A Lagrangian Model for Irregular Waves and Wave Kinematics

2003 ◽  
Vol 125 (2) ◽  
pp. 94-102 ◽  
Author(s):  
Svein Helge Gjøsund
Keyword(s):  
Iterative Method ◽  
Irregular Waves ◽  
Lagrangian Model ◽  
Surface Zone ◽  
Wave Interactions ◽  
Wave Flume ◽  
Wave Kinematics ◽  
Eulerian Formulation ◽  
The Waves ◽  
Good Agreement

It has proven difficult to describe the kinematics in irregular waves satisfactorily, in particular for the surface zone in broad-banded waves. A Lagrangian approach offers distinct advantages in this respect, eliminating the need for extrapolation of solutions or “stretching” of coordinates. This paper presents a model of irregular waves based on superposition of linear Lagrangian wave components, using an iterative method to obtain the Eulerian solution. This approach yields theoretically consistent results everywhere in the waves, and comparisons with wave flume measurements show good agreement. Also, the linear Lagrangian model includes wave interactions that would be nonlinear in an Eulerian formulation.

scholarly journals Nonlinear run-ups of regular waves on sloping structures

2012 ◽  
Vol 12 (12) ◽  
pp. 3811-3820 ◽  
Author(s):  
T.-W. Hsu ◽  
S.-J. Liang ◽  
B.-D. Young ◽  
S.-H. Ou
Keyword(s):  
Boussinesq Equations ◽  
Irregular Waves ◽  
Coastal Structures ◽  
Regular Waves ◽  
Wave Flume ◽  
Coastal Risk ◽  
Run Up ◽  
Two Parameters ◽  
Prediction Capability ◽  
Good Agreement

Abstract. For coastal risk mapping, it is extremely important to accurately predict wave run-ups since they influence overtopping calculations; however, nonlinear run-ups of regular waves on sloping structures are still not accurately modeled. We report the development of a high-order numerical model for regular waves based on the second-order nonlinear Boussinesq equations (BEs) derived by Wei et al. (1995). We calculated 160 cases of wave run-ups of nonlinear regular waves over various slope structures. Laboratory experiments were conducted in a wave flume for regular waves propagating over three plane slopes: tan α =1/5, 1/4, and 1/3. The numerical results, laboratory observations, as well as previous datasets were in good agreement. We have also proposed an empirical formula of the relative run-up in terms of two parameters: the Iribarren number ξ and sloping structures tan α. The prediction capability of the proposed formula was tested using previous data covering the range ξ ≤ 3 and 1/5 ≤ tan α ≤ 1/2 and found to be acceptable. Our study serves as a stepping stone to investigate run-up predictions for irregular waves and more complex geometries of coastal structures.

Stochastic nonlinear shoaling of directional spectra

1997 ◽  
Vol 345 ◽  
pp. 79-99 ◽  
Author(s):  
Y. AGNON ◽  
A. SHEREMET
Keyword(s):  
Kinetic Equation ◽  
Deterministic Model ◽  
Laboratory Data ◽  
Spectral Evolution ◽  
Wave Interactions ◽  
A Value ◽  
Surface Wave Field ◽  
The Waves ◽  
Gravity Surface ◽  
Good Agreement

We derive a deterministic directional shoaling model and a stochastic directional shoaling model for a gravity surface wave field, valid for a beach with parallel depth contours accounting for refraction and nonlinear quadratic (three wave) interactions. A new phenomenon of non-resonant spectral evolution arises due to the medium inhomogeneity. The kernels of the kinetic equation depend on the bathymetry through an integral operator. Preliminary tests carried out on laboratory data for a unidirectional case indicate that the stochastic model also works rather well beyond the region where the waves may be regarded as nearly Gaussian. The limit of its applicability is decided by the dispersivity of the medium (relative to the nonlinearity). Good agreement with both laboratory data and the underlying deterministic model is found up to a value of about 1.5 for the spectral peak Ursell number. Beyond that only the deterministic model matches the measurements.

Deterministic Reproduction of Nonlinear Waves

2002 ◽  
Author(s):  
Jesper Skourup ◽  
Martin J. Sterndorff
Keyword(s):  
Time Series ◽  
Nonlinear Waves ◽  
Second Order ◽  
Irregular Waves ◽  
Regular Waves ◽  
Order Model ◽  
Wave Flume ◽  
Non Linear ◽  
The Waves ◽  
Second Order Model

A method for deterministic reproduction of non-linear long-crested waves has been implemented. The model is used for non-linear reproduction of measured wave time series from a model test programme in a wave flume. Regular waves, irregular waves and focused waves have been reproduced with the model. Based on measured surface elevation time series at one location in the flume the elevation time series and the kinematics have been reproduced at another location using both linear theory and the second order model. The numerical results have been compared with measurements and it is found that the second order model is able to reproduce the correct shape of the waves as they propagate in the flume — even when the waves are highly non-linear.

APPLICATION OF ACOUSTIC METHODS IN RESEARCHES OF THE BOTTOM SEDIMENT DYNAMICS

2018 ◽  
Author(s):  
Б. Дивинский ◽  
B. Divinskiy ◽  
И. Грюне ◽  
I. Gryune ◽  
Р. Косьян ◽  
...  
Keyword(s):  
Suspended Sediment ◽  
Sediment Concentration ◽  
Irregular Waves ◽  
Single Frequency ◽  
Contactless Measurement ◽  
Measurement Means ◽  
Uniform Field ◽  
Wave Flume ◽  
Acoustic Methods ◽  
Back Scattering

Acoustic methods belong to contactless measurement means, possess high spatial and time resolution. Thus, the use of multifrequency allows directly profile both concentration and granulometric structure of the suspended substances. In 2008 in the Big Wave Flume (Hanover, Germany) by efforts of the Russian and German scientists there have been carried out the experiment on studying the bottom material suspension laws under the influence of irregular waves. The Aquascat 1000 acoustic back scattering sensor (ABS) manufactured by British company Aquatec (www.aquatecsubsea.com), equipped by a three-frequency transmitter with frequencies 1,0, 2,0 and 3,84 MHz, has been set on distance of 0,75 m from the bottom and 111 m from wave generator at the total depth of 3,2 m. Several dozen series of measurements at various parameters of surface waves have been carried out. The general picture of suspension is so that the external dynamic influence (currents, wave movements, turbulence, gravitation forces) creates a non-uniform field (gradient) of the suspended particles and in most cases due to this the average size of particles undergoes to the spatial-time variations. For this reason while defining the mass concentration of suspended sediment, using the single frequency transmitter there is necessity for numerous definition of the suspension granulometric structure what by isn’t always possible. If two and more frequencies are used the observed results comparison can give the information on average diameters of particles and on that basis the calculation of suspended sediment concentration is possibleLet's emphasize the basic advantages of back scattering acoustic gauges usage: – Obtaining the particles sizes and concentration distribution profiles is possible; – The initial granulometric structure of bottom sediments can be unknown (at use of several frequencies). The following can be referred to some lacks of the device: – The system should be calibrated in laboratory conditions; – In a positive feedback conditions the iterative computing process can converge to zero or to infinity. In this case experiments with a variation of carrier frequencies chosen for the analysis allow partially solve the problem (say experiments with different frequencies pairs, as 2/1 of MHz or 4/2 MHz).

Kajian Model Fisik Pengaruh Freeboard dan Susunan Buis Beton Sebagai Pemecah Gelombang Tenggelam Ambang Rendah (Pegar) Dalam Mereduksi Gelombang

2017 ◽  
Vol 1 (2) ◽  
pp. 34
Author(s):  
Zulkarnain Zulkarnain ◽  
Nadjadji Anwar
Keyword(s):  
Low Cost ◽  
Relative Depth ◽  
Submerged Breakwater ◽  
Wave Flume ◽  
Concrete Cylinder ◽  
Engineering Department ◽  
Sea Area ◽  
The Waves ◽  
Transmission Test ◽  
Better Than

The Research Center and Development of Water (Puslitbang) is currently developing the Submerged Breakwater in shallow sea area (PEGAR). The author is interested to examine the material that easily obtained in the field of RCP concrete cylinder. The observation is how it to be ability in function as submerged breakwater an go green and low cost. The physical model of wave transmission test is how the response to the structure in ability to damping of wave as the breakwater function. In this research breakwater used is submerged breakwater type by using concrete cylinder (buis beton). The purpose from this research is to know how the response of breakwater structure to the waves through it, with some variation of the structure by creating a structure with three variations of the arrangement and freeboard that is the relative depth with the crest width is constant. The wave generated test in this study is using regular waves in wave flume at FTSP Civil Engineering Department of Institute Technology Ten November. From the analysis of the effect of the installation of submerged breakwater by using concrete cylinder to the wave damping value, it can be concluded that the factors that are very influential is the freeboard and the composition of concrete cylinder. Scenario A (rigid vertical massive) is capable of producing the smallest value of kt is 0.33. As for scenario B (rigid horyzontal massive) with a damping value of 0.5, while the scenario C (rigid permeable) is only able to produce kt value of 0.71. Scenario A is better than scenario B and C Because the position of arrangement of A is very good used to damp wave in small or big freeboard conditions.

scholarly journals Wave Breaking in Undular Bores with Shear Flows

Water Waves ◽  
2021 ◽  
Author(s):  
Maria Bjørnestad ◽  
Henrik Kalisch ◽  
Malek Abid ◽  
Christian Kharif ◽  
Mats Brun
Keyword(s):  
Turbulent Flows ◽  
Wave Breaking ◽  
Vries Equation ◽  
Kdv Equation ◽  
Flow Depth ◽  
Present Contribution ◽  
Undular Bore ◽  
Wave Flume ◽  
The Kdv Equation ◽  
The Waves

AbstractIt is well known that weak hydraulic jumps and bores develop a growing number of surface oscillations behind the bore front. Defining the bore strength as the ratio of the head of the undular bore to the undisturbed depth, it was found in the classic work of Favre (Ondes de Translation. Dunod, Paris, 1935) that the regime of laminar flow is demarcated from the regime of partially turbulent flows by a sharply defined value 0.281. This critical bore strength is characterized by the eventual breaking of the leading wave of the bore front. Compared to the flow depth in the wave flume, the waves developing behind the bore front are long and of small amplitude, and it can be shown that the situation can be described approximately using the well known Kortweg–de Vries equation. In the present contribution, it is shown that if a shear flow is incorporated into the KdV equation, and a kinematic breaking criterion is used to test whether the waves are spilling, then the critical bore strength can be found theoretically within an error of less than ten percent.

Experimental Wave Flume Tests in ROV-Wave Interaction Effects on the Line Tension for a Work Class ROV in Splash Zone

2021 ◽  
Author(s):  
Michael Binsar Lubis ◽  
Mehrdad Kimiaei
Keyword(s):  
Time History ◽  
Wave Interaction ◽  
Line Tension ◽  
Irregular Waves ◽  
Splash Zone ◽  
Remotely Operated Vehicle ◽  
Wave Flume ◽  
Flume Tests ◽  
Tension Time ◽  
Work Class

Abstract Integrity and stability of Remotely Operated Vehicle (ROV) when passing through the splash zone is one of the main concerns in the design of an ROV-umbilical system. Due to the lightweight nature of ROV in water, the umbilical experiences repetitive rapid transitions between slack and taut as the ROV travels through the splash zone. These rapid transitions induce tension spikes in the umbilical, namely snap forces, that can endanger the launch and recovery of an ROV. Therefore, it is important to ensure that the tension spikes do not exceed the safe working load of the umbilical. In this study, launch and recovery of a deep-water work class ROV are experimentally investigated using a 1:10 scaled ROV model through a series of wave flume tests. Different regular and irregular waves are generated in the flume while the ROV model is hung over the flume in four different positions. The tension time-history in the line is measured and recorded using a load cell at the top-end of the line. A simplified numerical model for launch and recovery of the ROV is developed and the numerical results are compared with the experimental ones. It is shown that the presented simplified model can be accurately used for analysis of launch and recovery of the ROV.

scholarly journals The spin-up of a linearly stratified fluid in a sliced, circular cylinder

2016 ◽  
Vol 806 ◽  
pp. 254-303
Author(s):  
R. J. Munro ◽  
M. R. Foster
Keyword(s):  
Circular Cylinder ◽  
Rossby Waves ◽  
Rotation Axis ◽  
A Priori ◽  
Propagation Speed ◽  
Stratified Fluid ◽  
Decay Rates ◽  
The Waves ◽  
Western Half ◽  
Good Agreement

A linearly stratified fluid contained in a circular cylinder with a linearly sloped base, whose axis is aligned with the rotation axis, is spun-up from a rotation rate $\unicode[STIX]{x1D6FA}-\unicode[STIX]{x0394}\unicode[STIX]{x1D6FA}$ to $\unicode[STIX]{x1D6FA}$ (with $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FA}\ll \unicode[STIX]{x1D6FA}$) by Rossby waves propagating across the container. Experimental results presented here, however, show that if the Burger number $S$ is not small, then that spin-up looks quite different from that reported by Pedlosky & Greenspan (J. Fluid Mech., vol. 27, 1967, pp. 291–304) for $S=0$. That is particularly so if the Burger number is large, since the Rossby waves are then confined to a region of height $S^{-1/2}$ above the sloped base. Axial vortices, ubiquitous features even at tiny Rossby numbers of spin-up in containers with vertical corners (see van Heijst et al.Phys. Fluids A, vol. 2, 1990, pp. 150–159 and Munro & Foster Phys. Fluids, vol. 26, 2014, 026603, for example), are less prominent here, forming at locations that are not obvious a priori, but in the ‘western half’ of the container only, and confined to the bottom $S^{-1/2}$ region. Both decay rates from friction at top and bottom walls and the propagation speed of the waves are found to increase with $S$ as well. An asymptotic theory for Rossby numbers that are not too large shows good agreement with many features seen in the experiments. The full frequency spectrum and decay rates for these waves are discussed, again for large $S$, and vertical vortices are found to occur only for Rossby numbers comparable to $E^{1/2}$, where $E$ is the Ekman number. Symmetry anomalies in the observations are determined by analysis to be due to second-order corrections to the lower-wall boundary condition.

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