Radiation of waves by a cylinder submerged in water with ice floe or polynya

Abstract

The problems of radiation (sway, heave and roll) of surface and flexural-gravity waves by a submerged cylinder are investigated for two configurations, concerning; (i) a freely floating finite elastic plate modelling an ice floe, and (ii) two semi-infinite elastic plates separated by a region of open water (polynya). The fluid of finite depth is assumed to be inviscid, incompressible and homogeneous. The linear two-dimensional problems are formulated within the framework of potential-flow theory. The method of mass sources distributed along the body contour is applied. The corresponding Green's function is obtained by using matched eigenfunction expansions. The radiation load (added mass and damping coefficients) and the amplitudes of vertical displacements of the free surface and elastic plates are calculated. Reciprocity relations which demonstrate both symmetry of the radiation load coefficients and the relation of damping coefficients with the far-field form of the radiation potentials are found. It is shown that wave motion essentially depends on the position of the submerged body relative to the elastic plate edges. The results of solving the radiation problem are compared with the solution of the diffraction problem. It is noted that resonant frequencies in the radiation problem correlate with those frequencies at which the reflection coefficient in the diffraction problem has a local minimum.

Wave excited motion of a body floating on water confined between two semi-infinite ice sheets

“…We consider the problem of a body floating on the open water surface between two semiinfinite ice sheets, as shown in Fig.1. Each of the ice sheets is assumed to have uniform density, thickness and draught, or 11 , h  and 1 d for the left ice sheet and 22 , h  and 2 d for the right one, respectively. The density of water is defined as  .…”

“…As added mass and damping coefficients in these two equations are frequency dependent, their roots are not able to be obtained explicitly. We may plot two curves with 22 Figure 8(a) shows that there is one natural frequency in heave. When the wave frequency is at the natural frequency, or at the resonance, Fig.7(b) shows a large peak in heave response at around 1.19…”

“…In such a case,   0 can be approximated as an incoming wave from open water at x   ,   0 is the reflection from the semi-infinite ice sheet and   0 is the transmitted wave. Then, we can define the reflection and transmission coefficients as those in the case of a semi-infinite ice sheet as follows approximately satisfy the energy conversation 622…”

Wave diffraction and radiation by a vertical circular cylinder standing in a three-dimensional polynya

“…The work listed above is mainly about interaction of wave with ice sheet. When a body is present, Sturova (2015) considered a two-dimensional horizontal cylinder submerged in polynya while Ren et al (2016) and Li et al (2018) considered a floating body. For the three-dimensional diffraction problem, Malenica & Korobkin (2003) investigated the interaction between waves and a vertical cylinder clamped by a finite ring-shaped ice sheet.…”

Diffraction of hydroelastic waves by multiple vertical circular cylinders

“…In addition to the work above on interaction between cylinders with the free surface waves, the interaction of hydroelastic waves with ocean structures also has become increasingly relevant and important for polar engineering. These kinds of problems elicited strong interest from many authors, for example: two-dimensional works by Sturova [22][23][24], Ren et al [25], and Li et al [26][27][28]-for a submerged/floating body in a polynya; and similar threedimensional work by Ren et al [29]. In some cases, the free surface in the polynya may become frozen as well, and the surface of offshore structures becomes directly connected to the edge of ice sheet.…”