Author

# G. Alker

Bio: G. Alker is an academic researcher from Imperial College London. The author has contributed to research in topics: Asymptotic expansion & Free surface. The author has an hindex of 1, co-authored 1 publications receiving 7 citations.

Topics: Asymptotic expansion, Free surface, Amplitude, Cylinder, Surface wave

##### Papers

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TL;DR: In this paper, it was proved that there are no eigensolutions of the infinite vertical barrier problem containing waves which are purely outgoing, and it was shown how this can be used to predict the wave amplitude to a higher order than that of the matching solution.

Abstract: A long circular cylinder half immersed in the free surface of an ideal fluid undergoes small time periodic motions. The method of matched asymptotic expansions is used to give a solution in the high frequency limit. Of particular interest are the surface waves generated by this motion, and a three term asymptotic series for their amplitude is found. It is proved that there are no eigensolutions of the infinite vertical barrier problem containing waves which are purely outgoing, and it is shown how this can be used to predict the wave amplitude to a higher order than that of the matching solution.

7 citations

TL;DR: In this paper , the synchronous enhancem ent of Ca II H & K was detected with the short-period planetary orbit in H D 179949 and was consistent with planet-induced chrom ospheric heating by agnetic rather than tidal interaction.

Abstract: W e have detected the synchronous enhancem ent ofCa II H & K em ission with the short-period planetary orbit in H D 179949. H igh-resolution spectra taken on threeobserving runsextending m orethan a yearshow theenhancem ent coincides with (cid:30) (cid:24) 0 (the sub-planetary point) ofthe 3.093-day orbit with the e(cid:11)ect persisting for m ore than 100 orbits. The synchronous enhancem ent is consistent with planet-induced chrom ospheric heating by m agnetic rather than tidalinteraction.Som ethingwhich can only becon(cid:12)rm ed by furtherobservations. Independentobservationsareneeded to determ ine whetherthestellarrotation is sychronous with the planet’s orbit. O fthe (cid:12)ve 51 Peg-type system s m onitored, H D 179949 showsthegreatestchrom ospheric H & K activity.Three othersshow signi(cid:12)cant nightly variations but the lack of any phase coherence prevents us saying whetherthe activity isinduced by the planet.O urtwo standards, (cid:28) Ceti no such

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TL;DR: In this paper, the problem of the scattering of a surface wave in a nonviscous, incompressible fluid of infinite depth by a fully submerged, rigid, stationary sphere has been reduced to the solution of an infinite set of linear algebraic equations for the expansion coefficients in spherical harmonics of the velocity potential.

Abstract: The problem of the scattering of a surface wave in a nonviscous, incompressible fluid of infinite depth by a fully submerged, rigid, stationary sphere has been reduced to the solution of an infinite set of linear algebraic equations for the expansion coefficients in spherical harmonics of the velocity potential. These equations are easily solved numerically, so long as the sphere is not too close to the surface. The approach has been to formulate the problem as an integral equation, expand the Green's function, the velocity potential of the incident wave, and the total velocity potential in spherical harmonics, impose the boundary condition at the surface of the sphere, and carry out the integrations. The scattering cross section has been evaluated numerically and is shown to peak for values of the product of radius and wave number somewhat less than unity. Also, the Born approximation to the cross section is obtained in closed form.

17 citations

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5 citations

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TL;DR: In this paper, the authors extend the known asymptotic forms, in heave and sway, of the wave amplitude radiated by bodies at high frequency to other geometries by way of the solution of certain potential problems.

Abstract: The aim of this work is to extend the known asymptotic forms, in heave and sway, of the wave amplitude radiated by bodies at high frequency. Both two- and three-dimensional geometries will be considered, the prototype problems being the circular cylinder and sphere respectively, each with its centre in the mean free surface. The method is, in principle, applicable to other geometries by way of the solution of certain potential problems much simpler than the finite-frequency surface-wave problem.

4 citations

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TL;DR: In this article, matched asymptotic expansions were used to extend the short-wave transmission coefficient T by the addition of the terms of order 1/N 5, (log N ) 2 /N 6 and log N / N 6 as N → ∞ (where N = the length of the cylinder radius).

Abstract: The method of matched asymptotic expansions is used to extend the short-wave asymptotics of the transmission coefficient T by the addition of the terms of order 1/ N 5 , (log N ) 2 / N 6 and log N / N 6 as N → ∞ (where N = wavenumber times cylinder radius). The result is the formula
\begin{eqnarray*}
T &=& \frac{2{\rm i}}{\pi N^4}\exp (-2{\rm i}N)\left[1+\frac{4\log N}{\pi N}-\frac{4}{\pi N} \bigg(2-\gamma-\log 2+\frac{{\rm i}\pi}{8}\bigg)+\frac{8(\log N)^2}{\pi^2N^2}\right.\\
&& \left.-\frac{8\log N}{\pi^2N^2}\bigg(5-2\gamma - \log 4+\frac{{\rm i}\pi}{4}\bigg)\right] + O\bigg(\frac{1}{N^6}\bigg)\quad {\rm as}\;N\rightarrow \infty
\end{eqnarray*} (where γ = Euler's constant). The first term above is that derived rigorously by Ursell (1961) using an integral-equation method; the second term is that added by Leppington (1973) using matched asymptotic expansions; and the next three terms are those derived in this paper. Significant agreement between numerical values of T obtained from the completed fifth-order asymptotics and those obtained using Ursell's multipole expansions is demonstrated for 8 [les ] N [les ] 20 (table 2). The extensions of the perturbation expansions for the potential in the various fluid sub-domains (used in the method of matched expansions) provide some interesting cross-checks, between the solutions for potentials occurring later in the series and determined at advanced matching stages, with those for potentials occurring earlier on and determined independently at an earlier stage in the matching process. Some examples are given.

1 citations