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Generation of wave motion in fluid with inhomogeneous ice cover

Presented by: 
Izolda Sturova
Friday 10th November 2017 - 14:30 to 15:00
INI Seminar Room 1
The dynamic perturbations occurring in fluid and ice cover as a result of the action ofmechanical external force have been thoroughly studied in the linear treatment for aninfinitely extended homogeneous ice cover, which is modeled by a thin isotropicelastic plate floating on the surface of a fluid of constant depth. In reality, the icecover is not homogeneous, since it can cover not the entire upper boundary of a fluid,but only its part, and also there may be the cracks and the patches of ice-free water init. The effect of such complex boundary conditions on the wave motion is in the initialstage of the study.

We present a review of the solutions for several 2-D and 3-D problems. The timeharmonicproblem describing small oscillations (sway, heave and roll) of a horizontalcylinder is considered for four classes of hydroelastic system: i) a floating semiinfiniteelastic plate; ii) two semi-infinite elastic plates connected by the vertical andflexural rotational springs as a model of a partially frozen crack in an ice sheet; iii) afloating elastic platform of finite length; iv) two semi-infinite elastic plates separatedby a region of open water (polynya). The hydrodynamic load (added mass anddamping coefficients) and the amplitudes of vertical displacements of the free surfaceand elastic plates are calculated as functions of the cylinder oscillation frequency andthe location of the cylinder with respect to the plate edges.

The 3-D problem is considered for time-periodic external pressure and a load uniformly moving along the rectilinear edge of the ice cover. By analogy with the 2-D case, the first two classes of hydroelastic system are considered, as well as the effect of the solid vertical wall while the edge of the ice cover adjacent to the wall can be either clamped or free. In the problem of time-periodic external pressure, it is shown that for semi-infinite elastic plate contacting with free surface of water and for two non-identical semi-infinite plates, divided by crack, the directions of predominantwave propagation are allocated under some angle to the crack. In the case of two identical semi-infinite plates, divided by a crack, the edge wave guide mode is excited.The edge wave is most excited is the case of semi-infinite plate with a free edge near a solid vertical wall.

In the case of moving load, the 3-D pictures of generated waves in fluid and in ice cover are built for various speeds of motion. It is shown that in case of two identical semi-infinite plates, divided by a crack, two edge waveguide modes with different wave numbers exist for supercritical values of speed motion. For the vehicle moving with supercritical speed one mode is extending in front of moving load and other mode behind it. The wave forces acting on moving vehicle are investigated for various speeds of motion.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons