# Motion of Submerged Body in a Frozen Channel with Compressed Porous Ice
## 1 Introduction  
Recently, the problems of wave motion in a fluid in the presence of a thin elastic plate floating on the upper boundary of the fluid have been actively studied. Well-studied are the problems associated with the propagation of flexural-gravity waves in ice covers, which arise due to the action of non-stationary external loads on the floating ice plate. The Kirchhoff-Love model is commonly used, which describes the plate considering only its flexural rigidity and inertia. For such models, the straight-line motion of the external load has been extensively studied in both stationary and non-stationary cases. An extensive list of literature on this topic can be found in [1, 2]. However, tensile or compressive forces can arise in an ice cover due to the effects of wind, currents, or temperature variations [3]. In the three-dimensional case, three types of forces exist: longitudinal, transverse, and shear (combined) [4]. The behavior of free hydroelastic waves under conditions of non-uniform compression was studied in [5], and the behavior of steady wave motion under external load was investigated in [6]. The kinematic properties of hydroelastic waves arising from periodic and impulsive disturbances under conditions of uniform and non-uniform compression were deeply studied in [7]. In [8], acceptable values of compression parameters ensuring the correctness of the mathematical formulation were investigated, and the regions of existence of hydroelastic waves with positive group speed were determined. Additionally, the influence of periodic and impulsive loading was studied. Together with those described above, another large class of problems is the study of the interaction between ice and a body immersed in liquid. The influence of an submerged body on the ice cover and the effects of the ice cover on the fluid flow near the body have been studied in [9; 10]. Many authors consider problems of ice cover behaviour assuming that the ice plate thickness is constant. However, in natural conditions ice is not homogeneous and therefore it is important to study models in which the ice thickness will be variable [11; 12]. It is obtained that changing the ice cover thickness distribution, as in [12] for example, leads to changes in the pattern of flexural-gravity waves, changes in their critical velocities and distributions of deflections and stresses in the ice plate. The two-dimensional problem of a pulsating point source placed in a fluid of infinite depth was analysed in [13]. The solution was sought in the form of a superposition of standing and travelling waves. It was shown that the frequencies of standing and travelling waves coincide with the frequency of the source oscillations, and the amplitudes and wave numbers of the resulting flexural-gravity waves depend strongly on the thickness and elastic properties of the ice plate. In [14] a three-dimensional problem on the response of the ice cover to uniform and straight-line motion of a dipole for a long time was considered. The dipole approximations used to model the flow around a sphere submerged in a liquid [15; 16]. It has been shown that the ice cover perturbations caused by the motion of a spherical body modelled by a dipole are significantly different depending on the velocity of the body. When the body moves with a subcritical velocity, it causes a local deflection of the ice cover and quickly decays with distance from the body. In the case of body motion with supercritical velocity, wave-type disturbances appear in the ice cover. In addition to ice covers with variable thicknesses and non-uniform compression, another type of ice heterogeneity--porosity--is actively investigated nowadays. Moreover, porous structures are often used to dissipate the energy of gravity waves, for example, in wave attenuators. Single or multiple porous plates--horizontal, vertical, or inclined--are commonly used. The main advantage of horizontal plates is that they have weak interaction with horizontal fluid flows [17].