Evaluation of the Wavelike Disturbance in the Kelvin Wave Source Potential

1988 ◽  
Vol 32 (01) ◽  
pp. 44-53 ◽  
Author(s):  
J. J. M. Baar ◽  
W. G. Price
Keyword(s):  
Numerical Evaluation ◽  
Field Component ◽  
Near Field ◽  
Neumann Series ◽  
Series Expansions ◽  
Effective Solution ◽  
Kelvin Wave ◽  
Wave Source ◽  
Series Representations ◽  
Single Integral

This paper discusses the numerical evaluation of the characteristic Kelvin wavelike disturbance trailing downstream from a translating submerged source. Mathematically the function describing the wavelike disturbance is expressed as a single integral with infinite integration limits and a rapidly oscillatory integrand. Numerical integration of such integrals is both cumbersome and time-consuming. Attention is therefore focused on two complementary Neumann-series expansions which were originally derived by Bessho [1].2 Numerically stable algorithms are presented for the accurate and efficient evaluation of the two series representations. When used in combination with the Chebyshev expansions for the nonoscillatory near-field component which were recently obtained by Newman [2], the present algorithms provide an effective solution to the numerical difficulties associated with the evaluation of the Kelvin wave source potential.

Numerical evaluation of a full-wave antenna model for near-field applications

2012 ◽  
Vol 11 (2) ◽  
pp. 155-165 ◽  
Author(s):  
A.P. Tran ◽  
C. Warren ◽  
F. André ◽  
A. Giannopoulos ◽  
S. Lambot
Keyword(s):  
Numerical Evaluation ◽  
Near Field ◽  
Full Wave ◽  
Wave Antenna ◽  
Antenna Model

Developments in the calculation of the wavemaking resistance of ships

1988 ◽  
Vol 416 (1850) ◽  
pp. 115-147 ◽  
Keyword(s):  
Three Dimensional ◽  
Source Distribution ◽  
Rectilinear Motion ◽  
Kelvin Wave ◽  
Distribution Method ◽  
Wave Source ◽  
Qualitative And Quantitative ◽  
Theoretical Predictions ◽  
Computational Aspects ◽  
Quantitative Manner

The wavemaking resistance of a rigid ship in steady rectilinear motion at the free surface of a previously calm ocean is evaluated by means of a linearized three-dimensional potential-flow formulation. Solutions to the disturbance potential of the steady perturbed flow about the moving ship are obtained by means of a Kelvin wave source distribution method. Particular emphasis is placed on computational aspects and accurate and efficient algorithms for the evaluation of the fundamental Kelvin wave source potential function are discussed. To illustrate the proposed method, experimental and theoretical predictions are compared for a variety of ship forms. In general, this approach shows the correct behaviour of the variation of the wavemaking resistance with forward speed in both a qualitative and quantitative manner.

scholarly journals A semi-analytic method to compute Feynman integrals applied to four-loop corrections to the $$ \overline{\mathrm{MS}} $$-pole quark mass relation

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Matteo Fael ◽  
Fabian Lange ◽  
Kay Schönwald ◽  
Matthias Steinhauser
Keyword(s):  
Quark Mass ◽  
Numerical Evaluation ◽  
Dimensionless Parameter ◽  
Series Expansions ◽  
Analytic Method ◽  
Coefficient Function ◽  
Mass Relation ◽  
Kinematic Range ◽  
Numerical Accuracy ◽  
Feynman Integrals

Abstract We describe a method to numerically compute multi-loop integrals, depending on one dimensionless parameter x and the dimension d, in the whole kinematic range of x. The method is based on differential equations, which, however, do not require any special form, and series expansions around singular and regular points. This method provides results well suited for fast numerical evaluation and sufficiently precise for phenomenological applications. We apply the approach to four-loop on-shell integrals and compute the coefficient function of eight colour structures in the relation between the mass of a heavy quark defined in the $$ \overline{\mathrm{MS}} $$ MS ¯ and the on-shell scheme allowing for a second non-zero quark mass. We also obtain analytic results for these eight coefficient functions in terms of harmonic polylogarithms and iterated integrals. This allows for a validation of the numerical accuracy.

Source properties of a Blue MT. Lake earthquake

1976 ◽  
Vol 66 (3) ◽  
pp. 677-683
Author(s):  
John G. Anderson ◽  
Jon B. Fletcher
Keyword(s):  
New York ◽  
Spectral Analysis ◽  
Field Component ◽  
Near Field ◽  
Earthquake Source ◽  
Dislocation Model ◽  
S Wave ◽  
Wave Pulse ◽  
Hypocentral Distance ◽  
Source Radius

abstract An accelerogram obtained at Blue Mt. Lake, New York is remarkable for the simplicity of its S-wave pulse. This results from (1) a nearly complete absence of scattering and reflections as second arrivals on the accelerogram, and (2) a very elementary earthquake source. The earthquake identified with this accelerogram had a magnitude mb = 2.2 and a hypocentral distance of about 1 km from the accelerometer. Spectral analysis of the S wave indicates the earthquake had a moment of 8 × 1018 dyne-cm, and a source radius of 20 to 40 m. When the accelerogram is integrated to obtain displacement, there is a step offset of about 5μ associated with a near-field component of the S-wave pulse. The S-wave, including the step offset, can be matched in remarkable detail by a dislocation model with a moment of 8.4 × 1018 dyne-cm.

Evaluation of the Wave-Resistance Green Function: Part 2—The Single Integral on the Centerplane

1987 ◽  
Vol 31 (03) ◽  
pp. 145-150 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Green Function ◽  
Arbitrary Order ◽  
Asymptotic Series ◽  
Neumann Series ◽  
Absolute Accuracy ◽  
Double Integral ◽  
Vertical Coordinate ◽  
Recursive Scheme ◽  
Thin Region ◽  
Single Integral

Effective series expansions are derived for the evaluation of the single integral in the potential of a submerged source which moves with constant velocity, when the source and field point are in the same longitudinal centerplane. In conjunction with the polynomial approximations for the double integral component which have been derived in Part 1 of this work, the present results facilitate the computation of the source potential or Green function. Three complementary domains of the centerplane are considered, with different expansions developed for use in each domain. The principal expansion is based on a Neumann series which is effective for small or moderate distances from the origin, except in a thin region near the free surface. To deal with the latter domain an asymptotic expansion is derived in ascending powers of the vertical coordinate. Both of these expansions are refined by subtracting a simpler component with the same behavior at the origin, and relating this component to Dawson's integral. Special algorithms for the evaluation of the latter function are presented in the Appendix. The third and final expansion, based upon the method of steepest descents, is effective at large distances from the origin. This asymptotic series is derived by a systematic recursive scheme to permit an arbitrary order of the approximation. Used in conjunction with the first two expansions, this permits the single integral to be evaluated with an absolute accuracy of six decimals throughout the centerplane.

The Water Depth Effect on Ship Pressure Distribution and Surface Wave

2012 ◽  
Vol 166-169 ◽  
pp. 3071-3074
Author(s):  
Tao Miao ◽  
Zhi Hong Zhang ◽  
Chong Wang ◽  
Ju Bin Liu ◽  
Jian Nong Gu
Keyword(s):  
Pressure Distribution ◽  
Steady Motion ◽  
Finite Depth ◽  
Wave Pattern ◽  
Integral Function ◽  
Kelvin Wave ◽  
Depth Effect ◽  
Wave Source ◽  
The Difference ◽  
Rankine Sources

Applying linear marine hydrodynamics theory, the Kelvin wave source Green function of steady motion in finite depth was decomposed to three parts: array of simple Rankine sources, local distribution and wave part. Both at subcritical and supercritical speed, the singularity of integral function were eliminated by different integral path. The Kelvin source was distributed on the surface of ship by panel method, and the ship pressure distribution and wave pattern of ship in finite depth were calculated. The difference and connection between finite and infinite depth results were compared. It can provide the theoretical arithmetic base of improving the ship seaworthiness, increasing the speed and optimization of ship in river and offshore strip.

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