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.

Numerical Calculation of Second-Order Wave Resistance

1977 ◽  
Vol 21 (02) ◽  
pp. 94-106
Author(s):  
Young S. Hong
Keyword(s):  
Numerical Calculation ◽  
Steady Motion ◽  
Order Theory ◽  
Iteration Scheme ◽  
Wave Resistance ◽  
Second Order ◽  
Lagrangian Coordinates ◽  
Restricted Range ◽  
First Order ◽  
First Order Theory

The wave resistance due to the steady motion of a ship was formulated in Lagrangian coordinates by Wehausen [1].2 By introduction of an iteration scheme the solutions for the first order and second order3 were obtained. The draft/length ratio was assumed small in order to simplify numerical computation. In this work Wehausen's formulas are used to compute the resistance numerically. A few models are selected and the wave resistance is calculated. These results are compared with other methods and experiments. Generally speaking, the second-order resistance shows better agreement with experiment than first-order theory in only a restricted range of Froude number, say 0.25 to 0.35, and even here not uniformly. For larger Froude numbers it underestimates seriously.

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 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.

scholarly journals Modeling Free-surface Solitary Waves with Smoothed Particle Hydrodynamics

2017 ◽  
Author(s):  
Balázs Tóth
Keyword(s):  
Free Surface ◽  
Solitary Waves ◽  
Kdv Equation ◽  
Order Approximation ◽  
Three Dimensional ◽  
Order Theory ◽  
Second Order ◽  
Weakly Compressible ◽  
Particle Hydrodynamics ◽  
Smoothed Particle

A three-dimensional weakly compressible Smoothed ParticleHydrodynamics (SPH) solver is presented and applied tosimulate free-surface solitary waves generated in a quasi twodimensionaldam-break experiment. Test cases are constructedbased on the measurement layouts of a dam-break experiment.The simulated wave propagation speeds are compared to theexact solutions of the Korteweg-de Vries (KdV) equation as afirst order theory, and to a second order iterative approximationinvestigated in the literature. Free surface shapes of differentsimulation cases are investigated as well. The results show goodagreement with the free surface shapes of the KdV equation aswell as with the second order approximation of solitary wavepropagation speeds.

A Method of Computing Nonlinear Wave Resistance of Thin Ships by Coordinate Straining

1975 ◽  
Vol 19 (03) ◽  
pp. 149-154
Author(s):  
G. Dagan
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Nonlinear Wave ◽  
Wave Resistance ◽  
Second Order ◽  
Forward Displacement ◽  
Nonlinear Solution ◽  
First Order ◽  
Body Boundary ◽  
Flow Domain

A systematical procedure is derived for determining the distribution of sources along the centerplane of a thin ship which generate a flow (and the associated wave resistance) satisfying the free-surface and body boundary conditions at second order. The method relies on a mapping of the flow domain onto a new domain by slightly straining the coordinates. The horizontal straining is selected such that the nonlinear solution should be easily derived from the first-order (Michell) solution in the strained domain. The results are shown to be similar to those obtained by Guilloton's method, but new features, such as the forward displacement of the bow singularities, are present.

A Perturbation Analysis of the Wavemaking of a Ship, with an Interpretation of Guilloton’s Method

1975 ◽  
Vol 19 (03) ◽  
pp. 140-148
Author(s):  
F. Noblesse
Keyword(s):  
Approximate Solution ◽  
Free Surface ◽  
Perturbation Analysis ◽  
Order Approximation ◽  
Second Order ◽  
Regular Perturbation ◽  
First Order ◽  
Perturbation Problem ◽  
Sinkage And Trim ◽  
Basic Ideas

A thin-ship perturbation analysis, suggested by Guilloton's basic ideas, is presented. The analysis may be regarded as an application of Lighthill's method of strained coordinates to a regular perturbation problem. An inconsistent second-order approximation in which the Laplace equation is satisfied to first order, and the boundary conditions both at the free surface and on the ship hull are satisfied to second order, is derived. When sinkage and trim, incorporated into the present analysis, are ignored, this approximate solution is shown to be essentially equivalent to the method of Guilloton.

Improved Approach to the Streamline Curvature Method in Turbomachinery

1987 ◽  
Vol 109 (3) ◽  
pp. 213-217 ◽  
Author(s):  
S. Abdallah ◽  
R. E. Henderson
Keyword(s):  
Flow Field ◽  
Velocity Gradient ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Second Order ◽  
Curvilinear Coordinates ◽  
First Order ◽  
Streamline Curvature ◽  
Stators And Rotors ◽  
Streamline Curvature Method

Quasi three dimensional blade-to-blade solutions for stators and rotors of turbomachines are obtained using the Streamline Curvature Method (SLCM). The first-order velocity gradient equation of the SLCM, traditionally solved for the velocity field, is reformulated as a second-order elliptic differential equation and employed in tracing the streamtubes throughout the flow field. The equation of continuity is then used to calculate the velocity. The present method has the following advantages. First, it preserves the ellipticity of the flow field in the solution of the second-order velocity gradient equation. Second, it eliminates the need for curve fitting and strong smoothing under-relaxation in the classical SLCM. Third, the prediction of the stagnation streamlines is a straightforward matter which does not complicate the present procedure. Finally, body-fitted curvilinear coordinates (streamlines and orthogonals or quasi-orthogonals) are naturally generated in the method. Numerical solutions are obtained for inviscid incompressible flow in rotating and non-rotating passages and the results are compared with experimental data.

Second-order theory of flow in three-dimensional deforming media

1974 ◽  
Vol 10 (6) ◽  
pp. 1217-1228 ◽  
Author(s):  
Giuseppe Gambolati
Keyword(s):  
Three Dimensional ◽  
Order Theory ◽  
Second Order ◽  
Theory Of Flow

A feasible theory for analysis

1994 ◽  
Vol 59 (3) ◽  
pp. 1001-1011 ◽  
Author(s):  
Fernando Ferreira
Keyword(s):  
Polynomial Time ◽  
Order Theory ◽  
Second Order ◽  
First Order ◽  
Weak König’S Lemma ◽  
König’S Lemma ◽  
Computable Functions

AbstractWe construct a weak second-order theory of arithmetic which includes Weak König's Lemma (WKL) for trees defined by bounded formulae. The provably total functions (with -graphs) of this theory are the polynomial time computable functions. It is shown that the first-order strength of this version of WKL is exactly that of the scheme of collection for bounded formulae.

Waves and wave resistance of thin bodies moving at low speed: the free-surface nonlinear effect

1975 ◽  
Vol 69 (2) ◽  
pp. 405-416 ◽  
Author(s):  
G. Dagan
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Surface Condition ◽  
Perturbation Expansion ◽  
Wave Resistance ◽  
The Body ◽  
Thin Body ◽  
Two Dimensional ◽  
First Order ◽  
Flow Past

The linearized theory of free-surface gravity flow past submerged or floating bodies is based on a perturbation expansion of the velocity potential in the slenderness parameter e with the Froude number F kept fixed. It is shown that, although the free-wave amplitude and the associated wave resistance tend to zero as F → 0, the linearized solution is not uniform in this limit: the ratio between the second- and first-order terms becomes unbounded as F → 0 with ε fixed. This non-uniformity (called ‘the second Froude number paradox’ in previous work) is related to the nonlinearity of the free-surface condition. Criteria for uniformity of the thin-body expansion, combining ε and F, are derived for two-dimensional flows. These criteria depend on the shape of the leading (and trailing) edge: as the shape becomes finer the linearized solution becomes valid for smaller F.Uniform first-order approximations for two-dimensional flow past submerged bodies are derived with the aid of the method of co-ordinate straining. The straining leads to an apparent displacement of the most singular points of the body contour (the leading and trailing edges for a smooth shape) and, therefore, to an apparent change in the effective Froude number.

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