Oblique wave scattering by a circular cylinder submerged beneath an ice-cover (original) (raw)
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Water wave scattering by a nearly circular cylinder submerged beneath an ice-cover
Journal of Marine Science and Application, 2015
Assuming linear theory, the two-dimensional problem of water wave scattering by a horizontal nearly circular cylinder submerged in infinitely deep water with an ice cover modeled as a thin-elastic plate floating on water, is investigated here. The cross-section of the nearly circular cylinder is taken as r=a(1+δC(θ)), where a is the radius of the corresponding circular cross-section of the cylinder, δ is a measure of small departure of the cross-section of the cylinder from its circularity and C(θ) is the shape function. Using a simplified perturbation technique the problem is reduced to two independent boundary value problems up to first order in δ. The first one corresponds to water wave scattering by a circular cylinder submerged in water with an ice-cover, while the second problem describes wave radiation by a submerged circular cylinder and involves first order correction to the reflection and transmission coefficients. The corrections are obtained in terms of integrals involving the shape function. Assuming a general Fourier expansion of the shape function, these corrections are evaluated approximately. It is well known that normally incident wave trains experience no reflection by a circular cylinder submerged in infinitely deep water with an ice cover. It is shown here that the reflection coefficient also vanishes up to first order for some particular choice of the shape function representing a nearly circular cylinder. For these cases, full transmission occurs, only change is in its phase which is depicted graphically against the wave number in a number of figures and appropriate conclusions are drawn.
Wave scattering by a circular cylinder half-immersed in water with an ice-cover
International Journal of Engineering Science, 2009
The problem of scattering of water waves obliquely incident on a fixed long circular cylinder half-immersed in deep water with an ice-cover is investigated here. The ice-cover is modelled as an elastic plate of very small thickness. The problem is formulated using the method of multipoles. This leads to an infinite system of linear equations which are solved numerically by truncation. The reflection and transmission coefficients are obtained and depicted graphically against the wave number for various values of the angle of incidence and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. The effect of ice-cover is seen to increase the reflection coefficient and to decrease the transmission coefficient.
Wave scattering by a horizontal circular cylinder in a two-layer fluid with an ice-cover
International Journal of Engineering Science, 2007
In a two-layer fluid wherein the upper layer is of finite depth and bounded above by a thin but uniform layer of icecover modelled as a thin elastic sheet and the lower layer is infinitely deep below the interface, time-harmonic waves with a given frequency can propagate with two different wavenumbers. The wave of smaller wavenumber propagates along the ice-cover while wave of higher wavenumber propagates along the interface. In this paper problems of wave scattering by a horizontal circular cylinder submerged in either the lower or in the upper layer due to obliquely as well as normally incident wave trains of both the wave numbers are investigated by using the method of multipole expansions. The effect of the presence of ice-cover on the various reflection and transmission coefficients due to incident waves at the ice-cover and the interface is depicted graphically in a number of figures.
Scattering of water waves by thin vertical plate submerged below ice-cover surface
Applied Mathematics and Mechanics-english Edition, 2011
The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of a hypersingular integral equation by a suitable application of Green's integral theorem in terms of difference of potential functions across the barrier. This integral equation is solved by a collocation method using a finite series involving Chebyshev polynomials. Reflection and transmission coefficients are obtained numerically and presented graphically for various values of the wave number and ice-cover parameter.
Wave scattering by a thin vertical barrier submerged beneath an ice-cover in deep water
Applied Ocean Research, 2010
The two-dimensional problem of water wave scattering by a thin inclined semi-infinite rigid barrier submerged in infinitely deep water covered by a thin uniform ice sheet modelled as an elastic plate, is investigated here. It is formulated in terms of a hypersingular integral equation for the discontinuity of the potential function across the barrier. The integral equation is solved numerically by approximating the discontinuity by a finite series involving Chebyshev polynomials of second kind multiplied by an appropriate weight function. The reflection and transmission coefficients are obtained approximately and their numerical estimates for the vertical barrier for different values of the ice-cover parameters and the wave number are found. In the absence of the ice-cover, known results for a free surface are recovered. The reflection and transmission coefficients for the vertical barrier are depicted graphically against the wave number for various values of the ice-cover parameters.
Scattering of water waves by thick rectangular barriers in presence of ice cover
Journal of Ocean Engineering and Science, 2020
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2013
for the 29th Intl Workshop on Water Waves and Floating Bodies, Osaka (Japan), March 30 –April 02, 2014 Radiation of Waves by a Cylinder Submerged in the Fluid beneath an Elastic Ice Sheet with a Partially Frozen Crack by I.V. Sturova Lavrentyev Institute of Hydrodynamics of SB RAS, pr. Lavrentyeva 15, Novosibirsk, 630090, Russia E-mail: sturova@hydro.nsc.ru Highlights: • Using the method of matched eigenfunction expansions for the velocity potentials, the mathematical problem is handled for solution. • Reciprocity relations are newly found which relate the damping coefficients of the submerged body to the far-field form of the radiation potentials.
Oblique wave scattering by undulations on the bed of an ice-covered ocean
Archives of Mechanics, 2004
The problem of oblique wave scattering by cylindrical undulations on the bed of an ice-covered ocean is investigated by using a simplified perturbation analysis. The first-order potential function satisfies a boundary value problem (BVP) which is solved by employing the Green integral theorem after constructing an appropriate Green function. Analytical expressions for the first-order reflection and transmission coefficients are then obtained from the solution of this BVP, in terms of the integrals involving the shape function describing undulations. Three particular forms of the shape function are considered for which the reflection and transmission coefficients up to the first-order are obtained exactly.
Scattering of surface waves by a vertical truncated structured cylinder
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2022
This paper describes the solution to the problem of scattering of plane incident waves on water of constant depth by a bottom mounted circular cylinder, extending partially through the depth, which has an internal structure comprised of closely spaced thin vertical barriers between which fluid is allowed to flow. The problem is solved under full depth-dependent linearized water wave theory using an effective medium equation to describe the fluid motion in cylinder and effective boundary conditions to match that flow to the fluid region outside the cylinder. The interest in this problem lies in the development of novel solution methods for fully three-dimensional water wave interaction with bathymetric plate arrays. Results computed using this theory are compared with a shallow water approximation based on the recent work of Marangos & Porter (2021 Shallow water theory for structured bathymetry. Proc. R. Soc. A 477 , 20210421.) and with accurate computations of an exact representatio...
Oblique incidence of surface waves on an elastic plate
Journal of Applied Mechanics and Technical Physics, 1999
Some of the authors of this publication are also working on these related projects: Behavior of restricted ice cover under local dynamic load View project Izolda V. Sturova Russian Academy of Sciences 75 PUBLICATIONS 337 CITATIONS SEE PROFILE All content following this page was uploaded by Izolda V. Sturova on 22 September 2014. The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately.