Fluid Dynamics

, Volume 53, Issue 1, pp 49–58 | Cite as

Motion of an External Load over a Semi-Infinite Ice Sheet in the Subcritical Regime

  • I. V. Sturova


The three-dimensional problem of steady-state forced vibrations of fluid and semiinfinite ice sheet under the action of a local external load traveling along the rectilinear sheet edge at a constant velocity is considered. Two cases are analyzed. In the first case the fluid surface outside the ice sheet is free and in the second the fluid is confined by a rigid vertical wall and the ice sheet edge adjacent to the wall can be both clamped and free. The ice sheet is simulated by a thin elastic isotropic plate floating on the surface of fluid of finite depth. The load traveling velocity is assumed to be not higher than the minimum phase velocity of the flexural-gravity waves (subcritical regime). The solution to the linear problem is obtained by means of the integral Fourier transform and matching the expansions of the velocity potential in the vertical eigenfunctions. Examples of the numerical investigation of the ice sheet and fluid displacements are given.

Key words

linear wave theory inhomogeneous ice sheet traveling load 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. A. Squire, R. J. Hosking, A. D. Kerr, and P. J. Langhorne, Moving Loads on Ice Plates (Kluwer Academic Publ., Dordrecht, 1996).CrossRefGoogle Scholar
  2. 2.
    V. M. Kozin, A. V. Pogorelova, V. L. Zemlyak, V. Yu. Vereshchagin, E. G. Rogozhnikova, D. Yu. Kipin, and A. A. Matyushina, Experimental and Theoretical Investigations of the Dependence of Parameters of the Flexural-Gravity Waves Propagating in a Floating Plate on Their Excitation Conditions (Press of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 2016) [in Russian].Google Scholar
  3. 3.
    S. F. Dotsenko, “Steady Flexural-Gravity Three-DimensionalWaves Initiated by Traveling Perturbations,” in: Tsunami and Internal Waves (Marine Hydrophysical Institute of the Academy of Sciences of the Ukrainian SSR, Sevastopol, 1976), pp. 144–155 [in Russian].Google Scholar
  4. 4.
    L. V. Cherkesov, Wave Hydrodynamics (Naukova Dumka, Kiev, 1980) [in Russian].Google Scholar
  5. 5.
    F. Milinazzo, M. Shinbrot, and N. W. Evans, “A Mathematical Analysis of the Steady Response of Floating Ice to the UniformMotion of a Rectangular Load,” J. Fluid Mech. 287, 173–197 (1995).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    V. D. Zhestkaya and V. M. Kozin, Investigation of the Possibilities of Destruction of Ice Sheet by Amphibious Air-Cushion Vehicles Using the Resonance Method (Dal’nauka, Vladivostok, 2003) [in Russian].Google Scholar
  7. 7.
    P. Brocklehurst, “HydroelasticWaves and Their Interaction with Fixed Structures,” PhD Thesis (University of East Anglia, UK, 2012).Google Scholar
  8. 8.
    K. Shishmarev, T. Khabakhpasheva, and A. Korobkin, “The Response of Ice Cover to a LoadMoving along a Frozen Channel,” Applied Ocean Research 59, 313–326 (2016).CrossRefGoogle Scholar
  9. 9.
    J. V. Wehausen and E. V. Laitone, “Surface Waves,” in: Encyclopedia of Physics (Springer Verlag, Berlin, 1960), Vol. 9, pp. 446–814.zbMATHGoogle Scholar
  10. 10.
    S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells (2nd ed., McGraw-Hill,New York a.o., 1959; Fizmatgiz, Moscow, 1966).zbMATHGoogle Scholar
  11. 11.
    A. A. Savin and A. S. Savin, “Three-Dimensional Problem of Disturbing an Ice Cover by a Dipole Moving in Fluid,” Fluid Dynamics 50 (5), 613–620 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    I. V. Sturova, “Action of Periodic Surface Pressure on an Ice Cover in the Vicinity of a VerticalWall,” J. Appl. Mech. Tech. Phys. 58 (1), 80–88 (2017).ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Lavrent’ev Hydrodynamic Institute of the Siberian Branch of the Russian Academy of SciencesNovosibirskRussia

Personalised recommendations