Phenomenon of predominant orientation of a submerged elliptical cylinder under the action of surface waves

Abstract

UDC 532.595 In many of problems of body rolling caused by waves, it is of interest to study body motion that is established after a long period (compared with the wave period). Body drift is an example of such slow motion. Stationary forces and moments that cause this motion are determined by solving the nonlinear problem of wave-body interaction. To this end, the method of perturbations with the surface-incident-wave amplitude as a small parameter is commonly used. Second-order forces were first studied by Ogilvie (1), who found the vertical drift of a free submerged circular cylinder of neutral buoyancy under the action of surface waves. The second-order theory which is applied in ship hydrodynamics is given in great detail in (2). The problem of orientation of a submerged body about the horizontal axis is the least understood. This problem is of great interest, since quite small values of the res'~oring forces and moments are typical of submerged bodies. The stationary second-order wave moment acting upon a submerged ellipsoid of revolution was determined by Lee and Newman (7). It has been shown that under the action of incident periodic waves a moment arises that lowers the part of the ellipsoid that first meets the waves. In this paper, the behavior of a submerged elliptical cylinder which can rotate freely about the horizontal axis under the action of incident waves is studied theoretically and experimentally. Initially, when the liquid is not perturbed, the cylinder is in neutral equilibrium. Special attention is given to the study of the conditions of existence of steady (on the average) states of the cylinder that are consistent with the parameters of the waves incident on the body. The second-order averaged moment was determined theoretically for an infinite reservoir and for the case of reflection from a wave breaker, observed experimentally. It was shown that in the absence of reflected waves the orientation of an elliptical cylinder for a given submersion depends on the wavelength. If reflection occurs, the dependence of the orientation on the reflection coefficient and the phase of the reflected wave becomes more significant. Experimental data are in good agreement with the calculation results. In the experiments we found, in addition, some regimes in which the behavior of the system was dependent on the initial conditions. Under small perturbations, the cylinder oscillates about a certain mean position, while under strong perturbations (shocks) it begins to rotate under the action of waves. The experimental investigation of the behavior of an elliptical cylinder under the action of waves was carried out in a reservoir which was 4.5 m in length, 0.2 m in width, and 0.8 m in height. A schematic diagram of the setup is shown in Fig. 1. The reservoir had a wave maker 1 of the plunger type, which