Generation of internal gravity waves by an oscillating horizontal disc

Martin, P. A.; Smith, Stefan G. Llewellyn

doi:10.1098/rspa.2011.0193

Cited by 14 publications

(12 citation statements)

References 23 publications

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“…This is our radiation condition. It has been used previously [3,24], and it has been shown to be consistent with causality in the time-domain [21]. As a result,…”

mentioning

confidence: 79%

“…The total energy transported away, E out , is found by integrating over the beam cross-section [21,31]: The remaining integral is (4/a)K(k) sec θ c using (6.3), whence E out = E in (see (8.2)), as expected. We conclude by noting that results for a circular piston are readily obtained by setting a = b (k = 0).…”

Section: 7] Givesmentioning

confidence: 98%

“…In the far field, the time-averaged energy transport vector is Iζ, with I = (ρ 0 /2)Re {pv } [21,31]. Substituting for p and v gives…”

mentioning

confidence: 99%

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Generation of Internal Gravity Waves by an Oscillating Horizontal Elliptical Plate

Martin¹,

Smith²

2012

SIAM J. Appl. Math.

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Abstract. Time-harmonic oscillations of a horizontal plate generate internal gravity waves in an unbounded stratified fluid. A plane-wave (Fourier) decomposition is used in which waves with outgoing group velocity are selected. The pressure and the velocity in the far field are estimated in terms of the Fourier transform of the pressure jump across the plate. Explicit solutions are obtained for arbitrary prescribed motions of an elliptical plate. Energy is confined to certain wave beams, bounded by conical characteristic surfaces of the underlying hyperbolic partial differential equation; the solution itself is not axisymmetric. The details of the beam structure are complicated (because each characteristic surface has a vertical axis of symmetry, whereas the elliptical plate does not), but they emerge naturally from the asymptotic method, a method that has wider applicability. Results for analogous piston problems are also obtained; these problems arise when a piece of a rigid horizontal plane is forced to oscillate, thus generating waves above the plane.

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“…This is our radiation condition. It has been used previously [3,24], and it has been shown to be consistent with causality in the time-domain [21]. As a result,…”

mentioning

confidence: 79%

Section: 7] Givesmentioning

confidence: 98%

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Generation of Internal Gravity Waves by an Oscillating Horizontal Elliptical Plate

Martin¹,

Smith²

2012

SIAM J. Appl. Math.

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“…Earlier, efforts were made to remove the logarithmic singularity embedded in the integral representation (22) before applying the final boundary condition. As a result the integro-differential operator K emerged in (30) having a singular component and a regular part.…”

Section: Methodsmentioning

confidence: 99%

Linearised water wave problems involving submerged horizontal plates

Porter

2015

Applied Ocean Research

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“…Furthermore, results show that the system of equations converges rapidly with increasing truncation size. This general approach forms the basis of recent work on similar problems involving submerged plates by [7] and has similarities to work by [8] for radiation of internal gravity waves by discs oscillating in a stratified fluid and [9] for scattering of surface waves by cracks in elastic solids.…”

Section: Introductionmentioning

confidence: 99%

Surface wave interaction with rigid plates lying on water

Porter

2016

Wave Motion

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Surface wave interaction with rigid plates lying on water Richard PorterSchool of Mathematics, University of Bristol, Bristol, BS8 1TW, UK AbstractIn this paper, a variety of problems concerned with the interaction of water waves with fixed horizontal plates lying on the surface of a fluid are investigated.Firstly, solutions are presented to the problem of the scattering of incident waves by: (i) infinitely-long plates of constant finite width (often referred to as the two-dimensional 'finite dock problem') and (ii) finite plates which are either rectangular or parallelogram-shaped. Secondly, hydrodynamic coefficients due to forced motions of plates are also considered. Finally, eigenvalue problems associated with free oscillations of the surface in long channels of uniform width and finite rectangular holes in an otherwise infinite rigid plate covering the surface are considered.A common method of solution is applied to all problems which involves using Fourier transforms to derive integral equations for unknown potentials over finite regions of space occupied by either plates or the free surface. Integral equations are converted, using the Galerkin method, into secondkind infinite systems of algebraic equations. In each problem numerical approximations to the solutions are found to converge rapidly with increasing truncation size of the infinite system making this approach both numerically efficient and accurate. Some comparisons with existing results are made, and new results for finite plates are demonstrated.

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Generation of internal gravity waves by an oscillating horizontal disc

Cited by 14 publications

References 23 publications

Generation of Internal Gravity Waves by an Oscillating Horizontal Elliptical Plate

Generation of Internal Gravity Waves by an Oscillating Horizontal Elliptical Plate

Linearised water wave problems involving submerged horizontal plates

Surface wave interaction with rigid plates lying on water

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