Calculation and measurement of conical beams of three-dimensional periodic internal waves excited by a vertically oscillating piston

Bardakov, R. N.; Vasil’ev, A. Yu.; Chashechkin, Yu. D.

doi:10.1134/s0015462807040114

Cited by 18 publications

(18 citation statements)

References 6 publications

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“…Such is not the case with broadside oscillations: then viscosity is expected to play a lesser role. Inviscid calculations were presented by Sarma & Krishna (1972), Lai & Lee (1981) and Gabov & Pletner (1988), while Bardakov, Vasil'ev & Chashechkin (2007) carried out viscous experiments.…”

Section: Comparison With the Axisymmetric Casementioning

confidence: 99%

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Tangential oscillations of a circular disk in a viscous stratified fluid

Davis

Smith

2010

J. Fluid Mech.

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A complete solution is obtained for the wave field generated by the time-harmonic edgewise oscillations of a horizontal circular disk in an incompressible stratified viscous fluid. The linearized equations of viscous internal waves and the no-slip condition on the rigid disk are used to derive sets of dual integral equations for the fluid velocity and vorticity. The dual integral equations are solved by analytic reduction to sets of linear algebraic equations. Asymptotic results confirm that this edgewise motion no longer excites waves in the small-viscosity limit. Broadside oscillations and the effect of density diffusion are also considered.

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Section: Comparison With the Axisymmetric Casementioning

confidence: 99%

“…There have been some previous studies of internal waves that explicitly considered diffusion, among others Thomas & Stevenson (1973), Kistovich & Chashechkin (1995) and Bardakov et al (2007). The analysis in § § 2-5 can be carried out in an analogous fashion and only the main results are given here.…”

Section: The Effect Of Density Diffusionmentioning

confidence: 99%

Tangential oscillations of a circular disk in a viscous stratified fluid

Davis

Smith

2010

J. Fluid Mech.

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“…Mathematically, this problem is simpler than a disc problem because the velocity is prescribed over the whole plane, z = 0. See, for example, Chashechkin et al (2004) and Bardakov et al (2007); these papers include both theoretical and experimental results.…”

Section: Introductionmentioning

confidence: 99%

Generation of internal gravity waves by an oscillating horizontal disc

Martin

Smith

2011

Proc. R. Soc. A.

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Internal gravity waves are generated in a stratified fluid by arbitrary forced oscillations of a horizontal disc. The wave fields are calculated in both the time domain and the frequency domain. In the time domain, an initial-value problem is solved using Laplace transforms; causality is imposed. In the frequency domain (time-harmonic oscillations), a radiation condition is imposed: a plane-wave (Fourier) decomposition is used in which waves with outgoing group velocity are selected. It is shown that both approaches lead to the same solution, once transient effects are ignored. Then, a method is given for calculating the far-field, using asymptotic approximations of double integrals. It is shown that the total energy flux is outwards, for arbitrary forcings of the disc. Further investigations of energy transport are made with a view to clarifying the nature of radiation conditions in the frequency domain.

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“…It can also be used for "piston problems," where fluid occupies the region z > 0 above a rigid floor in which is mounted an oscillating vibrator or piston. Such problems have been studied extensively by Chashechkin and his colleagues [2,6,7,28,29]. They are easier to solve, formally, because the normal velocity is prescribed everywhere over the plane z = 0, whereas the plate problem leads to a mixed boundary-value problem.…”

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confidence: 99%

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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Calculation and measurement of conical beams of three-dimensional periodic internal waves excited by a vertically oscillating piston

Cited by 18 publications

References 6 publications

Tangential oscillations of a circular disk in a viscous stratified fluid

Tangential oscillations of a circular disk in a viscous stratified fluid

Generation of internal gravity waves by an oscillating horizontal disc

Generation of Internal Gravity Waves by an Oscillating Horizontal Elliptical Plate

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