Resonant destabilization of a floating homogeneous ice layer

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 52, Issue 3, 2001, Pages 397-420

  Brevdo, Leonid ^a  

^a AIX MARSEILLE UNIVERSITY   (France)

Author keywords

Destabilization; Floating ice layer; Logarithmic growth; Resonant frequencies; Resonant ice breaking mechanism

Indexed keywords

EID: 0035533246     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001553     Document Type: Article

References (28)

1. A. Bers, Theory of absolute and convective instabilities. In: Int. Congress on Waves and Instabilities in Plasmas (Eds. G. Auer and F. Cap), pp. B1-B52. Innsbruck, Austria 1973.
2. L. Brevdo, A study of absolute and convective instabilities with an application to the Eady model. Geophys. Astrophys. Fluid Dyn. 40 (1988), 1-92.
3. L. Brevdo, Spatially amplifying waves in plane Poiseuille flow. Z. angew. Math. Mech. 72 (1992), 163-174.
4. L. Brevdo, Convectively unstable wave packets in the Blasius boundary layer. Z. angew. Math. Mech. 75 (1995), 423-436.
5. L. Brevdo, On the stability of Lamb modes. Acta Mechanica 117 (1996), 71-80.
6. L. Brevdo, Wave packets, signaling and resonances in a homogeneous waveguide. J. Elasticity 49(3) (1998), 201-237.
7. L. Brevdo, Axisymmetric resonant disturbances in a homogeneous waveguide. Europ. J. Mech. A/Solids 17 (1998), 979-999.
8. L. Brevdo, High-order resonances in a homogeneous waveguide. Z. angew. Math. Phys. 50 (1999), 152-169.
9. L. Brevdo, Three-dimensional logarithmic resonances in a homogeneous elastic waveguide. Europ. J. Mech. A /Solids 19 (2000), 121-137.
10. L. Brevdo and A. Il'ichev, Exponential neutral stability of a floating ice layer. Z. angew. Math. Phys. 49 (1998), 401-419.
11. R. J. Briggs, Electron-stream Interaction with Plasmas, MIT Press 1964.
12. L. K. Forbes, Surface waves of large amplitude beneath an elastic sheet. Part 1. High order series solution. J. Fluid Mech. 169 (1986), 409-428.
13. L. K. Forbes, Surface waves of large amplitude beneath an elastic sheet. Part 2. Galerkin series expansion. J. Fluid Mech. 188 (1988), 491-508.
14. ie, Paris 1973.
15. D. Gottlieb, M. Y. Hussaini and S. A. Orszag, Theory and applications of spectral methods. In: Spectral Methods for Partial Differential Equations (Eds. R. G. Voigt, D. Gottlieb and M. Y. Hussaini), pp. 1-54, SIAM Philadelphia, 1984.
16. P. V. Hobbs, Ice Physics. Clarendon Press, Oxford 1974.
17. A. Il'ichev and K. Kirchgässner, Nonlinear water waves beneath an elastic ice-sheet. Manuscript, Universität Stuttgart, 1997.
18. A. T. Il'ichev and A. V. Marchenko, Nonlinear waveguides in resonance three-wave interaction in an ideal fluid with surface effects. BRAS Physics/Supplement Physics of Vibrations 59 (1995), 98-107.
19. A. T. Il'ichev and A. Yu. Semenov, Stability of solitary waves in dispersive media described by a fifth-order evolution equation. Theoret. Comput. Fluid Dynamics 3 (1992), 307-326.
20. A. V. Marchenko, Long waves in a shallow liquid under an ice cover. J. Appl. Math. Mech. 52 (1988), 180-183.
21. A. V. Marchenko and A. Yu. Semenov, Edge waves in a shallow liquid under an elastic plate with a crack. Mech. Zhidk. i Gaza 4 (1994), 185-189.
22. A. Müller and R. Ettema, Dynamic response of an ice-breaker hull to ice breaking. In: Proc. IHAR Ice Symp., Hamburg II (1984), 287-296.
23. S. A. Orszag, Accurate solution of the Orr-Sommerfeld stability equation. J. Fluid Mech. 50 (1971), 689-703.
24. R. Peyret, Introduction to Spectral Methods. von Karman Institute Lecture Series 1986-04, Rhode-Saint Genese, Belgium, 1986.
25. R. M. S. M. Schulkes, R. J. Hisking and A. D. Sneyd, Waves due to a steadily moving source on a floating ice plate. Part 2. J. Fluid Mech. 180 (1987), 297-318.
26. V. A. Squire, On the critical angle for ocean waves entering shore fast ice. Cold Reg. Sci. Tech. 10 (1984), 59-68.
27. J. J. Stocker, Water Waves. Wiley-Interscience 1957.
28. E. O. Tuck, An inviscid theory for sliding flexible sheets. J. Austral. Math. Soc. B23 (1982), 403-415.