Plunger-type wavemaker theory

Wu, Yung-Chao

doi:10.1080/00221688809499206

Cited by 21 publications

(34 citation statements)

References 2 publications

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“…In this situation, other numerical schemes have been tried. Wu [32,33] has collocated at M points, with M > N, leading to an overdetermined system, which he solved in a least-squares sense: in [32], he used N = 5 and M = 20 for an inclined flat wavemaker; in [33], (with a = c/h), and found that their method did not converge for a > 1. Later, McKee [15] obtained results up to a = 1.25 by using a Shanks transform.…”

Section: Methodsmentioning

confidence: 99%

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Havelock wavemakers, Westergaard dams and the Rayleigh hypothesis

Martin

1992

J Eng Math

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Water of constant finite depth fills a semi-infinite channel, with a wavemaker, W, at one end. The generation of small-amplitude gravity waves by harmonic oscillations of W leads to a linear boundary-value problem for a velocity potential, 4). For vertical, plane wavemakers, there is a theory due to Havelock in which t h is represented as a convergent series of eigenfunctions, with coefficients determined by the boundary condition on W. We show that the same representation (with different coefficients) can also be used for some wavemakers with other shapes; the allowable geometries and forcings are determined. This is a hydrodynamic analogue of the so-called Rayleigh hypothesis in the theory of gratings. Similar results obtain for the hydrodynamic loading of dams due to short-duration earthquakes.

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Section: Methodsmentioning

confidence: 99%

“…The same geometry has been considered by other authors, using rectangular eigenfunctions [10,15,32]. Other geometries have been considered using rectangular eigenfunctions [33], null-field methods [13,21] and perturbation methods [10,21].…”

Section: Introductionmentioning

confidence: 99%

Havelock wavemakers, Westergaard dams and the Rayleigh hypothesis

Martin

1992

J Eng Math

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“…Ellix and Arumugam stated that part of the difference was due to leakage underneath the plunger causing motion in the flume behind the wavemaker. Wu (1988) formulated the first-order plunger-type wavemaker problem for triangularly-shaped plungers in finite-depth water . He invoked the firstorder Laplace equation and the bottom and free surface boundary conditions as given in Table 7.1.…”

Section: Plunger-type Wavemakermentioning

confidence: 99%

“…The potential problem formulated by Wu (1988) for the finite-depth plunger-type wavemaker cannot be solved analytically, so Wu introduced a semi-empirical method which involved a least-squares matching of the boundary conditions at discrete points to determine unknown coefficients.…”

Section: Plunger-type Wavemakermentioning

confidence: 99%

Laboratory Wave Generation

Hughes¹

1993

Advanced Series on Ocean Engineering

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Wave generation capability has evolved from the time when researchers were completely at the mercy of a limited technology to the present where the capability of wave generators and computers exceeds the current understanding of wave dynamic processes." ...Ed Funke and Etienne Mansard (1987) ' This paper was the source of the quotation opening this chapter. 2 English translation by M. Pilch. Physical Models and Laboratory Techniques in Coastal Engineering Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/25/15. For personal use only. 7.2. TWO-DIMENSIONAL GOVERNING EQUATIONS Physical Models and Laboratory Techniques in Coastal Engineering Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/25/15. For personal use only. CHAPTER 7. LABORATORY WAVE GENERATION Multiplying both sides of Eqn. 7.49 by cosh[ki(h + z)], integrating the equation between z = -h and z = 0, and arranging gives A -USo , f °h f (z) cosh[kl (h + z)] dz (7.50) 2k1 f °h cosh2 [kl (h + z)] dz All of the summation terms have gone to zero because of orthogonality considerations given by the Sturm-Liouville theory (Dean and Dalrymple 1984). Similarly, multiplying Eqn. 7.49 by cos[k3, (z + h)] and performing the integration causes the progressive wave term to go to zero yieldingThe final step is to formulate the solution for the first-order wavemaker problem. The sea surface elevation in the wave tank is found by substituting the velocity potential given by Eqn. 7.46 into the first-order dynamic free surface boundary condition given by Eqn. 7.22 and evaluating the boundary condition at z = 0, i.e., 171(x,t) = oA cosh( klh)cos( klx -at) + 9+ sin(at ) E Cn ek i n x cos ( k3. h) (7.52) n =1 9Far from the wave board all of the summation terms will disappear, and to first order , the sea surface will be represented as the progressive wave solution 171(x,t ) = 2 cos ( klx -at ) (7.53)where H is the wave height . Equating Eqns . 7.52 and 7. 53 and discarding the series terms gives the basic wavemaker relationship H = 2o-A cosh(klh) (7.54) 9where A is given by Eqn . 7.50. Solution for a specific type of wavemaker is found by substituting for f ( z) in Eqn . 7.50 and solving the integrals. Physical Models and Laboratory Techniques in Coastal Engineering Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/25/15. For personal use only. P. _ a tanh kh l smh kh + 1 ( 1 -cosh kh) ( pghSo l kh (si.nh 2kh + 2kh l L kh ] z T J Physical Models and Laboratory Techniques in Coastal Engineering Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/25/15. For personal use only.

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“…While an analytical solution does not exist to solve for wave amplitude, several numerical CHAPTER 2. BACKGROUND AND LITERATURE REVIEW solutions exist like those formulated by Wang [23] and Wu [24]. The main disadvantage of plunger-type wavemakers is that they require longer channels to achieve wave stabilization; however, as it will be shown in Section 5.1.1, it is theoretically possible to achieve stable waves with the available test section length in the flume tank.…”

Section: Plunger-type Wavemakersmentioning

confidence: 99%

Control, Simulation, and Testbed Development for Improving Maritime Launch and Recovery Operations

McPhee¹

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Improvements to launch and recovery operations at sea are driven by the desire to increase safety and operational availability. This thesis presents various tools to improve motion compensation strategies in maritime launch and recovery: a 3D computer simulator to examine wave synchronization, a signal prediction algorithm for Go-NoGo states and a hardware setup to simulate ship and wave motion. The 3D simulator of towed body dynamics was advanced to model the wave interactions with the cable and towed body as the body exits the water. Small scale simulations were run to investigate the inclusion of wave synchronization in established active heave compensation strategies where the hypothesis that wave synchronization would reduce variations in cable tension was not supported; the simulations demonstrated that wave synchronization increased variations in cable tension compared to simulations not using motion compensation. The use of a signal prediction method that forecasts a periodic signal based only on historic data of the signal was explored. The method is a means to predict safe breach events where the prediction algorithm was advanced and tuned to determine Go-NoGo states. A Go scenario identified by the mean and one standard deviation of the predicted signal was found to produce a Go-NoGo signal that agreed most with the desired Go-NoGo signal for forecasts up to 10 s. For the development of laboratory equipment for the Carleton University flume tank, a ship motion simulator was designed and built to emulate 5 degrees-of-freedom of ship motion and a kinematic analysis was performed to characterize the system workspace. For producing waves in the flume tank, a design methodology was developed for the design of a plunger-type wavemaker. A numerical model for determining the wave amplitude to actuator stroke length ratio was advanced to include the effects of a flow current. The design methodology enables the designer to select an appropriate actuator and plunger shape based on an operating point that incorporates multiple design variables.

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Plunger-type wavemaker theory

Cited by 21 publications

References 2 publications

Havelock wavemakers, Westergaard dams and the Rayleigh hypothesis

Havelock wavemakers, Westergaard dams and the Rayleigh hypothesis

Laboratory Wave Generation

Control, Simulation, and Testbed Development for Improving Maritime Launch and Recovery Operations

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