Experiments in Fluids 5, 66-72 (1987) Experiments in Fluids © Springer-Verlag 1987 Measurements of two- and three-dimensional waves in a channel, including the vicinity of cut-off frequencies L. Shemer, E. Kit and T. Miloh Dept. of Fluid Mechanics, Faculty of Engineering, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, Israel Abstract. Measurements of water wave profiles were performed in a rectangular flume equipped with a modular wavemaker. This particular wavemaker could generate both two- and three-dimen- sional waves. A method is proposed to evaluate quantitatively the deviations of a spacial flow field from the two-dimensional one. Plane propagating waves, as well as pure sloshing waves with their crests parallel to the walls, were generated in the flume. In all cases the measured amplitudes were compared against linear theory predictions. 1 Introduction It is well known (Garrett 1970; Mahony 1972; Barnard & Pritchard 1972), that even a perfectly plane wavemaker, operating in a rectangular channel, can produce, in addi- tion to a plane propagating wave, a complex pattern of so called "cross waves". On the other hand, a wavemaker which is not exactly plane, generates, together with the propagating wave, a system of so-called "sloshing waves" (Barnard et al. 1977). These two types of waves are in fact standing waves with their crests perpendicular to the wavemaker. Both sloshing and cross waves have a wave length 2 across the channel which is related to the channel width b; they have an integer number of half wavelengths in b, so that n 2/2 = b; where n is denoted as the "mode" of the wave. Sloshing waves are generated at the fre- quency of the wavemaker, when the wavemaker is oper- ating in a non-symmetrical manner. Cross waves differ from sloshing waves in the sense that they represent a non- linear phenomenon with a basic frequency half of that of the wavemaker. Since most laboratory facilities are hampered by a finite channel length, a beach for wave energy absorption is usually placed at the channel far end. In practice wave absorption is never perfect, in the sense that some of the energy is being reflected away from the beach; thus the actual propagating wave in the flume may be contaminat- ed by both the reflected wave and the cross, or sloshing waves, as well as by random noise. A least square method, which is usually used to determine the reflection coeffi- cient in the channel (Mansard & Funke 1980), was used here to decompose the signal and to separate the incident, the reflected and the sloshing components of the measured wave field. The present work was carried out in the wave flume of the Faculty of Engineering, Tel-Aviv University. This experimental facility is unique in the sense that its modular wavemaker consists of four separate units which may be operated independently and thus make it possible to generate both two-dimensional and three-dimensional waves. In the first stage of the study the wavemaker was operated as a plane one, so that two-dimensional progres- sive waves were generated, and the reflection coefficients were determined. Also determined were the experimental conditions for the generation of the sloshing waves and the dependence of the amplitude of these waves on the frequency. Some of the experiments were repeated for a wavemaker.with a prescribed deviation from the plane form. This was achieved by oscillating one of the wave- maker moduli at an amplitude which differed slightly from the common amplitude of the rest of the paddles. During the later stage the wavemaker was operated in the "sloshing" mode, so that only sloshing waves of either 1st or 2nd mode were generated in the flume. The general pattern of the plane and sloshing waves was compared with the linear theory given in Wehausen (1974). 2 Experimental facility and data processing Experiments were performed in a wave tank which is 18 m long, 1.2 m wide and 0.9 m deep (Fig. 1). The tank has transparent side walls and windows at the bottom which allow viewing of flow from various directions. A beach for wave energy absorption is placed at the downstream end of the tank. The beach is made of a rubberized hair; it starts at the distance of 14 m from the wavemaker and gradually rises towards the water surface with a slope of 1/3.