scholarly journals Hydrodynamic Features of an Undular Bore Traveling on a 1:20 Sloping Beach

Water ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 1556 ◽  
Author(s):  
Chang Lin ◽  
Wei-Ying Wong ◽  
Ming-Jer Kao ◽  
James Yang ◽  
Rajkumar V. Raikar ◽  
...  
Keyword(s):  
Free Surface ◽  
Pressure Gradient ◽  
Peak Level ◽  
Horizontal Velocity ◽  
Surface Elevation ◽  
Free Surface Elevation ◽  
Undular Bore ◽  
Run Up ◽  
The Moment ◽  
Sloping Beach

The hydrodynamic characteristics, including local and convective accelerations as well as pressure gradient in the horizontal direction, of the external stream of an undular bore propagating on a 1:20 sloping beach are experimentally studied. A bore with the water depth ratio of 1.70 was generated downstream of a suddenly lifted gate. A high-speed particle image velocimetry was employed to measure the velocity fields during the run-up and run-down motions. The time series of free surface elevation and velocity field/profile of the generated bore, comprising a pure bore accompanied by a series of dispersive leading waves, are first demonstrated. Based on the fast Fourier transform (FFT) and inverse FFT (IFFT) techniques, the free surface elevation of leading waves and the counterpart of pure bore are acquired separately at a specified measuring section (SMS), together with the uniform horizontal velocity of the pure bore. The effect of leading-wave-induced velocity shift on the velocity profiles of the generated bore are then evaluated at the SMS. To understand the calculation procedure of accelerations and pressure gradient, three tabulated forms are provided as illustrative examples. Accordingly, the relationships among the partially depth-averaged values of the non-dimensional local acceleration, convective acceleration, total acceleration and pressure gradient of the generated/pure bore acquired at the SMS versus the non-dimensional time are elucidated. The trends in the non-dimensional accelerations and pressure gradient of the external stream of generated bore are compared with those of the pure bore. During the run-up motion from the instant of arrival of the bore front to the moment of the peak level at the SMS, continuous decrease in the onshore uniform horizontal velocity, and successive deceleration of the pure bore in the onshore direction are evidenced, exhibiting the pure bore under the adverse pressure gradient with decreasing magnitude. However, the pure bore once ridden by the leading waves is decelerated/accelerated spatially and accelerated/decelerated temporally in the onshore direction during the rising/descending free surface of each leading wave. This fact highlights the effect of pre-passing/post-passing of the leading wave crest on the velocity distribution of generated bore. It is also found that, although the leading waves have minor contribution on the power spectrum of the free surface elevation as compared with that of the pure bore, the leading waves do play an important role on the magnitudes of both accelerations and pressure gradient. The largest magnitude of the acceleration contributed by the leading waves is around 26 times the counterpart contributed by the pure bore. Further, during the run-down motion right after the moment for the peak level of the bore, a linear increase in the magnitude of the offshore uniform horizontal velocity and a constant local acceleration with increasing time are both identified. The partially depth-averaged value of the non-dimensional pressure gradient is equal to a small negative constant (−0.0115) in the offshore direction, indicating that the bore is subject to a constant favorable pressure gradient.

scholarly journals Characteristics of Accelerations and Pressure Gradient during Run-Down of Solitary Wave over Very Steep Beach: A Case Study

Water ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 523 ◽  
Author(s):  
Chang Lin ◽  
Wei-Ying Wong ◽  
Rajkumar V. Raikar ◽  
Hwung-Hweng Hwung ◽  
Ching-Piao Tsai
Keyword(s):  
Free Surface ◽  
Pressure Gradient ◽  
Flow Separation ◽  
Adverse Pressure Gradient ◽  
Time Interval ◽  
Primary Vortex ◽  
Two Phase ◽  
Run Up ◽  
The Moment ◽  
External Stream

An experimental investigation is performed to elucidate the variations of accelerations and pressure gradients in the external stream of retreating flow during the run-down phase of a non-breaking solitary wave, propagating over a 1:3 sloping beach. Two solitary waves that have the incident wave heights (H0) of 2.9 and 5.8 cm, with respective still water depths (h0) of 8.0 and 16.0 cm (Cases A and B), were generated in a wave flume, resulting in the incident wave-height to water-depth ratios (H0/h0) being identically equal to 0.363. The latter case was only used to highlight the non-dimensional features of the wave celerity, the time history of horizontal velocity and the breaker type, which all exhibit similarity to those of the former. Two flow visualization techniques such as particle trajectory method and fluorescent dye strip and a high-speed particle image velocimetry (HSPIV) were utilized to provide the flow images and velocity fields. Based on the ensemble-averaged velocity fields and profiles, the partially depth-averaged (i.e., excluding the part in the boundary layer) values of accelerations and pressure gradient at a specified measuring section are then smoothed by a symmetric five-point smoothing scheme. Eventually, the smoothed values of the accelerations and pressure gradient are used to highlight the dynamic features of the external stream of retreating flow. It is found that, at the section of the incipient flow separation, the non-dimensional local acceleration (with respect to the gravity acceleration) in the offshore direction keeps increasing from the moment at which the run-up motion ends to the counterpart at which the incipient flow separation occurs. Afterwards, growth of the primary vortex develops with its core translating offshore. The corresponding non-dimensional local acceleration at the (moving) core section increases to a maximum of around 1.0 at the instant for occurrence of the hydraulic jump with abrupt rise of the free surface; and then decreases to zero at time for transformation of the curling jet into the projecting jet. The results exhibit that the external stream of retreating flow is accelerated temporally in the offshore direction for the interval between the time for the end of run-up motion and that for the formation of projecting jet. However, for later time interval up to generation of the two-phase flow field, the non-dimensional local acceleration in the offshore direction varies from zero to a negative maximum of −2.117 at the moment for the projecting jet heading downward before the impingement. It then decreases in magnitude continuously. The trend reveals that the external stream is decelerated temporally in the offshore direction for this later time interval. Further, at the section of the incipient flow separation, the non-dimensional pressure gradient (also with reference to the gravity acceleration) in the offshore direction increases from 0.225 for the time at which the run-up motion ends to 0.721 for the instant at which the incipient flow separation takes place. The trend highlights the external stream being under increasing adverse pressure gradient and more decelerated spatially with the increasing time, thus resulting in occurrence of the incipient flow separation. Afterwards, the value of the non-dimensional pressure gradient keeps increasing and eventually reaches a positive maximum of 2.011 and then decreases consecutively until the two-phase flow field is generated. In addition, due to the influence of acceleration of the external stream in the offshore direction, the non-dimensional vorticity of primary vortex core increases with increasing time up to the moment for occurrence of the projecting jet. Nevertheless, the non-dimensional vorticity of primary vortex core keeps decreasing with increasing time T for the later time interval due to the influence of deceleration of the external stream in the offshore direction. Finally, considerably large magnitudes of the non-dimensional accelerations and pressure gradient greater than 1.5 taking place at two non-dimensional times are worthy of noting. The negative maximum value of the non-dimensional convective acceleration equal to −2.005 appears at the instant for the occurrence of hydraulic jump. In addition, the negative maximum values of the non-dimensional local acceleration, total acceleration and pressure gradient unexpectedly as high as −2.117, −1.694 and 2.011, respectively, appear simultaneously at time for the projecting jet heading towards the retreating free surface. Under such a situation, the external stream of retreating flow is highly decelerated in the offshore direction under the fairly large adverse pressure gradient, thus forcing the retreating flow to move upwards rapidly. Meanwhile, the non-dimensional local acceleration in the vertical direction is surprisingly found to be 3.37. The result strongly reconfirms the evident rise of the free surface in the vicinity of the core section and reveals very rapid change from negative, via nearly zero, to positive vertical velocity.

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 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 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.

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.

Experimental Studies of Hydrodynamic Interaction of Two Bodies in Waves

2015 ◽  
Author(s):  
Quan Zhou ◽  
Ming Liu ◽  
Heather Peng ◽  
Wei Qiu
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Potential Flow ◽  
Numerical Solutions ◽  
Experimental Studies ◽  
Low Frequency ◽  
Surface Elevation ◽  
Linear Potential ◽  
Free Surface Elevation ◽  
Two Bodies

There are challenges in the prediction of low-frequency load and especially the resonant free surface elevation between two bodies in close proximity. Most of the linear potential-flow based seakeeping programs currently used by the industry over-predict the free surface elevation between the vessels/bodies and hence the low-frequency loadings on the hulls. Various methods, such as the lid technique, have been developed to suppress the unrealistic values of low-frequency forces by introducing artificial damping coefficients. However, without the experimental data, it is challenging to specify the coefficients. This paper presents the experimental studies of motions of two bodies with various gaps and the wave elevations between bodies. Model tests were performed at the towing tank of Memorial University. The objective was to provide benchmark data for further numerical studies of the viscous effect on the free surface predictions. The experimental data were compared with numerical solutions based on potential flow methods. The effect of tank walls were examined. Preliminary uncertainty analysis was also carried out.

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