scholarly journals A General Spectral Approach to the Time-Domain Evolution of Linear Water Waves Impacting on a Vertical Elastic Plate

2010 ◽  
Vol 70 (7) ◽  
pp. 2308-2328 ◽  
Author(s):  
Malte A. Peter ◽  
Michael H. Meylan
Keyword(s):  
Elastic Plate ◽  
Time Domain ◽  
Water Waves ◽  
Spectral Approach ◽  
Domain Evolution ◽  
The Time Domain ◽  
Vertical Elastic Plate ◽  
Linear Water Waves

scholarly journals Generalized eigenfunction method for floating bodies

2011 ◽  
Vol 667 ◽  
pp. 544-554 ◽  
Author(s):  
COLM J. FITZGERALD ◽  
MICHAEL H. MEYLAN
Keyword(s):  
Time Domain ◽  
Water Waves ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Two Dimensions ◽  
Floating Body ◽  
Floating Bodies ◽  
Abstract Wave Equation ◽  
Generalized Eigenfunction ◽  
The Time Domain

We consider the time domain problem of a floating body in two dimensions, constrained to move in heave and pitch only, subject to the linear equations of water waves. We show that using the acceleration potential, we can write the equations of motion as an abstract wave equation. From this we derive a generalized eigenfunction solution in which the time domain problem is solved using the frequency-domain solutions. We present numerical results for two simple cases and compare our results with an alternative time domain method.

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.

The singularity expansion method and near-trapping of linear water waves

2014 ◽  
Vol 755 ◽  
pp. 230-250 ◽  
Author(s):  
Michael H. Meylan ◽  
Colm J. Fitzgerald
Keyword(s):  
Water Waves ◽  
Expansion Method ◽  
Rigid Bodies ◽  
Trapped Modes ◽  
Trapped Mode ◽  
Generalized Eigenfunction ◽  
The Time Domain ◽  
Eigenfunction Method ◽  
Time Dependent Solution ◽  
Linear Water Waves

AbstractThe problem of near-trapping of linear water waves in the time domain for rigid bodies or variations in bathymetry is considered. The singularity expansion method (SEM) is used to give an approximation of the solution as a projection onto a basis of modes. This requires a modification of the method so that the modes, which grow towards infinity, can be correctly normalized. A time-dependent solution, which allows for possible trapped modes, is introduced through the generalized eigenfunction method. The expression for the trapped mode and the expression for the near-trapped mode given by the SEM are shown to be closely connected. A numerical method that allows the SEM to be implemented is also presented. This method combines the boundary element method with an eigenfunction expansion, which allows the solution to be extended analytically to complex frequencies. The technique is illustrated by numerical simulations for geometries that support near-trapping.

scholarly journals Micromagnetic analysis of dynamical bubble-like solitons based on the time domain evolution of the topological density

2014 ◽  
Vol 115 (17) ◽  
pp. 17D139 ◽  
Author(s):  
Vito Puliafito ◽  
Luis Torres ◽  
Ozhan Ozatay ◽  
Thomas Hauet ◽  
Bruno Azzerboni ◽  
...  
Keyword(s):  
Time Domain ◽  
Domain Evolution ◽  
The Time Domain ◽  
Topological Density

Linear water waves: the horizontal motion of a structure in the time domain

2012 ◽  
Vol 709 ◽  
pp. 289-312 ◽  
Author(s):  
P. McIver
Keyword(s):  
Time Domain ◽  
Water Waves ◽  
Initial Conditions ◽  
Horizontal Motion ◽  
Floating Structure ◽  
Start Up ◽  
Specific Calculations ◽  
Linearized Theory ◽  
Infinitesimal Disturbance ◽  
The Time Domain

AbstractThe framework of the linearized theory of water waves in the time domain is used to examine the horizontal motion of an unrestrained floating structure. One of the principal assumptions of the theory is that an infinitesimal disturbance of the rest state will lead to an infinitesimal motion of the fluid and structure. It has been known for some time that for some initial conditions the theory predicts an unbounded horizontal motion of the structure that violates this assumption, but the possibility does not appear to have been examined in detail. Here some circumstances that lead to predictions of large motions are identified and, in addition, it is shown that not all non-trivial initial conditions lead to violations of the assumptions. In particular, it is shown that the horizontal motion of a floating structure remains bounded when it is initiated by the start up of a separate wave maker. The general discussion is supported by specific calculations for a vertical circular cylinder.

Measurement of PMD using the time-domain evolution of the Stokes vector

2012 ◽  
Author(s):  
T. Anderson ◽  
S. Chen ◽  
D. Hewitt ◽  
A. Tran ◽  
D. Beaman ◽  
...  
Keyword(s):  
Time Domain ◽  
Stokes Vector ◽  
Domain Evolution ◽  
The Time Domain

scholarly journals Time-Dependent Motion of a Floating Circular Elastic Plate

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 29
Author(s):  
Michael H. Meylan
Keyword(s):  
Elastic Plate ◽  
Time Domain ◽  
Single Frequency ◽  
Complex Motion ◽  
Matching Method ◽  
Gaussian Profile ◽  
Focused Wave ◽  
The Time Domain ◽  
Incident Waves ◽  
Focused Wave Group

The motion of a circular elastic plate floating on the surface is investigated in the time-domain. The solution is found from the single frequency solutions, and the method to solve for the circular plate is given using the eigenfunction matching method. Simple plane incident waves with a Gaussian profile in wavenumber space are considered, and a more complex focused wave group is considered. Results are given for a range of plate and incident wave parameters. Code is provided to show how to simulate the complex motion.

scholarly journals Time-Dependent Motion of a Floating Circular Elastic Plate

2020 ◽  
Author(s):  
Michael Meylan
Keyword(s):  
Elastic Plate ◽  
Time Domain ◽  
Single Frequency ◽  
Complex Motion ◽  
Matching Method ◽  
Gaussian Profile ◽  
Focused Wave ◽  
The Time Domain ◽  
Incident Waves ◽  
Focused Wave Group

The motion of a circular elastic plate floating on the surface is investigated in the time–domain. The solution is found from the single frequency solutions and the method to solve for the circular plate is given using the eigenfunction matching method. Simple plane incident waves with a Gaussian profile in wavenumber space are considered and a more complex focused wave group is considered. Results are given for a range of plate and incident wave parameters are investigated. Code is provided to show how to simulate the complex motion.

Scattering of water waves by a submerged thin vertical elastic plate

2013 ◽  
Vol 84 (2) ◽  
pp. 207-217 ◽  
Author(s):  
Rumpa Chakraborty ◽  
B. N. Mandal
Keyword(s):  
Elastic Plate ◽  
Water Waves ◽  
Vertical Elastic Plate
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