Nonlinear ice sheet/liquid interaction in a channel with an obstruction

Ni, Baoyu, Semenov, Yuriy, Khabakhpasheva, Tatyana ORCID:, Parau, Emilian ORCID: and Korobkin, Alexander ORCID: (2024) Nonlinear ice sheet/liquid interaction in a channel with an obstruction. Journal of Fluid Mechanics, 983. ISSN 0022-1120

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The interaction between the flow in a channel with an obstruction on the bottom and an elastic sheet representing the ice covering the liquid is considered for the case of steady flow. The mathematical model based on the velocity potential theory and the theory of thin elastic shells fully accounts for the nonlinear boundary conditions at the elastic sheet/liquid interface and on the bottom of the channel. The integral hodograph method is employed to derive the complex velocity potential of the flow, which contains the velocity magnitude at the interface in explicit form. This allows one to formulate the coupled ice/liquid interaction problem and reduce it to a system of nonlinear equations in the unknown magnitude of the velocity at the interface. Case studies are carried out for a semi-circular obstruction on the bottom of the channel. Three flow regimes are studied: a subcritical regime, for which the interface deflection decays upstream and downstream; an ice supercritical and channel subcritical regime, for which two waves of different lengths may exist; and a channel supercritical regime, for which the elastic wave is found to extend downstream to infinity. All these regimes are in full agreement with the dispersion equation. The obtained results demonstrate a strongly nonlinear interaction between the elastic and the gravity wave near the first critical Froude number where their lengths approach each other. The interface shape, the bending moment and the pressure along the interface are presented for wide ranges of the Froude number and the obstruction height.

Item Type: Article
Uncontrolled Keywords: elastic waves,surface gravity waves,wave-structure interactions,condensed matter physics,mechanics of materials,mechanical engineering,applied mathematics ,/dk/atira/pure/subjectarea/asjc/3100/3104
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Fluid and Solid Mechanics
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Depositing User: LivePure Connector
Date Deposited: 04 Apr 2024 16:31
Last Modified: 17 May 2024 16:30
DOI: 10.1017/jfm.2024.177


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