The results support the hypothesis that the breaking region imparts a shearing force along the forward slope equal to the component of its weight in that direction. The force produces a turbulent, momentum-deficient wake similar to the wake of a towed, two-dimensional body in an infinite fluid. The vertical thickness of the wake grows in proportion to the square root of distance behind the breaker. The momentum deficit is approximately equal to the maximum momentum flux of a Stokes wave with the same phase speed as the breaker. The surface profile measurements yield several results: the proper independent variables describing the wave are its speed and the slope of its forward face. The relation between breaking wavelength and speed follows the finite-amplitude Stokes wave equation. The amplitude and the vertical extent of the breaking region are both proportional to the phase speed squared; however, they are not functions of the slope of the forward face of the wave. The breaking region has a small oscillation in its length with a regular period of 4.4 the period of a wave with phase speed equal to the hydrofoil speed. The amplitude of the oscillation diminishes with time. It is believed that this oscillation is due to wave components produced when the foil is started from rest.

scholarly journals Nonlinear Spatial Localized Strain Waves

2018 ◽  
Vol 183 ◽  
pp. 02030
Author(s):  
Vladimir I. Erofeev ◽  
Sergey I. Gerasimov ◽  
Alexey O. Malkhanov
Keyword(s):  
Equations Of State ◽  
Numerical Models ◽  
Hydrodynamic Instability ◽  
Light Sources ◽  
Third Order ◽  
Simultaneous Excitation ◽  
Wave Guides ◽  
Determination Of Parameters ◽  
The Waves

A possible way of study of single waves in solids is discussed. The soliton is one of these waves without shape and parameters varying. Soliton deformation parameters are connected with the elastic moduli of the third order that allows defining values of these moduli by means of the measured solitondeformation parameters in various type waveguides made of the same material. The conditions under which a soliton can exist in a rod are analytically determined. For simultaneous excitation of loading in several wave guides two new energetic photosensitive structures (the mixtures are given) initiated by means of short light impulses of noncoherent light sources are proposed. Conditions of excitation of the waves on the basis of multipoint optical initiation loading impulses are described. As a technique for registration the shadowgraph visualization is proposed. It is discussed, how the problem connected to the use of energetic initiation structures consisting in the power background illumination can be solved. The shadow scheme with the use of a tiny dot explosive light source (Tbr ~41 kK) allows to carry out modelling experiments on research of slabbing actions, jet formations, fluffings, hydrodynamic instability during shock-wave loading of investigated samples, which makes it attractive for determination of parameters in equations-of-state for investigated materials, creation of numerical models and their validation. Some examples showing basic possibility of application of the declared techniques are included.

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 Wave concept of motion in mathematical models of the dynamics of two-dimensional media studying

2019 ◽  
Vol 5 (3-4) ◽  
pp. 8-15
Author(s):  
Andrij Andrukhiv ◽  
◽  
Bohdan Sokil ◽  
Mariia Sokil ◽  
◽  
...  
Keyword(s):  
Mathematical Models ◽  
Asymptotic Methods ◽  
Wave Theory ◽  
Single Frequency ◽  
Two Dimensional ◽  
Klein Gordon ◽  
Basic Parameters ◽  
The Impact ◽  
The Mathematical Model ◽  
The Waves

The methodology of the studying of dynamic processes in two-dimensional systems by mathematical models containing nonlinear equation of Klein-Gordon was developed. The methodology contains such underlying: the concept of the motion wave theory; the single - frequency fluctuations principle in nonlinear systems; the asymptotic methods of nonlinear mechanics. The aggregate content allowed describing the dynamic process for the undisturbed (linear) analogue of the mathematical model of movement. The value determining the impact of nonlinear forces on the basic parameters of the waves for the disturbed analogue is defined.

The Harmonic Structure of the Focused Wave in a Wave Flume

2021 ◽  
Author(s):  
Huixing Gao ◽  
Jianjun Zhou ◽  
Yang Song ◽  
Qinghe Fang
Keyword(s):  
Wave Theory ◽  
Higher Order ◽  
Stokes Wave ◽  
Wave Group ◽  
Harmonic Structure ◽  
Extreme Waves ◽  
Third Order ◽  
Wave Flume ◽  
Wave Elevation ◽  
Focused Wave

Abstract In recent years, extreme waves have attracted more and more attention due to its threat to offshore and coastal structures. It is essential to obtain further insight into the formation and propagation of the extreme waves. The formation of extreme waves mainly comes from the simultaneous focusing of wave group energy in the ocean. In the present study, the nonlinear characteristics of the extreme wave are experimentally investigated by the wave focusing method. The phase decomposition methods, both two-phases separation and four-phases separation methods, are used to obtain the higher harmonic elevation in the focused wave. The results show that the four-phases separation method can reasonably extract the first four harmonics. With the separated results, the nonlinear analysis of the wave elevation and velocity of the focused wave is carried out. It is found that the harmonics of the wave group focused at the same time, but the wave elevation and energy of higher-order harmonics are smaller than that of the overall wave. The Stokes wave theory can describe the variation of second-order harmonics satisfactorily. However, the Stokes wave theory cannot estimate third-order harmonics accurately. More work should be carried out to figure out the third-order wave interaction occurring during wave focusing. With a distributed wave gauge system, the wave evolution along the wave flume is measured. The evanescent modes significantly influence the wave group’s harmonic structure near the wavemaker. The coefficients of the higher-order harmonics are obtained from the measured elevations. The nonlinear wave elevation of the focused wave can be reconstructed with those coefficients basing on the linear theoretical solution, which is in good agreement with the experimental results.

Ultrasonic Characteristics of the Ultrasonic Grinding Process about the Nano-Ceramic Plate

2011 ◽  
Vol 418-420 ◽  
pp. 1690-1693 ◽  
Author(s):  
Ming Zhang ◽  
Yu Qing Wang ◽  
Feng Jiao
Keyword(s):  
High Efficiency ◽  
Skin Effect ◽  
Wave Theory ◽  
Ultrasonic Waves ◽  
Grinding Process ◽  
Ceramic Plate ◽  
Two Dimensional ◽  
Ultrasonic Grinding ◽  
The Waves ◽  
Order Surface

In this paper, the sand vibration test of the ultrasonic wave is done under ultrasonic vibration grinding. In this test, the "skin effect"is observed when the ultrasonic waves pass to the nano-ceramic plate, which is amplified by the ultrasonic horn. This phenomenon is analyzed by the second-order surface wave theory and the waves which pass to the workpiece are surface waves generated. These explain the good grinding surface quality and high efficiency under the two-dimensional ultrasonic grinding in the same conditions.

Ultrasonic Vibration Characteristics of Nano-Composite Ceramic in the Ultrasonic Polishing Process

2012 ◽  
Vol 522 ◽  
pp. 147-151
Author(s):  
Ming Zhang ◽  
Feng Jiao
Keyword(s):  
Surface Waves ◽  
High Efficiency ◽  
Three Dimensional ◽  
Wave Theory ◽  
Composite Ceramic ◽  
Ceramic Plate ◽  
Two Dimensional ◽  
Nano Composite ◽  
The Waves ◽  
Order Surface

The ultrasonic polishing test of the nanoZrO2-Al2O3composite ceramics is done under the two-dimensional ultrasonic polishing device, which is developed by us. In this process, the ultrasonic amplitude-frequency characteristic testing is done by the DASP software. There are certain amplitudes at some frequency points, which can be seen from the spectrum and the three-dimensional spectral array maps, but only one the largest amplitude appears. This shows the resonance points appear when the ultrasonic is passed to the nanocomposite ceramic plate after it is amplified by the horn. This phenomenon is analyzed by the second-order surface wave theory and the waves are surface waves, which are generated by surface waves. These explain the good polishing surface quality and high efficiency under the two-dimensional ultrasonic polishing in the same conditions.

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