scholarly journals A Modified k – ε Turbulence Model for a Wave Breaking Simulation

Water ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 2282
Author(s):  
Giovanni Cannata ◽  
Federica Palleschi ◽  
Benedetta Iele ◽  
Francesco Gallerano
Keyword(s):  
Energy Dissipation ◽  
Turbulence Model ◽  
Wave Breaking ◽  
A Priori ◽  
Time Dependent ◽  
Breaking Wave ◽  
Vertical Coordinate ◽  
Initial Wave ◽  
Proposed Model ◽  
Curvilinear Coordinate

We propose a two-equation turbulence model based on modification of the k − ε standard model, for simulation of a breaking wave. The proposed model is able to adequately simulate the energy dissipation due to the wave breaking and does not require any “a priori” criterion to locate the initial wave breaking point and the region in which the turbulence model has to be activated. In order to numerically simulate the wave propagation from deep water to the shoreline and the wave breaking, we use a model in which vector and tensor quantities are expressed in terms of Cartesian components, where only the vertical coordinate is expressed as a function of a time-dependent curvilinear coordinate that follows the free surface movements. A laboratory test is numerically reproduced with the aim of validating the turbulence modified k − ε model. The numerical results compared with the experimental measurements show that the proposed turbulence model is capable of correctly estimating the energy dissipation induced by the wave breaking, in order to avoid any underestimation of the wave height.

scholarly journals Formulation of the Reynolds equation on a time-dependent lubrication surface

2016 ◽  
Vol 472 (2187) ◽  
pp. 20160032 ◽  
Author(s):  
İ. Temizer ◽  
S. Stupkiewicz
Keyword(s):  
Reynolds Equation ◽  
Large Deformations ◽  
A Priori ◽  
Elastohydrodynamic Lubrication ◽  
Time Dependent ◽  
Soft Interfaces ◽  
The Third ◽  
Curvilinear Coordinate ◽  
Thin Fluid Film ◽  
Lubrication Effect

The Reynolds equation, which describes the lubrication effect arising through the interaction of two physical surfaces that are separated by a thin fluid film, is formulated with respect to a continuously evolving third surface that is described by a time-dependent curvilinear coordinate system. The proposed formulation essentially addresses lubrication mechanics at interfaces undergoing large deformations and a priori satisfies all objectivity requirements, neither of which are features of the classical Reynolds equation. As such, this formulation may be particularly suitable for non-stationary elastohydrodynamic lubrication problems associated with soft interfaces. The ability of the formulation to capture finite-deformation effects and the influence of the choice of the third surface are illustrated through analytical examples.

scholarly journals Estimation of Wave-Breaking Index by Learning Nonlinear Relation Using Multilayer Neural Network

2022 ◽  
Vol 10 (1) ◽  
pp. 50
Author(s):  
Miyoung Yun ◽  
Jinah Kim ◽  
Kideok Do
Keyword(s):  
Neural Network ◽  
Wave Height ◽  
Water Depth ◽  
Wave Breaking ◽  
Water Wave ◽  
Breaking Wave ◽  
Empirical Equations ◽  
Bottom Slope ◽  
Proposed Model ◽  
Deep Water Wave

Estimating wave-breaking indexes such as wave height and water depth is essential to understanding the location and scale of the breaking wave. Therefore, numerous wave-flume laboratory experiments have been conducted to develop empirical wave-breaking formulas. However, the nonlinearity between the parameters has not been fully incorporated into the empirical equations. Thus, this study proposes a multilayer neural network utilizing the nonlinear activation function and backpropagation to extract nonlinear relationships. Existing laboratory experiment data for the monochromatic regular wave are used to train the proposed network. Specifically, the bottom slope, deep-water wave height and wave period are plugged in as the input values that simultaneously estimate the breaking-wave height and wave-breaking location. Typical empirical equations employ deep-water wave height and length as input variables to predict the breaking-wave height and water depth. A newly proposed model directly utilizes breaking-wave height and water depth without nondimensionalization. Thus, the applicability can be significantly improved. The estimated wave-breaking index is statistically verified using the bias, root-mean-square errors, and Pearson correlation coefficient. The performance of the proposed model is better than existing breaking-wave-index formulas as well as having robust applicability to laboratory experiment conditions, such as wave condition, bottom slope, and experimental scale.

Analysis of Numerical Oscillation Problems in a Non Linear Time Dependent Mild Slope Model and First Developments for the Implementation of Wave Breaking

2008 ◽  
Author(s):  
Ana Catarina Zo´zimo ◽  
Conceic¸a˜o Fortes
Keyword(s):  
Energy Dissipation ◽  
Wave Breaking ◽  
Linear Time ◽  
Momentum Equation ◽  
Time Dependent ◽  
Theoretical Formulation ◽  
Dissipative Term ◽  
Mild Slope Equation ◽  
Non Linear ◽  
Work Done

In this paper, a description of the numerical model NMLSE is presented. This model solves the time dependent non linear mild slope equation, without including energy dissipation due to wave breaking [1]. Some modifications are made in the boundary conditions of the original version of the model in order to overcome the numerical oscillation problems detected in the work done by [2]. To evaluate the effectiveness of the new versions of the model, they are applied to test cases of the bibliography and to a bar-trough profile beach for which there are data from physical model tests. The basic theoretical formulation of a new momentum equation that includes energy dissipation due to wave breaking is also presented. The energy dissipation due to wave breaking is included through the addition of a dissipative term based in the eddy viscosity concept.

scholarly journals Statistical Characteristics of Wave Breakings and their Relation with the Wind Waves’ Energy Dissipation Based on the Field Measurements

2020 ◽  
Vol 36 (5) ◽  
Author(s):  
A. E. Korinenko ◽  
V. V. Malinovsky ◽  
V. N. Kudryavtsev ◽  
V. A. Dulov ◽  
◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Wind Speed ◽  
Wave Breaking ◽  
Wind Waves ◽  
Field Measurements ◽  
Sea Surface ◽  
Breaking Wave ◽  
Movement Velocity ◽  
Wide Range ◽  
The Waves

Purpose. The work is aimed at studying geometric similarity of wind wave breakings in natural conditions, estimating the Duncan constant which connects the wave energy dissipation conditioned by wave breakings, with distribution of the lengths of a breaking wave crests Λ(с). Methods and Results. The field measurements of the wave breaking characteristics were carried out at the stationary oceanographic platform located in the Golubaya Bay near the village Katsiveli. Geometric dimensions of the wave breakings’ active phase, velocities and directions of their movement were determined from the video records of the sea surface; simultaneously, the meteorological information was recorded and the surface waves’ characteristics were measured. Altogether 55 video records of the sea surface were obtained; duration of each of them was 40–60 minutes. The measurements were performed in a wide range of meteorological conditions and wave parameters (wind speed varied from 9.2 to 21.4 m/s). Conclusions. It is found that the probability densities of the ratio between the maximum length of a breaking and the length of a breaking wave, obtained in various wind and wave conditions are similar. The average value of this ratio is 0.1. Distributions of the wave breakings’ total length are constructed in the movement velocity intervals on a surface unit. It is shown that the experimental estimates of dependence of these distributions upon the wind speed and the wave breaking movement velocity are consistent with the theoretical predictions of O.M. Phillips (1985); at that no dependence on the waves’ age was found. Quantitative characteristics of the relation between the wave lengths’ distribution and the energy dissipation are obtained. The Duncan constant was estimated; it turned out to be equal to 1.8⋅10-3 and independent upon the waves’ and atmosphere parameters.

scholarly journals Statistical Characteristics of Wave Breakings and their Relation with the Wind Waves’ Energy Dissipation Based on the Field Measurements

2020 ◽  
Vol 27 (5) ◽  
Author(s):  
A. E. Korinenko ◽  
V. V. Malinovsky ◽  
V. N. Kudryavtsev ◽  
V. A. Dulov ◽  
◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Wind Speed ◽  
Wave Breaking ◽  
Wind Waves ◽  
Field Measurements ◽  
Sea Surface ◽  
Breaking Wave ◽  
Movement Velocity ◽  
Wide Range ◽  
The Waves

Purpose. The work is aimed at studying geometric similarity of wind wave breakings in natural conditions, estimating the Duncan constant which connects the wave energy dissipation conditioned by wave breakings, with distribution of the lengths of a breaking wave fronts Λ(с). Methods and Results. The field measurements of the wave breaking characteristics were carried out at the stationary oceanographic platform located in the Golubaya Bay near the Katsiveli village. Geometric dimensions of the wave breakings’ active phase, velocities and directions of their movement were determined from the video records of the sea surface; simultaneously, the meteorological information was recorded and the surface waves’ characteristics were measured. Altogether 55 video recordings (duration 40–50 mins) of the sea surface were obtained. The measurements were carried out in a wide range of meteorological conditions and wave parameters (wind speed varied from 9.2 to 21.4 m/s). Conclusions. It is found that the probability densities of the ratio between the maximum length of a breaking and the length of a breaking wave, obtained in various wind and wave conditions are similar. The average value of this ratio is 0.1. Distributions of the wave breakings’ total length are constructed in the movement velocity intervals on a surface unit. It is shown that the experimental estimates of dependence of these distributions upon the wind speed and the wave breaking movement velocity are consistent with the theoretical predictions of O.M. Phillips (1985); at that no dependence on the waves’ age was found. Quantitative characteristics of the relation between the wave lengths’ distribution and the energy dissipation are obtained. The Duncan constant was estimated; it turned out to be equal to 1.8·10-3 and independent upon the waves’ and atmosphere parameters.

scholarly journals Characteristics of Breaking Wave Forces on Piles over a Permeable Seabed

2021 ◽  
Vol 9 (5) ◽  
pp. 520
Author(s):  
Zhenyu Liu ◽  
Zhen Guo ◽  
Yuzhe Dou ◽  
Fanyu Zeng
Keyword(s):  
Wave Breaking ◽  
Stokes Equations ◽  
Slope Angle ◽  
Wave Force ◽  
Breaking Waves ◽  
Offshore Wind ◽  
Secondary Wave ◽  
Wave Forces ◽  
Breaking Wave ◽  
Breaking Wave Forces

Most offshore wind turbines are installed in shallow water and exposed to breaking waves. Previous numerical studies focusing on breaking wave forces generally ignored the seabed permeability. In this paper, a numerical model based on Volume-Averaged Reynolds Averaged Navier–Stokes equations (VARANS) is employed to reveal the process of a solitary wave interacting with a rigid pile over a permeable slope. Through applying the Forchheimer saturated drag equation, effects of seabed permeability on fluid motions are simulated. The reliability of the present model is verified by comparisons between experimentally obtained data and the numerical results. Further, 190 cases are simulated and the effects of different parameters on breaking wave forces on the pile are studied systematically. Results indicate that over a permeable seabed, the maximum breaking wave forces can occur not only when waves break just before the pile, but also when a “secondary wave wall” slams against the pile, after wave breaking. With the initial wave height increasing, breaking wave forces will increase, but the growth can decrease as the slope angle and permeability increase. For inclined piles around the wave breaking point, the maximum breaking wave force usually occurs with an inclination angle of α = −22.5° or 0°.

scholarly journals Assessment of Numerical Methods for Plunging Breaking Wave Predictions

2021 ◽  
Vol 9 (3) ◽  
pp. 264
Author(s):  
Shanti Bhushan ◽  
Oumnia El Fajri ◽  
Graham Hubbard ◽  
Bradley Chambers ◽  
Christopher Kees
Keyword(s):  
Solitary Wave ◽  
Wave Breaking ◽  
Large Scale ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Wave Crest ◽  
Breaking Wave ◽  
Rans Turbulence Models ◽  
Run Up ◽  
Better Than

This study evaluates the capability of Navier–Stokes solvers in predicting forward and backward plunging breaking, including assessment of the effect of grid resolution, turbulence model, and VoF, CLSVoF interface models on predictions. For this purpose, 2D simulations are performed for four test cases: dam break, solitary wave run up on a slope, flow over a submerged bump, and solitary wave over a submerged rectangular obstacle. Plunging wave breaking involves high wave crest, plunger formation, and splash up, followed by second plunger, and chaotic water motions. Coarser grids reasonably predict the wave breaking features, but finer grids are required for accurate prediction of the splash up events. However, instabilities are triggered at the air–water interface (primarily for the air flow) on very fine grids, which induces surface peel-off or kinks and roll-up of the plunger tips. Reynolds averaged Navier–Stokes (RANS) turbulence models result in high eddy-viscosity in the air–water region which decays the fluid momentum and adversely affects the predictions. Both VoF and CLSVoF methods predict the large-scale plunging breaking characteristics well; however, they vary in the prediction of the finer details. The CLSVoF solver predicts the splash-up event and secondary plunger better than the VoF solver; however, the latter predicts the plunger shape better than the former for the solitary wave run-up on a slope case.

Detailed Study on Breaking Wave Interactions With a Jacket Structure Based on Experimental Investigations

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Jithin Jose ◽  
Olga Podrażka ◽  
Ove Tobias Gudmestad ◽  
Witold Cieślikiewicz
Keyword(s):  
Wind Turbines ◽  
Wave Breaking ◽  
Offshore Structures ◽  
Offshore Wind ◽  
Wave Forces ◽  
Breaking Wave ◽  
Offshore Wind Turbines ◽  
Wave Parameters ◽  
Wave Slamming ◽  
Breaking Wave Forces

Wave breaking is one of the major concerns for offshore structures installed in shallow waters. Impulsive breaking wave forces sometimes govern the design of such structures, particularly in areas with a sloping sea bottom. Most of the existing offshore wind turbines were installed in shallow water regions. Among fixed-type support structures for offshore wind turbines, jacket structures have become popular in recent times as the water depth for fixed offshore wind structures increases. However, there are many uncertainties in estimating breaking wave forces on a jacket structure, as only a limited number of past studies have estimated these forces. Present study is based on the WaveSlam experiment carried out in 2013, in which a jacket structure of 1:8 scale was tested for several breaking wave conditions. The total and local wave slamming forces are obtained from the experimental measured forces, using two different filtering methods. The total wave slamming forces are filtered from the measured forces using the empirical mode decomposition (EMD) method, and local slamming forces are obtained by the frequency response function (FRF) method. From these results, the peak slamming forces and slamming coefficients on the jacket members are estimated. The breaking wave forces are found to be dependent on various breaking wave parameters such as breaking wave height, wave period, wave front asymmetry, and wave-breaking positions. These wave parameters are estimated from the wave gauge measurements taken during the experiment. The dependency of the wave slamming forces on these estimated wave parameters is also investigated.

Three-Dimensional Analysis of Closed-Die Forging Processes: Part 1: Formulation

1989 ◽  
Vol 203 (1) ◽  
pp. 33-37 ◽  
Author(s):  
C F Lugora ◽  
A N Bramley
Keyword(s):  
Theoretical Model ◽  
Energy Dissipation ◽  
Metal Flow ◽  
Three Dimensional ◽  
Total Rate ◽  
Die Forging ◽  
Closed Die Forging ◽  
Proposed Model ◽  
Optimum Velocity ◽  
Forging Load

In this series of papers, a theoretical model based on the upper bound elemental technique is presented for prediction of forging load and metal flow in three-dimensional closed-die forging processes. Three basic elements are introduced in order to partition a forging into simple elementary regions. An optimum velocity distribution within the forging is obtained by minimizing the total rate of energy dissipation using a simplex optimizing procedure. Applications of the proposed model are discussed in Part 2.

scholarly journals Crack-Considered Elastic Net Monitoring Model of Concrete Dam Displacement

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Jiingmei Zhang ◽  
Chongshi Gu
Keyword(s):  
Water Pressure ◽  
Elastic Net ◽  
Arch Dam ◽  
Time Dependent ◽  
Concrete Dams ◽  
Displacement Monitoring ◽  
Concrete Dam ◽  
Monitoring Model ◽  
Proposed Model ◽  
Dependent Component

Displacement monitoring data modeling is important for evaluating the performance and health conditions of concrete dams. Conventional displacement monitoring models of concrete dams decompose the total displacement into the water pressure component, temperature component, and time-dependent component. And the crack-induced displacement is generally incorporated into the time-dependent component, thus weakening the interpretability of the model. In the practical engineering modeling, some significant explaining variables are selected while the others are eliminated by applying commonly used regression methods which occasionally show instability. This paper proposes a crack-considered elastic net monitoring model of concrete dam displacement to improve the interpretability and stability. In this model, the mathematical expression of the crack-induced displacement component is derived through the analysis of large surface crack’s effect on the concrete dam displacement to improve the interpretability of the model. Moreover, the elastic net method with better stability is used to solve the crack-considered displacement monitoring model. Sequentially, the proposed model is applied to analyze the radial displacement of a gravity arch dam. The results demonstrate that the proposed model contributes to more reasonable explaining variables’ selection and better coefficients’ estimation and also indicate better interpretability and higher predictive precision.

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