scholarly journals Cloaking of a vertical cylinder in waves using variable bathymetry

2014 ◽  
Vol 750 ◽  
pp. 124-143 ◽  
Author(s):  
R. Porter ◽  
J. N. Newman
Keyword(s):  
Gravity Waves ◽  
Wave Equations ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Dimensional Problem ◽  
Practical Application ◽  
Surface Gravity Waves ◽  
Dimensional Boundary ◽  
Drift Force ◽  
Numerical Optimisation

AbstractThe paper describes a process which allows a vertical circular cylinder subject to plane monochromatic surface gravity waves to appear invisible to the far-field observer. This is achieved by surrounding the cylinder with an annular region of variable bathymetry. Two approaches are taken to investigate this effect. First a mild-slope approximation is applied to the governing linearised three-dimensional water wave equations to formulate a depth-averaged two-dimensional wave equation with varying wavenumber over the variable bathmetry. This is then solved by formulating a domain integral equation, solved numerically by discretisation. For a given set of geometrical and wave parameters, the bathymetry is selected by a numerical optimisation process and it is shown that the scattering cross-section is reduced towards zero with increasing refinement of the bathymetry. A fully three-dimensional boundary-element method, based on the WAMIT solver (see www.wamit.com) but adapted here to allow for depressions in the bed, is used to assess the accuracy of the mild-slope results and then further numerically optimise the bathymetry towards a cloaking structure. Numerical results provide strong evidence that perfect cloaking is possible for the fully three-dimensional problem. One practical application of the results is that cloaking implies a reduced mean drift force on the cylinder.

scholarly journals TOMOGRAPHY OF THE SOLAR INTERIOR

2006 ◽  
Vol 21 (22) ◽  
pp. 1701-1715 ◽  
Author(s):  
L. GIZON
Keyword(s):  
Gravity Waves ◽  
Acoustic Waves ◽  
Solar Surface ◽  
Three Dimensional ◽  
Magnetic Activity ◽  
Solar Interior ◽  
Turbulent Convection ◽  
Convective Structures ◽  
Surface Gravity Waves ◽  
Rich Spectrum

Solar oscillations consist of a rich spectrum of internal acoustic waves and surface gravity waves, stochastically excited by turbulent convection. They have been monitored almost continuously over the last ten years with high-precision Doppler images of the solar surface. The purpose of helioseismology is to retrieve information about the structure and the dynamics of the solar interior from the frequencies, phases and amplitudes of solar waves. Methods of analysis are being developed to make three-dimensional images of subsurface motions and temperature inhomogeneities in order to study convective structures and regions of magnetic activity, like sunspots.

scholarly journals Scattering of gravity waves by a periodically structured ridge of finite extent

2019 ◽  
Vol 871 ◽  
pp. 350-376 ◽  
Author(s):  
Agnès Maurel ◽  
Kim Pham ◽  
Jean-Jacques Marigo
Keyword(s):  
Gravity Waves ◽  
Time Domain ◽  
Water Waves ◽  
Classical Result ◽  
Water Channel ◽  
Three Dimensional ◽  
Dimensional Problem ◽  
Homogenized Model ◽  
The Time Domain ◽  
Finite Extent

We study the propagation of water waves over a ridge structured at the subwavelength scale using homogenization techniques able to account for its finite extent. The calculations are conducted in the time domain considering the full three-dimensional problem to capture the effects of the evanescent field in the water channel over the structured ridge and at its boundaries. This provides an effective two-dimensional wave equation which is a classical result but also non-intuitive transmission conditions between the region of the ridge and the surrounding regions of constant immersion depth. Numerical results provide evidence that the scattering properties of a structured ridge can be strongly influenced by the evanescent fields, a fact which is accurately captured by the homogenized model.

Acoustic radiation by ocean surface waves

2000 ◽  
Vol 415 ◽  
pp. 1-21 ◽  
Author(s):  
STEVE ARENDT ◽  
DAVID C. FRITTS
Keyword(s):  
Surface Waves ◽  
Gravity Waves ◽  
Acoustic Waves ◽  
Acoustic Radiation ◽  
Three Dimensional ◽  
Phase Speed ◽  
Ocean Surface ◽  
Surface Gravity ◽  
Ocean Surface Waves ◽  
Surface Gravity Waves

We calculate the radiation of acoustic waves into the atmosphere by surface gravity waves on the ocean surface. We show that because of the phase speed mismatch between surface gravity waves and acoustic waves, a single surface wave radiates only evanescent acoustic waves. However, owing to nonlinear terms in the acoustic source, pairs of ocean surface waves can radiate propagating acoustic waves if the two surface waves propagate in almost equal and opposite directions. We derive an analytic expression for the acoustic radiation by a pair of ocean surface waves, and then extend the result to the case of an arbitrary spectrum of ocean surface waves. We present some examples for both the two-dimensional and three-dimensional regimes. Of particular note are the findings that the efficiency of acoustic radiation increases at higher wavenumbers, and the fact that the directionality of the acoustic radiation is often independent of the shape of the spectrum.

scholarly journals Boundary element method for internal axisymmetric flow

1999 ◽  
Vol 5 (1) ◽  
pp. 55-81
Author(s):  
Alexander Gokhman ◽  
Dmitry Gokhman
Keyword(s):  
Boundary Element ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Velocity Fields ◽  
Fast Method ◽  
Dimensional Problem ◽  
Practical Application ◽  
Element Technique ◽  
Conditions At Infinity ◽  
Boundary Element Technique

We present an accurate fast method for the computation of potential internal axisymmetric flow based on the boundary element technique. We prove that the computed velocity field asymptotically satisfies reasonable boundary conditions at infinity for various types of inlet/exit. Computation of internal axisymmetric potential flow is an essential ingredient in the three-dimensional problem of computation of velocity fields in turbomachines. We include the results of a practical application of the method to the computation of flow in turbomachines of Kaplan and Francis types.

scholarly journals TIDAL INLET CURRENT--OCEAN WAVE INTERACTION

1972 ◽  
Vol 1 (13) ◽  
pp. 33 ◽  
Author(s):  
Lyndell Z. Hales ◽  
John B. Herbich
Keyword(s):  
Gravity Waves ◽  
Functional Relationship ◽  
Three Dimensional ◽  
Wave Interaction ◽  
Tidal Inlet ◽  
Surface Gravity Waves ◽  
Wave Characteristics ◽  
Wave Basin ◽  
Ocean Region ◽  
A Current

An experimental study was conducted in a three-dimensional wave basin to investigate the manner in which surface gravity waves propagating toward a tidal inlet are altered. Dimensional analysis of the pertinent variables indicates that a functional relationship exists between as many as five dimensionless terms, and the functional relationship is displayed in graphical non-dimensional form to apply to all scales. Results indicate the ebb current increases the steepness in the ocean region to such an extent that the wave begins to lose energy by the crest spilling down the front of the wave, and the wave characteristics in the inlet proper may never reach the breaking limit unless factors other than a current alone are involved.

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