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Corrigendum. Three-dimensional interaction between uniform current and a submerged horizontal cylinder in an ice-covered channel (Journal of Fluid Mechanics (2021) 928 (A4) DOI: 10.1017/jfm.2021.792)
No full textIn the Appendix B of Yang, Wu & Ren (2021), we made the statement that the Green function G has the symmetry property with respect to the field point P(x
1, y
1, z
1) and field point P
0(x
0, y
0, z
0), or G(x
1, y
1, z
1; x
0, y
0, z
0) = G(x
0, y
0, z
0; x
1, y
1, z
1). This is not always correct. The mistake arose from the statement below (B2) that 'Although G and ξ involve only the real part, we may use the whole complex function here'. In the derivations followed, the full complex functions of G
i and ξ
i (i = 0, 1) in (B1) and (B2) were directly used without taking their real parts, which led to an incorrect conclusion. However, it should be noted that when 0 < Fn < Fn
(1)
c , G
i and ξ
i contain only the k
0 component. G
(0)
i is fully real and ξ
(0)
i is fully imaginary, and they can be taken out of the operator Re{}. Therefore, the symmetry property is satisfied within this range. In summary, the symmetry property G(x
1, y
1, z
1; x
0, y
0, z
0) = G(x
0, y
0, z
0; x
1, y
1, z
1) holds only when 0 < Fn < Fn
(1)
c, and it is incorrect when Fn > Fn
(1)
c. This mistake is confined solely to the Appendix B, and it does not affect any other formulas or results presented in the paper.</p
Surface wave interaction with floating elastic plates in channels
No full textThe interaction between surface waves and a finite rectangular floating plate in a channel is considered analytically, while the location of the plate is not restricted. The mathematical model is based on the linear velocity potential flow theory for the fluid and the Kirchhoff-Love plate theory for the plate. The problem is converted into an integral equation through using the Green function. The second-order singularity associated with a body with no thickness is treated with the Dirac delta function. The developed scheme is used for case studies of various edge constraints. Extensive results are provided for the hydrodynamic forces acting on the plate and the wave reflection and transmission coefficients. The effects of wave frequency, channel width, plate length, and edge conditions are analyzed, and their physical implications are highlighted. Significant findings comprise the highly oscillatory nature of force curves, influenced by the natural frequencies of the channels and the length of the plate, and substantial effects of edge conditions and the plate position on the results.</p
Interaction between a uniform current and a submerged cylinder in a marginal ice zone
No full textThe interaction between a uniform current with a circular cylinder submerged in a fluid covered by a semi-infinite ice sheet is considered analytically. The ice sheet is modelled as an elastic thin plate, and the fluid flow is described by the linearised velocity potential theory. The Green function or the velocity potential due to a source is first obtained. As the water surface is divided into two semi-infinite parts with different boundary conditions, the Wiener-Hopf method (WHM) offers significant advantages over alternative approaches and is consequently adopted. To do that, the distribution of the roots of the dispersion equation for fluid fully covered by an ice sheet in the complex plane is first analysed systematically, which does not seem to have been done before. The variations of these roots with the Froude number are investigated, especially their effects or factorisation and decomposition required in the WHM. The result is verified by comparing with that obtained from the matched eigenfunction expansion method. Through differentiating the Green function with respect to the source position, the potentials due to multipoles are obtained, which are employed to construct the velocity potential for the circular cylinder. Extensive results are provided for hydrodynamic forces on the cylinder and wave profiles, and some unique features are discussed. In particular, it is found that the forces can be highly oscillatory with the Froude number when the body is below the ice sheet, whereas such an oscillation does not exist when the body is below the free surface.</p
Hydroelastic wave interaction with a circular crack of an ice-cover in a channel
No full textHydroelastic wave interaction with a circular crack of an ice-cover in a channel together with some related problems is considered, based on the linearized velocity potential theory and Kirchhoff plate theory. The domain decomposition method is adopted in the solution procedure. Two sub-domains are divided by the crack, one below the inner ice sheet and the other below the outer ice sheet. By using the Green function of an ice-covered channel, the velocity potential in the outer domain is established from the source distribution formula over an artificial vertical surface extended from the crack. The source distribution is expanded in both vertical and circumferential directions, which allows the velocity potential to be obtained in an explicit form with unknown coefficients. The velocity potential in the inner domain is expanded into a double series. An orthogonal inner product is used to impose continuity conditions on the artificial vertical surface and the edge conditions at the crack. The derived formulation is not just limited to the circular crack problem but can also be readily used in a variety of other problems, including wave diffraction by a surface-piercing vertical cylinder, polynya and circular disc floating on the free surface in a channel. Extensive results are provided for the forces on the inner ice sheet, the transmission and reflection coefficients. In particular, a detailed analysis is made on their behaviours near the natural frequencies of the channel, and the natural frequencies corresponding to the motion of the inner ice sheet.</p
Hydroelastic wave diffraction by a vertical circular cylinder standing in a channel with an ice cover
Full text linkThe problem of hydroelastic wave diffraction by a surface-piercing vertical circular cylinder mounted on the bottom of an ice-covered channel is considered. The ice sheet is modelled as an elastic thin plate with homogeneous properties, while the linearized velocity potential theory is adopted to describe the motion of the fluid. The solution starts from the Green function satisfying all other boundary conditions apart from that on the body surface. This is obtained through applying a Fourier transform in the longitudinal direction of the channel and adopting an eigenfunction expansion in the vertical direction. The boundary conditions on the side walls and ice edges are imposed through an orthogonal product. Through the Green function, the velocity potential due to a surface-piercing structure with arbitrary shape can be expressed through a source distribution formula derived in this work, in which only integrals over the body surface and its interaction line with the ice sheet need to be retained. For a vertical circular cylinder, the unknown source distribution can be expanded further into a Fourier series in the circumferential direction, and then the analytical solution of the velocity potential can be obtained further. Extensive results and discussions are provided for the hydrodynamic forces and vertical shear forces on the cylinder, as well as the deflection and strain of the ice sheet. In particular, the behaviour of the solution near one of the natural frequencies of the channel is investigated in detail
Three-dimensional interaction between uniform current and a submerged horizontal cylinder in an ice-covered channel
Full text linkThe problem of interaction of a uniform current with a submerged horizontal circular cylinder in an ice-covered channel is considered. The fluid flow is described by linearized velocity potential theory and the ice sheet is treated as a thin elastic plate. The potential due to a source or the Green function satisfying all boundary conditions apart from that on the body surface is first derived. This can be used to derive the boundary integral equation for a body of arbitrary shape. It can also be used to obtain the solution due to multipoles by differentiating the Green function with its position directly. For a transverse circular cylinder, through distributing multipoles along its centre line, the velocity potential can be written in an infinite series with unknown coefficients, which can be determined from the impermeable condition on a body surface. A major feature here is that different from the free surface problem, or a channel without the ice sheet cover, this problem is fully three-dimensional because of the constraints along the intersection of the ice sheet with the channel wall. It has been also confirmed that there is an infinite number of critical speeds. Whenever the current speed passes a critical value, the force on the body and wave pattern change rapidly, and two more wave components are generated at the far-field. Extensive results are provided for hydroelastic waves and hydrodynamic forces when the ice sheet is under different edge conditions, and the insight of their physical features is discussed
Coupled free vibrations of liquid in a three-dimensional rectangular container with an elastic cover
No full textThe coupled free vibration of liquid and its elastic cover, such as a plate or a membrane, in a three-dimensional rectangular tank is investigated through an analytical scheme based on the velocity potential theory for the flow and the linear elastic theory for the cover. For the fluid domain, the velocity potential is expanded into double cosine series along the longitudinal and transverse directions, respectively, with the corresponding eigenvalues determined from the impermeable conditions on the side walls. The vertical modes of the potential are obtained from the Laplace equation. The deflection of the rectangular cover is expanded into the same double cosine series to match the potential, together with additional terms for satisfying the edge conditions. The polynomials are used for these additional terms, which are then expanded into cosine series. For the expansions of the higher-order derivatives of the deflection, the derivatives of these polynomial terms are expanded into cosine series directly, rather than being obtained through differentiating the cosine series of the deflection, to avoid the non-convergent series. Through imposing the boundary conditions on the fluid–plate interface and edge conditions, an infinite matrix equation for the unknown coefficients can be established. The natural frequencies can be obtained when the determinant of the matrix is zero. In practical computation, the infinite matrix equation is truncated into finite size. Results are first provided for natural frequencies. This is followed by the corresponding natural mode shapes and principal strains distribution on the cover. The underlying physics of these results is then provided
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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