Abstract: Periodic hydroelastic waves propagating along an ice channel are studied. The channel has a rectangular cross section with finite depth and width. In the direction of hydroelastic wave propagation, the channel is unbounded. The channel is filled with a inviscid and incompressible liquid. The liquid is covered by a thin ice cover frozen to the channel walls. The ice thickness varies and can be arbitrary across the channel. Along the channel, ice thickness is constant. Liquid flow caused by ice deflections is potential. The problem is solved within the linear theory of hydroelasticity [1]. The ice is modeled by a thin elastic plate of variable thickness along the transverse coordinate. The plate is fixed on the channel walls. The considered coupled hydroelastic problem is reduced to the problem of wave profiles across the channel. The profiles are defined as a series of normal dry modes for a beam with variable thickness, whose decomposition coefficients must be determined. The normal modes are calculated using a piecewise linear approximation of the plate thickness in the cross section. The resulting solution across the channel is described by Bessel functions at intervals where the plate thickness varies linearly, and by trigonometric and hyperbolic functions where the thickness is approximated as a constant. The modes are constructed such that the corresponding deflections, inclinations, moments and shear forces are continuous. The dispersion relations of these hydroelastic waves, their phase velocities, and profiles across the channel are defined and investigated as a function of the parameters describing the change in ice thickness. Periodic hydroelastic waves in a channel with symmetric linearly varying ice thickness were studied in [2].

Cite: Shishmarev K. , Oglezneva К.
Characteristics of periodic hydroelastic waves in a frozen channel with a non- uniform thickness of ice.
Mathematics of Sea Ice and Ice Sheets 29-30 Nov 2023