scholarly journals EXPERIMENTAL STUDY OF SOLITARY WAVE EVOLUTION OVER A 3D SHALLOW SHELF

2011 ◽  
Vol 1 (32) ◽  
pp. 1 ◽  
Author(s):  
Patrick J. Lynett ◽  
David Swigler ◽  
Sangyoung Son ◽  
Duncan Bryant ◽  
Scott Socolofsky
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Turbulent Energy ◽  
Shelf Break ◽  
Plan View ◽  
Fluid Velocities ◽  
Water Region ◽  
Side Walls

A laboratory experiment was performed to investigate the three-dimensional turbulence and kinematic properties that develop due to a breaking solitary propagating over an irregular shallow water bathymetry. The bathymetry consisted of a deep water region connected to a shallow shelf via a relatively steep slope. The offshore boundary of the shelf break varied in the longshore direction, such that the shelf had a triangular shape in plan view, with the widest part of the shelf along the basin centerline. Free surface elevations and fluid velocities were measured using wave gauges and three-dimensional acoustic-Doppler velocimeters (ADVs), respectively. From the free surface elevations the evolution and runup of the wave was revealed; while from the ADVs, the velocity and turbulent energy was determined and specific turbulent events and coherent structures were identified. It was found that significant shoaling was confined to areas with gentler sloping bathymetry near the basin side walls and the runup varied weakly in the alongshore direction. The runup was characterized by a refraction-generated jetting mechanism caused by the convergence of water mass near the basin centerline. The jetting mechanism caused the greatest cross-shore velocities to be located near the basin centerline. The greatest turbulent events were well correlated to borefronts, of which there were four, caused by the leading wave, beach reflections, and shelf-trapped oscillations. Along the shelf break, a large, shallow-water eddy developed which was found to have a peculiar three-dimensional flow field, where maximum velocity components were found at mid-depth.

Three-Dimensional Weakly Nonlinear Shallow Water Waves Regime and its Traveling Wave Solutions

2018 ◽  
Vol 15 (03) ◽  
pp. 1850017 ◽  
Author(s):  
Aly R. Seadawy
Keyword(s):  
Free Surface ◽  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Waves ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Wave Solutions

The problem formulations of models for three-dimensional weakly nonlinear shallow water waves regime in a stratified shear flow with a free surface are studied. Traveling wave solutions are generated by deriving the nonlinear higher order of nonlinear evaluation equations for the free surface displacement. We obtain the velocity potential and pressure fluid in the form of traveling wave solutions of the obtained nonlinear evaluation equation. The obtained solutions and the movement role of the waves of the exact solutions are new travelling wave solutions in different and explicit form such as solutions (bright and dark), solitary wave, periodic solitary wave elliptic function solutions of higher-order nonlinear evaluation equation.

scholarly journals Entropy Wake Law for Streamwise Velocity Profiles in Smooth Rectangular Open Channels

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 654
Author(s):  
Domenica Mirauda ◽  
Maria Grazia Russo
Keyword(s):  
Free Surface ◽  
Cross Sections ◽  
Water Discharge ◽  
Longitudinal Velocity ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Streamwise Velocity ◽  
Open Channels ◽  
Entropy Model ◽  
Modified Entropy

In narrow open channels, the three-dimensional nature of the flow and the transport momentum from the sidewalls to the central region cause the maximum longitudinal velocity to occur below the water surface. The entropy model is unable to accurately describe the velocities near the free surface when the dip phenomenon exists. The present paper proposes a new dip-modified entropy law for steady open channel flows, which consists of three additional terms: the first one similar to Coles’ function; the second one linearly proportional to the logarithmic distance from the free surface; and the third one depending on the cubic correction near the maximum velocity. The validity of the new model was tested on a set of laboratory measurements carried out in a straight rectangular flume with smooth boundaries and for different values of water discharge, bottom slope, and aspect ratio. A detailed error analysis showed good agreement with the data measured through the present research and a more accurate prediction of the velocity-dip-position compared with the one evaluated through the original entropy model. In addition, the modified entropy wake law matched very well with other literature data collected in rectangular cross-sections with different flow conditions.

scholarly journals Numerical model of energy dissipation and shallow-water sloshing motions in tank under different coupled excitations

2021 ◽  
Author(s):  
Yan Su
Keyword(s):  
Free Surface ◽  
Energy Dissipation ◽  
Numerical Model ◽  
Shallow Water ◽  
Three Dimensional ◽  
Wave Crest ◽  
Surface Boundary ◽  
Transient Wave ◽  
Irregular Free Surface ◽  
Free Surface Oscillations

AbstractShallow-water sloshing motions in a three-dimensional rectangular tank are investigated. The Boussinesq-type equations in terms of velocity potential and the finite-difference scheme are applied for the solutions of numerical model. Through linking the rate of decay of the wave amplitudes to the energy dissipation due to the friction at the tank walls, a linear damping term is proposed and added into the free surface boundary condition. Taking the tank under excited frequencies near the lowest natural frequency, the maximum transient wave amplitudes and steady-state wave amplitudes of sloshing motions at the tank wall are presented and verified by the experimental results given in the literature. The characteristics of sloshing motions in tank under different coupled excitations are studied. The results indicate that coupled surge-sway excitations lead to the weaker nonlinear sloshing motions in tank than the single degree of freedom excitations. The intersection of sloshing wave crest lines finally tend to the diagonal line of the tank under the coupled surge-sway excitations with different amplitudes. And the irregular free surface oscillations appear at the corners of the tank excited by the coupled surge-sway-roll-pitch-yaw harmonic motions.

Three-dimensional flow evolution after a dam break

2010 ◽  
Vol 663 ◽  
pp. 456-477 ◽  
Author(s):  
A. FERRARI ◽  
L. FRACCAROLLO ◽  
M. DUMBSER ◽  
E. F. TORO ◽  
A. ARMANINI
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Shallow Water ◽  
Three Dimensional ◽  
Dam Break ◽  
Water Model ◽  
Navier Stokes ◽  
Finite Volume Scheme ◽  
Shallow Water Model ◽  
Weakly Compressible

In this paper, the wave propagation on a plane dry bottom after a dam break is analysed. Two mathematical models have been used and compared with each other for simulating such a dam-break scenario. First, the fully three-dimensional Navier–Stokes equations for a weakly compressible fluid have been solved using the new smooth particle hydrodynamics formulation, recently proposed by Ferrari et al. (Comput. Fluids, vol. 38, 2009, p. 1203). Second, the two-dimensional shallow water equations (SWEs) are solved using a third-order weighted essentially non-oscillatory finite-volume scheme. The numerical results are critically compared against the laboratory measurements provided by Fraccarollo & Toro (J. Hydraul. Res., vol. 33, 1995, p. 843). The experimental data provide the temporal evolution of the pressure field, the water depth and the vertical velocity profile at 40 gauges, located in the reservoir and in front of the gate. Our analysis reveals the shortcomings of SWEs in the initial stages of the dam-break phenomenon in reproducing many important flow features of the unsteady free-surface flow: the shallow water model predicts a complex wave structure and a wavy evolution of local free-surface elevations in the reservoir that can be clearly identified to be only model artefacts. However, the quasi-incompressible Navier–Stokes model reproduces well the high gradients in the flow field and predicts the cycles of simultaneous rapid decreasing and frozen stages of the free surface in the tank along with the velocity oscillations. Asymptotically, i.e. for ‘large times’, the shallow water model and the weakly compressible Navier–Stokes model agree well with the experimental data, since the classical SWE assumptions are satisfied only at large times.

Development of a three-dimensional numerical model to solve shallow-water equations in compound channels

2008 ◽  
Vol 35 (9) ◽  
pp. 963-974 ◽  
Author(s):  
F. Jazizadeh ◽  
A. R. Zarrati
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Free Surface Elevation ◽  
Compound Channels ◽  
Secondary Currents ◽  
Flood Plains ◽  
Rough Beds

Velocity gradient between main channel and flood plains in compound channels leads to the formation of a large shear layer and secondary currents between these two subsections. These phenomena in the interaction region bring about a complex three-dimensional nature of the flow in compound channels. To cope with these flows, many numerical investigations have utilized three-dimensional formulations with advanced turbulence models. However, the free surface in many of these models is fixed and rigid-lid assumption has been used. In the present research, three-dimensional shallow water equations were used to calculate the flow field in compound channels. Three-dimensional equations were integrated in layers and were combined with the continuity equation. In this formulation, free-surface elevation was calculated without the need to solve any additional equations. Velocity and bed shear stress distribution and the stage–discharge relationship in compound channels with smooth and rough beds and with different relative depths were analyzed to verify this model, and satisfactory results were obtained.

scholarly journals Three-dimensional water impact at normal incidence to a blunt structure

2016 ◽  
Vol 472 (2192) ◽  
pp. 20150849 ◽  
Author(s):  
I. K. Chatjigeorgiou ◽  
M. J. Cooker ◽  
A. A. Korobkin
Keyword(s):  
Free Surface ◽  
Contact Region ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Main Concern ◽  
Water Impact ◽  
Pressure Impulse ◽  
Water Region ◽  
Rigid Plane ◽  
The Impact

The three-dimensional water impact onto a blunt structure with a spreading rectangular contact region is studied. The structure is mounted on a flat rigid plane with the impermeable curved surface of the structure perpendicular to the plane. Before impact, the water region is a rectangular domain of finite thickness bounded from below by the rigid plane and above by the flat free surface. The front free surface of the water region is vertical, representing the front of an advancing steep wave. The water region is initially advancing towards the structure at a constant uniform speed. We are concerned with the slamming loads acting on the surface of the structure during the initial stage of water impact. Air, gravity and surface tension are neglected. The problem is analysed by using some ideas of pressure-impulse theory, but including the time-dependence of the wetted area of the structure. The flow caused by the impact is three-dimensional and incompressible. The distribution of the pressure-impulse (the time-integral of pressure) over the surface of the structure is analysed and compared with the distributions provided by strip theories. The total impulse exerted on the structure during the impact stage is evaluated and compared with numerical and experimental predictions. An example calculation is presented of water impact onto a vertical rigid cylinder. Three-dimensional effects on the slamming loads are the main concern in this study.

Prediction of Ship Motions Via a Three-Dimensional Time-Domain Method Following a Quad-Tree Adaptive Mesh Technique

2020 ◽  
Vol 27 (1) ◽  
pp. 29-38
Author(s):  
Teng Zhang ◽  
Junsheng Ren ◽  
Lu Liu
Keyword(s):  
Free Surface ◽  
Incident Wave ◽  
Time Domain ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Wave Profile ◽  
Time Domain Method ◽  
Ship Motions ◽  
Quad Tree ◽  
Mesh Technique

AbstractA three-dimensional (3D) time-domain method is developed to predict ship motions in waves. To evaluate the Froude-Krylov (F-K) forces and hydrostatic forces under the instantaneous incident wave profile, an adaptive mesh technique based on a quad-tree subdivision is adopted to generate instantaneous wet meshes for ship. For quadrilateral panels under both mean free surface and instantaneous incident wave profiles, Froude-Krylov forces and hydrostatic forces are computed by analytical exact pressure integration expressions, allowing for considerably coarse meshes without loss of accuracy. And for quadrilateral panels interacting with the wave profile, F-K and hydrostatic forces are evaluated following a quad-tree subdivision. The transient free surface Green function (TFSGF) is essential to evaluate radiation and diffraction forces based on linear theory. To reduce the numerical error due to unclear partition, a precise integration method is applied to solve the TFSGF in the partition computation time domain. Computations are carried out for a Wigley hull form and S175 container ship, and the results show good agreement with both experimental results and published results.

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