Extending the theoretical work of Biesel, a study is made of a flap-type wavemaker hinged in the middle of a wall. The first-order linearized hydrodynamic equations of motion are solved to obtain the velocity potential, which is composed of a wave part and a spatially transitory part. Characteristics of generated waves far away from the wavemaker are analyzed as to the wave profile, flap stroke, water particle excursions, and power con- sumption of the wavemaker. The importance of the spatially transitory part is discussed with regard to the role played by the inertia pressure, which gives rise to added inertia of the flap. Surface elevations very near the flap are found. The hydrodynamically induced torque and the total hydrodynamic force on the flap are computed. The computed results seem to be well explained by the differing behaviors of the normal pressure and of the iner- tia pressure with increasing water depth. HE theoretical foundation of laboratory wave- generating apparatus was developed in detail by Biesel 1 and coworkers of Grenoble, pertaining to two-dimension al irrotational motions in prismatic channels of rectangular cross-section. Following the classical wavemaker theory of Havelock, Biesel solved the first-order linearized hydrodynamic equations of motion to find the resultant wave motions caused by a wavemaker at one end of a channel. As examples, he considered two simple cases, namely, a piston- type wavemaker, and a flap-type wavemaker hinged at the bottom of a wall. A brief comparison was made of the two types of wavemaker with regard to the quality of generated waves, wavemaker stroke, and the total hydrodynamic force applied at the wavemaker. The validity of the first-order wavemaker theory was experimentally verified by Ursell, Dean, and Yu,2 with particular reference to a piston-type wavemaker. For all practical purposes, however, flap-type wavemakers in common use today are fabricated with their lower ends hinged in the middle of the wall, unlike the simple flap-type wavemaker investigated by Biesel.'An article by Taniguchi and Shibata3 reported that agreement was satisfactory bet- ween the predictions of the first-order wavemaker theory and the measurements conducted in the Mitsubishi Nagasaki ex- perimental tank. The Nagasaki tank was equipped with a flap- type wavemaker, whose flap draft (the distance from the un- disturbed mean water surface to the lower hinges of the flap) was 1.77 m, and the constant water depth was 6.31 m. Their measurements dealt with flap frequency, flap stroke, wave profile, and the reaction force at the piston rod of the hydraulic drive. As was pointed out by Taniguchi and Shibata, published theses on wavemakers are rather scarce, and few scattered technical data for wavemaker performance are available in the literature. In most descriptive reports of existing towing tank facilities,4'5'6 wavemakers seem to be somewhat cursorily treated without providing much technical information. A unified account of a flap-type wavemaker, including detailed analysis of the added inertia effect of the flap, which was not previously discussed, is presented here. Relevant theoretical considerations, based on the first-order linearized hydrodynamic equations of motion, are given and possible analytical approaches are used. Treating the flap draft as a parameter, numerical computations are carried out to study the quality of generated waves and the hydrodynamically in- duced force and torque on the flap. The added inertia effect of the flap, which is a consequence of the spatially transitory part of fluid motion, is closely examined with respect to the flap torque augmentation and water particle displacements near the wavemaker. The analysis of a flap-type wavemaker is of practical usefulness in that it can be utilized for more general purposes, including the determination of the added mass and the damping coefficient of thin vertical bodies in water.
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