scholarly journals Relation between orbital velocities, pressure and surface elevation in non-linear nearshore water waves

2021 ◽  
Author(s):  
Kévin Martins ◽  
Philippe Bonneton ◽  
David Lannes ◽  
Hervé Michallet
Keyword(s):  
Free Surface ◽  
Surface Energy ◽  
Water Waves ◽  
Energy Levels ◽  
Sea Surface ◽  
Surface Elevation ◽  
Linear Wave ◽  
Free Surface Elevation ◽  
High Frequencies ◽  
Non Linear

AbstractThe inability of the linear wave dispersion relation to characterize the dispersive properties of non-linear shoaling and breaking waves in the nearshore has long been recognised. Yet, it remains widely used with linear wave theory to convert between sub-surface pressure, wave orbital velocities and the free surface elevation associated with non-linear nearshore waves. Here, we present a non-linear fully dispersive method for reconstructing the free surface elevation from sub-surface hydrodynamic measurements. This reconstruction requires knowledge of the dispersive properties of the wave field through the dominant wavenumbers magnitude κ, representative in an energy-averaged sense of a mixed sea-state composed of both free and forced components. The present approach is effective starting from intermediate water depths - where non-linear interactions between triads intensify - up to the surf zone, where most wave components are forced and travel approximately at the speed of non-dispersive shallow-water waves. In laboratory conditions, where measurements of κ are available, the non-linear fully dispersive method successfully reconstructs sea-surface energy levels at high frequencies in diverse non-linear and dispersive conditions. In the field, we investigate the potential of a reconstruction that uses a Boussinesq approximation of κ, since such measurements are generally lacking. Overall, the proposed approach offers great potential for collecting more accurate measurements under storm conditions, both in terms of sea-surface energy levels at high frequencies and wave-by-wave statistics (e.g. wave extrema). Through its control on the efficiency of non-linear energy transfers between triads, the spectral bandwidth is shown to greatly influence non-linear effects in the transfer functions between sub-surface hydrodynamics and the sea-surface elevation.

scholarly journals Application of photogrammetry for spatial free surface elevation and velocity measurement in wave flumes

2018 ◽  
Vol 233 (3) ◽  
pp. 905-917
Author(s):  
Alan Fleming ◽  
Brian Winship ◽  
Gregor Macfarlane
Keyword(s):  
Free Surface ◽  
Ultraviolet Light ◽  
Water Surface ◽  
Surface Elevation ◽  
Linear Wave ◽  
Good Resolution ◽  
Free Surface Elevation ◽  
Pass Filter ◽  
Large Measurement ◽  
Measurement Area

This article presents a method for obtaining the spatial free surface elevation and velocity field for the water surface in a wave flume over a relatively large measurement area for this type of application (approximately 1.5 m × 1.5 m). The technique employs proprietary videogrammetry software to post-process stereo images captured by multiple synchronised machine vision cameras. Dimensional resolution and other limitations are similar to that experienced for particle imaging velocimetry systems ( x, y resolution of 2 mm). Imaging of the free surface was enabled by the use of millions of bespoke slightly positively buoyant fluorescent flakes. Ultraviolet light was used as the primary light source to excite the fluorescent flakes. Reflected ultraviolet light was attenuated by a high-pass filter fitted to the cameras so that only the emitted light from the fluorescent flakes was visible. The software was validated using a simple linear translation experiment. An application is demonstrated for the radiated wave field generated from a submerged sinusoidal heaving sphere for two cases: one single and five consecutive oscillations. Results agree with linear wave theory which indicates that the floating flakes had minimal impact on the water surface particle motion at the scale tested. It is, therefore, concluded that spatial measurement of the free surface elevation and velocity using the method presented has good resolution over a large measurement field. The flakes were found to follow the free surface well, but the measurement area is constrained to where the pattern of flakes exists in the image. Hence, application of floating markers is not suitable for experiments with significant outflow/upwelling which would wash away the floating markers from the intended measurement area.

Numerical Investigation of Focused Waves and Their Interaction With a Vertical Cylinder Using REEF3D

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Hans Bihs ◽  
Mayilvahanan Alagan Chella ◽  
Arun Kamath ◽  
Øivind Asgeir Arntsen
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Free Surface Flows ◽  
Surface Elevation ◽  
Numerical Wave Tank ◽  
Free Surface Elevation ◽  
Wave Tank ◽  
Numerical Wave ◽  
Focused Wave ◽  
The Impact

For the stability of offshore structures, such as offshore wind foundations, extreme wave conditions need to be taken into account. Waves from extreme events are critical from the design perspective. In a numerical wave tank, extreme waves can be modeled using focused waves. Here, linear waves are generated from a wave spectrum. The wave crests of the generated waves coincide at a preselected location and time. Focused wave generation is implemented in the numerical wave tank module of REEF3D, which has been extensively and successfully tested for various wave hydrodynamics and wave–structure interaction problems in particular and for free surface flows in general. The open-source computational fluid dynamics (CFD) code REEF3D solves the three-dimensional Navier–Stokes equations on a staggered Cartesian grid. Higher order numerical schemes are used for time and spatial discretization. For the interface capturing, the level set method is selected. In order to test the generated waves, the time series of the free surface elevation are compared with experimental benchmark cases. The numerically simulated free surface elevation shows good agreement with experimental data. In further computations, the impact of the focused waves on a vertical circular cylinder is investigated. A breaking focused wave is simulated and the associated kinematics is investigated. Free surface flow features during the interaction of nonbreaking focused waves with a cylinder and during the breaking process of a focused wave are also investigated along with the numerically captured free surface.

Nonlinear Wave Crest Distribution on a Vertical Breakwater

2018 ◽  
Author(s):  
Valentina Laface ◽  
Giovanni Malara ◽  
Felice Arena ◽  
Ioannis A. Kougioumtzoglou ◽  
Alessandra Romolo
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Vertical Wall ◽  
Surface Elevation ◽  
Wave Crest ◽  
Height Distribution ◽  
Free Surface Elevation ◽  
Pressure Transducers ◽  
Pressure Time ◽  
Time Histories

The paper addresses the problem of deriving the nonlinear, up to the second order, crest wave height probability distribution in front of a vertical wall under the assumption of finite spectral bandwidth, finite water depth and long-crested waves. The distribution is derived by relying on the Quasi-Deterministic representation of the free surface elevation in front of the vertical wall. The theoretical results are compared against experimental data obtained by utilizing a compressive sensing algorithm for reconstructing the free surface elevation in front of the wall. The reconstruction is pursued by starting from recorded wave pressure time histories obtained by utilizing a row of pressure transducers located at various levels. The comparison shows that there is an excellent agreement between the proposed distribution and the experimental data and confirm the deviation of the crest height distribution from the Rayleigh one.

scholarly journals On generation and propagation of tsunamis in a shallow running ocean

1978 ◽  
Vol 1 (3) ◽  
pp. 373-390
Author(s):  
Lokenath Debnath ◽  
Uma Basu
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Relative Magnitude ◽  
Ocean Floor ◽  
Surface Elevation ◽  
Free Surface Elevation ◽  
Surface Disturbance ◽  
Fourier And Laplace Transforms ◽  
The Given ◽  
Integral Solutions

A theory is presented of the generation and propagation of the two and the three dimensional tsunamis in a shallow running ocean due to the action of an arbitrary ocean floor or ocean surface disturbance. Integral solutions for both two and three dimensional problems are obtained by using the generalized Fourier and Laplace transforms. An asymptotic analysis is carried out for the investigation of the principal features of the free surface elevation. It is found that the propagation of the tsunamis depends on the relative magnitude of the given speed of the running ocean and the wave speed of the shallow ocean. When the speed of the running ocean is less than the speed of the shallow ocean wave, both the two and the three dimensional free surface elevation represent the generation and propagation of surface waves which decay asymptotically ast−12for the two dimensional case and ast−1for the three dimensional tsunamis. Several important features of the solution are discussed in some detail. As an application of the general theory, some physically realistic ocean floor disturbances are included in this paper.

Focused Plunging Breaking Waves Impact on Cylinder Group in Deep Water

2021 ◽  
Author(s):  
Ting Cui ◽  
Arun Kamath ◽  
Weizhi Wang ◽  
Lihao Yuan ◽  
Duanfeng Han ◽  
...  
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Breaking Waves ◽  
Surface Elevation ◽  
Relative Distance ◽  
Structural Safety ◽  
Wave Forces ◽  
Free Surface Elevation ◽  
Single Cylinder ◽  
Numerical Wave

Abstract The correct estimation of wave loading on a cylinder in a cylinder group under different impact scenarios is essential to determine the structural safety of coastal and offshore structures. This scenario differs from the interaction of waves with a single cylinder but not a lot of studies focus on cylinder groups under different arrangements. In this study, the interaction between plunging breaking waves and cylinder groups in deep water is investigated using the two-phase flow model in REEF3D, an open-source computational fluid dynamics program. The Reynolds-averaged Navier-Stokes equation with the two equation k–Ω turbulence model is adopted to resolve the numerical wave tank, with free surface calculated using the level set method. In this study, focused waves in deep water were modeled with a fixed wave steepness method. Wave breaking occurs when the steepness of the wave crest front satisfies the breaking criteria. The model is validated by comparing the numerical wave forces and free surface elevation with measurements from experiments. The computational results show fairly good agreement with experimental data for both free surface elevation and wave forces. Four cases are simulated to investigate the interaction of breaking waves with a cylinder group with different relative distance, number of cylinders and arrangement. Results show that breaking wave forces on the upstream cylinder are smaller than on a single cylinder with a relative distance of one cylinder diameter. The wave forces on cylinders in the pile group are effected by the relative distance between cylinders. The staggered arrangement has a significant influence on the wave forces on the first and second cylinder. The interaction inside a cylinder group mostly happens between the neighbouring cylinders. These interactions are also effected by the relative distance and the numbers of the neighbouring cylinders.

scholarly journals Non-linear wave equations for free surface flow over a bump

2020 ◽  
Vol 62 (2) ◽  
pp. 159-169
Author(s):  
Shino Sakaguchi ◽  
Keisuke Nakayama ◽  
Thuy Thi Thu Vu ◽  
Katsuaki Komai ◽  
Peter Nielsen
Keyword(s):  
Free Surface ◽  
Wave Equations ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Linear Wave ◽  
Non Linear ◽  
Linear Wave Equations

On uniqueness and solvability in the linearized two-dimensional problem of a supercritical stream about a surface-piercing body

1995 ◽  
Vol 450 (1939) ◽  
pp. 233-253 ◽  
Keyword(s):  
Free Surface ◽  
Linear Relation ◽  
Existence Of Solutions ◽  
Surface Elevation ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Free Surface Elevation ◽  
Unique Existence ◽  
Velocity Circulation ◽  
Well Posed

Uniqueness and solvability theorems are proved for a well-posed formulation of the two-dimensional Neumann-Kelvin problem (the modified Neumann-Kelvin problem) in the case, when a body is partly immersed in a supercritical stream. Uniqueness is provided by two supplementary conditions which prescribe (i) additional flux at infinity downstream due to presence of body and (ii) a linear relation between the free-surface elevation at stern point and the velocity circulation along wetted contour. Two versions of source method are developed to find a solution. The first version is simpler, but it fails for some irregular values of the body’s velocity. In the second ver­sion complex sources’ strengths are used, avoiding irregular values and establishing the unique existence of solutions.

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