Numerical model of a causal and fractional all-frequency wave equation for lossy media

2013 ◽  
Author(s):  
Margaret Wismer
Keyword(s):  
Wave Equation ◽  
Numerical Model ◽  
Frequency Wave ◽  
Lossy Media

A causal and fractional all-frequency wave equation for lossy media

2011 ◽  
Vol 130 (4) ◽  
pp. 2195-2202 ◽  
Author(s):  
Sverre Holm ◽  
Sven Peter Näsholm
Keyword(s):  
Wave Equation ◽  
Frequency Wave ◽  
Lossy Media

Calibration of a Time-Domain Hydrodynamic Model for A 12 MW Semi-Submersible Floating Wind Turbine

2021 ◽  
Author(s):  
Carlos Eduardo Silva de Souza ◽  
Nuno Fonseca ◽  
Petter Andreas Berthelsen ◽  
Maxime Thys
Keyword(s):  
Numerical Model ◽  
Wind Turbine ◽  
Time Domain ◽  
Quadratic Model ◽  
Wave Loads ◽  
Frequency Wave ◽  
Load Models ◽  
Wave Drift ◽  
Floating Wind Turbine ◽  
Decay Tests

Abstract Design optimization of mooring systems is an important step towards the reduction of costs for the floating wind turbine (FWT) industry. Accurate prediction of slowly-varying horizontal motions is needed, but there are still questions regarding the most adequate models for low-frequency wave excitation, and damping, for typical FWT concepts. To fill this gap, it is fundamental to compare existing load models against model tests results. This paper describes a calibration procedure for a three-columns semi-submersible FWT, based on adjustment of a time-domain numerical model to experimental results in decay tests, and tests in waves. First, the numerical model and underlying assumptions are introduced. The model is then validated against experimental data, such that the adequate load models are chosen and adjusted. In this step, Newman’s approximation is adopted for the second-order wave loads, using wave drift coefficients obtained from the experiments. Calm-water viscous damping is represented as a linear and quadratic model, and adjusted based on decay tests. Additional damping from waves is then adjusted for each sea state, consisting of a combination of a wave drift damping component, and one component with viscous nature. Finally, a parameterization procedure is proposed for generalizing the results to sea states not considered in the tests.

Wave Energy-Driven Resonant Sea-Water Pump

1997 ◽  
Vol 119 (3) ◽  
pp. 191-195 ◽  
Author(s):  
S. P. R. Czitrom
Keyword(s):  
Numerical Model ◽  
Sea Water ◽  
Scale Model ◽  
Water Pump ◽  
Incoming Wave ◽  
Frequency Wave ◽  
Variable Volume ◽  
Mass Spring ◽  
Air Compression ◽  
Compression Chamber

A wave-driven sea-water pump which operates by resonance is described. Oscillations in the resonant and exhaust ducts perform similar to two mass-spring systems coupled by a third spring acting for the compression chamber. Performance of the pump is optimized by means of a variable volume air compression chamber (patents pending) which tunes the system to the incoming wave frequency. Wave tank experiments with an instrumented, 1:20-scale model of the pump are described. Performance was studied under various wave and tuning conditions and compared to a numerical model which was found to describe the system accurately. Successful sea trials at an energetic coastline provide evidence of the system’s viability under demanding conditions.

scholarly journals Simulation of laser propagation in a plasma with a frequency wave equation

2008 ◽  
Vol 227 (4) ◽  
pp. 2610-2625 ◽  
Author(s):  
S. Desroziers ◽  
F. Nataf ◽  
R. Sentis
Keyword(s):  
Wave Equation ◽  
Frequency Wave ◽  
Laser Propagation

The Fresnel volume and transmitted waves

Geophysics ◽  
2004 ◽  
Vol 69 (3) ◽  
pp. 653-663 ◽  
Author(s):  
Jesper Spetzler ◽  
Roel Snieder
Keyword(s):  
Wave Equation ◽  
Fresnel Zone ◽  
Wave Theory ◽  
Three Dimensions ◽  
Ray Theory ◽  
Finite Frequency ◽  
Frequency Wave ◽  
Reflected Waves ◽  
Band Limited ◽  
Propagation Of Waves

In seismic imaging experiments, it is common to use a geometric ray theory that is an asymptotic solution of the wave equation in the high‐frequency limit. Consequently, it is assumed that waves propagate along infinitely narrow lines through space, called rays, that join the source and receiver. In reality, recorded waves have a finite‐frequency content. The band limitation of waves implies that the propagation of waves is extended to a finite volume of space around the geometrical ray path. This volume is called the Fresnel volume. In this tutorial, we introduce the physics of the Fresnel volume and we present a solution of the wave equation that accounts for the band limitation of waves. The finite‐frequency wave theory specifies sensitivity kernels that linearly relate the traveltime and amplitude of band‐limited transmitted and reflected waves to slowness variations in the earth. The Fresnel zone and the finite‐frequency sensitivity kernels are closely connected through the concept of constructive interference of waves. The finite‐frequency wave theory leads to the counterintuitive result that a pointlike velocity perturbation placed on the geometric ray in three dimensions does not cause a perturbation of the phase of the wavefield. Also, it turns out that Fermat's theorem in the context of geometric ray theory is a special case of the finite‐frequency wave theory in the limit of infinite frequency. Last, we address the misconception that the width of the Fresnel volume limits the resolution in imaging experiments.

scholarly journals Non-spherical bubble dynamics in a compressible liquid. Part 1. Travelling acoustic wave

2010 ◽  
Vol 659 ◽  
pp. 191-224 ◽  
Author(s):  
Q. X. WANG ◽  
J. R. BLAKE
Keyword(s):  
Wave Equation ◽  
Numerical Model ◽  
Acoustic Wave ◽  
Compressible Liquid ◽  
Wave Frequency ◽  
Liquid Jet ◽  
Approximate Theory ◽  
Spherical Bubble ◽  
Spherical Bubbles ◽  
Bubble Behaviour

Micro-cavitation bubbles generated by ultrasound have wide and important applications in medical ultrasonics and sonochemistry. An approximate theory is developed for nonlinear and non-spherical bubbles in a compressible liquid by using the method of matched asymptotic expansions. The perturbation is performed to the second order in terms of a small parameter, the bubble-wall Mach number. The inner flow near the bubble can be approximated as incompressible at the first and second orders, leading to the use of Laplace's equation, whereas the outer flow far away from the bubble can be described by the linear wave equation, also for the first and second orders. Matching between the two expansions provides the model for the non-spherical bubble behaviour in a compressible fluid. A numerical model using the mixed Eulerian–Lagrangian method and a modified boundary integral method is used to obtain the evolving bubble shapes. The primary advantage of this method is its computational efficiency over using the wave equation throughout the fluid domain. The numerical model is validated against the Keller–Herring equation for spherical bubbles in weakly compressible liquids with excellent agreement being obtained for the bubble radius evolution up to the fourth oscillation. Numerical analyses are further performed for non-spherical oscillating acoustic bubbles. Bubble evolution and jet formation are simulated. Outputs also include the bubble volume, bubble displacement, Kelvin impulse and liquid jet tip velocity. Bubble behaviour is studied in terms of the wave frequency and amplitude. Particular attention is paid to the conditions if/when the bubble jet is formed and when the bubble becomes multiply connected, often forming a toroidal bubble. When subjected to a weak acoustic wave, bubble jets may develop at the two poles of the bubble surface after several cycles of oscillations. A resonant phenomenon occurs when the wave frequency is equal to the natural oscillation frequency of the bubble. When subjected to a strong acoustic wave, a vigorous liquid jet develops along the direction of wave propagation in only a few cycles of the acoustic wave.

scholarly journals A new moving boundary shallow water wave equation numerical model

2007 ◽  
Vol 49 ◽  
pp. 605
Author(s):  
Joe Sampson ◽  
Alan Easton ◽  
Manmohan Singh
Keyword(s):  
Wave Equation ◽  
Numerical Model ◽  
Shallow Water ◽  
Water Wave ◽  
Moving Boundary ◽  
Shallow Water Wave

Very low frequency wave propagation numerical model

2013 ◽  
Author(s):  
Guillaume Jamet ◽  
Claude Guennou ◽  
Laurent Guillon ◽  
Jean-Yves Royer
Keyword(s):  
Wave Propagation ◽  
Numerical Model ◽  
Low Frequency ◽  
Frequency Wave ◽  
Very Low Frequency
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