The nonlinear hydroelastic waves propagating beneath an infinite ice sheet floating on an inviscid fluid of finite depth are investigated analytically. The approximate series solutions for the velocity potential and the wave surface elevation are derived, respectively, by an analytic approximation technique named homotopy analysis method (HAM) and are presented for the second-order components. Also, homotopy squared residual technique is employed to guarantee the convergence of the series solutions. The present formulas, different from the perturbation solutions, are highly accurate and uniformly valid without assuming that these nonlinear partial differential equations (PDEs) have small parameters necessarily. It is noted that the effects of water depth, the ice sheet thickness, and Young’s modulus are analytically expressed in detail. We find that, in different water depths, the hydroelastic waves traveling beneath the thickest ice sheet always contain the largest wave energy. While with an increasing thickness of the sheet, the wave elevation tends to be smoothened at the crest and be sharpened at the trough. The larger Young’s modulus of the sheet also causes analogous effects. The results obtained show that the thickness and Young’s modulus of the floating ice sheet all greatly affect the wave energy and wave profile in different water depths.

Effects of underlying uniform current on the nonlinear hydroelastic waves generated due to an infinite floating plate are studied analytically, under the hypotheses that the fluid is homogeneous, incompressible, and inviscid. For the case of irrotational motion, the Laplace equation is the governing equation, with the boundary conditions expressing a balance among the hydrodynamics, the uniform current, and elastic force. It is found that the convergent series solutions, obtained by the homotopy analysis method (HAM), consist of the nonlinear hydroelastic wave profile and the velocity potential. The impacts of important physical parameters are discussed in detail. With the increment of the following current intensity, we find that the amplitudes of the hydroelastic waves decrease very slightly, while the opposing current produces the opposite effect on the hydroelastic waves. Furthermore, the amplitudes of waves increase very obviously for higher opposing current speed but reduce very slightly for higher following current speed. A larger amplitude of the incident wave increases the hydroelastic wave deflections for both opposing and following current, while for Young’s modulus of the plate there is the opposite effect.

Nonlinear hydroelastic interaction among a floating elastic plate, a train of deepwater waves, and a current which decays exponentially with depth is studied analytically. We introduce a stream function to obtain the governing equation with the dynamic boundary condition expressing a balance among the hydrodynamic, the shear currents, elastic, and inertial forces. We use the Dubreil-Jacotin transformation to reformulate the unknown free surface as a fixed location in the calculations. The convergent analytical series solutions for the floating plate deflection are obtained with the aid of the homotopy analysis method (HAM). The effects of the shear current are discussed in detail. It is found that the phase speed decreases with the increase of the vorticity parameter in the opposing current, while the phase speed increases with the increase of the vorticity parameter in the aiding current. Larger vorticity tends to increase the horizontal velocity. In the opposing current, the horizontal velocity under the wave crest delays more quickly as the depth increases than that of waves under the wave trough, while in the aiding current case, there is the opposite effect. Furthermore, the larger vorticity can sharpen the hydroelastic wave crest and smooth the trough on an opposing current, while it produces an opposite effect on an aiding current.

The phase distortion caused by ocean turbulence will deform the spiral acoustic wave and disperse to other topological modes, resulting in crosstalk between the signals, which significantly interferes with the transmission of the spiral acoustic signal. The Gerchberg-Saxton (GS) algorithm can rapidly solve the correction phase and effectively restrain the influence of ocean turbulence on spiral acoustic communication. In this paper, the mode purity of single-mode spiral acoustic waves under different topological modes, turbulence intensity, and transmission distance is given to study the phase correction effect of the GS algorithm.

The nonlinear hydroelastic response of very large floating structures (VLFSs) or an ice sheet floating on the surface of deep water, idealized as a semi-infinite thin elastic plate, is investigated analytically in the case of nonlinear incident waves. Assuming that the fluid is inviscid and incompressible and the motion is irrotational, we consider incident progressive waves with a given angular frequency within the framework of potential flow theory. With the aid of the homotopy analysis method (HAM), the convergent analytical series solutions are derived by solving the simultaneous equations in which we apply a convergence-control parameter to obtain convergent solutions with relatively few terms. The clear calculation results are represented to show nonlinear wave-plate interaction. The effects of different physical parameters, including incident wave amplitude, Young’s modulus, the thickness and density of the plate on the wave scattering, and the hydroelastic response of the floating plate, are considered. We find that the variations of the plate stiffness, thickness, and density greatly change amount of wave energy which is reflected into the open water region and is transmitted into the plate-covered region. Further, the hydroelastic response of the plate also can be affected by the amplitude of incident wave.