Influence of wave board type on bounded long waves

Sand, Stig E.; Donslund, Bjarne

doi:10.1080/00221688509499362

Cited by 11 publications

(8 citation statements)

References 4 publications

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“…Second-order wavemaker theory has a long history of development going back at least to Fontanet (1961) for regular waves. Ottesen-Hansen et al (1980), Sand (1982) and Sand and Donslund (1985) discussed the second-order long wave generation in the laboratory. Hudspeth and Sulisz (1991) derived the complete second-order Eulerian theory for waves generated by a monochromatic wave paddle motion with special emphasis on Stokes drift and return flow in wave flumes.…”

Section: Introductionmentioning

confidence: 99%

Second-order theory for coupling 2D numerical and physical wave tanks: Derivation, evaluation and experimental validation

Yang

Liu

Bingham

et al. 2013

Coastal Engineering

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a b s t r a c t a r t i c l e i n f oA full second-order theory for coupling numerical and physical wave tanks is presented. The ad hoc unified wave generation approach developed by Zhang et al. [Zhang, H., Schäffer, H.A., Jakobsen, K.P., 2007. Deterministic combination of numerical and physical coastal wave models. Coast. Eng. 54, 171-186] is extended to include the second-order dispersive correction. The new formulation is presented in a unified form that includes both progressive and evanescent modes and covers wavemaker configurations of the piston-and flap-type. The second order paddle stroke correction allows for improved nonlinear wave generation in the physical wave tank based on target numerical solutions. The performance and efficiency of the new model is first evaluated theoretically based on second order Stokes waves. Due to the complexity of the problem, the proposed method has been truncated at 2D and the treatment of regular waves, and the re-reflection control on the wave paddle is also not included. In order to validate the solution methodology further, a series of nonlinear, periodic waves based on stream function theory are generated in a physical wave tank using a piston-type wavemaker. These experiments show that the new second-order coupling theory provides an improvement in the quality of nonlinear wave generation when compared to existing techniques.

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Section: Introductionmentioning

confidence: 99%

Second-order theory for coupling 2D numerical and physical wave tanks: Derivation, evaluation and experimental validation

Yang

Liu

Bingham

et al. 2013

Coastal Engineering

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“…An eigenfunction solution for the fluid motion generated by a generic planar wavemaker is presented that may also be used to analyze waves generated by TYPE E double-actuated wave generators. The eigenfunction solution for a generic planar wavemaker appears to be easier to apply in numerical codes than the solution given by Flick and Guza (1980) or by Sand and Donslund (1985). The generic transfer functions {5/4} for both piston (S*) and hinged (S *) wavemakers are derived from a conservation of energy flux principle which equates the total average dimensionless power of the double-actuated TYPE E wave generator to the dimensionless energy flux of the propagating wave.…”

Section: Résumémentioning

confidence: 99%

“…(1) appear to be more robust and easier to apply in numerical codes than those used by Flick and Guza (1980) or by Sand and Donslund (1985) because the amplitude of the wavemaker need not be restricted to the value at the still-water-level {zlh = 0); and the draft of the hinge need not be forced to minus infinity (dlh -» -°°) in order to recover a piston-only wavemaker.…”

mentioning

confidence: 96%

TYPE E double-actuated wavemakers

Hudspeth

Grassa

Medina

et al. 1994

Journal of Hydraulic Research

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The Ploeg and Funke TYPE E double-actuated wavemaker has been calibrated at the CEPYC-CEDEX Laboratory in Madrid, Spain. TYPE E double-actuated wavemakers are capable of operating as piston-only, hinged-only, or simultaneously as both piston and hinged wavemakers. An eigenfunction expansion for the fluid motion generated by a generic planar wavemaker of variable-draft is used to describe the motion of double-actuated wavemakers. This generic solution appears to be more robust and easier to apply in numerical codes than the ones that require the amplitude of the wavemaker stroke be specified at the still-water-level and that require the draft of the hinge to be forced to minus infinity in order to recover a piston wavemaker. The dimensionless transfer functions for the ratio of the wavemaker stroke to the wave amplitude are derived by equating the total average power generated by both actuators to the energy flux in the propagating wave. The solution is not unique because both the ratio of the amplitude of the piston actuator to the amplitude of the hinge actuator and the relative phase angle between the motion of the two actuators are arbitrary. Experimental verifications of the theory are given for each actuator operating independently as well as for three ratios of the piston amplitude to hinge amplitude when the relative phase angle is zero. These calibrations indicate that TYPE E double-actuated wavemakers are perhaps the optimum wavemakers for simulating double-peaked spectra such as the six parameter Ochi-Hubble spectra where the hinge actuator is optimum for generating the higher frequency components. RÉSUMÉUn générateur de houle a double actionneur (TYPE E dans la classification de Ploeg et Funke) a été calibre au laboratoire CEPYC-CEDEX a Madrid en Espagne. Les générateurs de houle du TYPE E cumulent les possibilités d'opérer en mode piston, en mode volet ou simultanément en mode mixte piston/volet. Une decomposition du mouvement du fluide produit par un batteur plan de cote variable par rapport au fond sur une base de fonctions propres données est adoptée pour représenter le mouvement de générateur de houle a double actionneur. Cette solution générale apparaït plus robuste et plus facile a appliquer dans les codes numériques que celles qui imposent que l'amplitude du mouvement du batteur soit spécifiée au niveau de la surface libre au repos ou qui obligent a forcer la cote du batteur volet a "moins l'infini" pour retrouver un batteur piston. Les fonctions de transfert adimensionnelles donnant le rapport de la course du batteur a l'amplitude de la houle sont obtenues en égalant l'énergie totale délivrée par les deux actionneurs au flux d'énergie de la houle générée. La solution obtenue n'est pas unique ïi cause des valeurs arbitrages pouvant être choisies pour le rapport des amplitudes de l'actionncur piston et de l'actionneur volet d'une part, et pour le déphasage relatif entre les

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“…They also described tests that demonstrated the successful suppression of unwanted long-wave energy. Sand and Donslund (1985) gave examples of model studies that illustrated model response differences between first-order irregular waves, and irregular waves with correctly generated second-order bound long waves. Sand and Donslund also extended the second-order wavemaker solution to include the case of a hinged wave board with variable draft, and they presented a unified set of equations for practical implementation in the laboratory.…”

Section: Correct Reproduction Of Bound Long Wavesmentioning

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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Influence of wave board type on bounded long waves

Cited by 11 publications

References 4 publications

Second-order theory for coupling 2D numerical and physical wave tanks: Derivation, evaluation and experimental validation

Second-order theory for coupling 2D numerical and physical wave tanks: Derivation, evaluation and experimental validation

TYPE E double-actuated wavemakers

Laboratory Wave Generation

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