A Comparative Study of Eddy Viscosity Type Models for Simulating Wave Breaking Induced Energy Dissipation in Boussinesq Models

An experimental study of energy dissipation in two-dimensional unsteady plunging breakers and an eddy viscosity model to simulate the dissipation due to wave breaking are reported in this paper. Measured wave surface elevations are used to examine the characteristic time and length scales associated with wave groups and local breaking waves, and to estimate and parameterize the energy dissipation and dissipation rate due to wave breaking. Numerical tests using the eddy viscosity model are performed and we find that the numerical results well capture the measured energy loss. In our experiments, three sets of characteristic time and length scales are defined and obtained: global scales associated with the wave groups, local scales immediately prior to breaking onset and post-breaking scales. Correlations among these time and length scales are demonstrated. In addition, for our wave groups, wave breaking onset predictions using the global and local wave steepnesses are found based on experimental results. Breaking time and breaking horizontal length scales are determined with high-speed imaging, and are found to depend approximately linearly on the local wave steepness. The two scales are then used to determine the energy dissipation rate, which is the ratio of the energy loss to the breaking time scale. Our experimental results show that the local wave steepness is highly correlated with the measured dissipation rate, indicating that the local wave steepness may serve as a good wave-breaking-strength indicator. To simulate the energy dissipation due to wave breaking, a simple eddy viscosity model is proposed and validated with our experimental measurements. Under the small viscosity assumption, the leading-order viscous effect is incorporated into the free-surface boundary conditions. Then, the kinematic viscosity is replaced with an eddy viscosity to account for energy loss. The breaking time and length scales, which depend weakly on wave breaking strength, are applied to evaluate the magnitude of the eddy viscosity using dimensional analysis. The estimated eddy viscosity is of the order of 10−3 m2s−1 and demonstrates a strong dependence on wave breaking strength. Numerical simulations with the eddy viscosity estimation are performed to compare to the experimental results. Good agreement as regards energy dissipation due to wave breaking and surface profiles after wave breaking is achieved, which illustrates that the simple eddy viscosity model functions effectively.

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A Comparative Study of Wave Breaking Models in a High-Order Spectral Model

Volume 7B: Ocean Engineering ◽

10.1115/omae2017-61664 ◽

2017 ◽

Cited By ~ 1

Author(s):

Betsy R. Seiffert ◽

Guillaume Ducrozet

Keyword(s):

Free Surface ◽

Energy Dissipation ◽

Boundary Conditions ◽

Wave Breaking ◽

Water Surface ◽

Eddy Viscosity ◽

Breaking Waves ◽

Surface Boundary ◽

Diffusion Term ◽

Surface Boundary Conditions

We examine the implementation of two different wave breaking models into the nonlinear potential flow solver HOS-NWT. HOS-NWT is a computationally efficient, open source code that solves for surface elevation in a numerical wave tank using the High-Order Spectral (HOS) method [1]. The first model is a combination of a kinematic wave breaking onset criteria proposed by Barthelemey, et al. [2] and validated by Saket, et al. [3], and an energy dissipation mechanism proposed by Tian, et al. [4, 5]. The wave breaking onset parameter is based on the ratio of local energy flux velocity to the local crest velocity. Once breaking is initiated, an eddy viscosity parameter is estimated based on the pre-breaking local wave geometry, as described in [4, 5]. This eddy viscosity is then added as a diffusion term to the kinematic and dynamic free surface boundary conditions for the duration of wave breaking. Results implementing this wave breaking mechanism in HOS-NWT have shown that the model can successfully calculate the surface elevation and corresponding frequency spectra, as well as the energy dissipation associated with breaking waves [6–8]. The second model implemented to account for wave breaking in HOS-NWT is based on the method proposed by Chalikov, et al. [9–11]. This model defines wave breaking onset by the curvature of the water surface and defines the wave as broken if it exceeds a certain value. A diffusion term is added to the kinematic and dynamic free surface boundary conditions which dissipates energy based on the local curvature of the water surface, which is consequently not constant in space nor time. Calculations made using the two models are compared with large scale experimental measurements conducted at the Hydrodynamics, Energetics and Atmospheric Environment Lab (LHEEA) at Ecole Centrale de Nantes. Comparison of calculations with measurements suggest that both models are successful at predicting wave breaking onset and energy dissipation. However, the model proposed by Barthelemy, et al. [2] and Tian, et al. [4] can be applied without knowing anything about the breaking waves a priori, whereas the model proposed by Chalikov [9] requires tuning to specific conditions.

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Comparative Study of Different Cost Functions Between Neighbors for Optimizing Energy Dissipation in WSN

IEEE Systems Journal ◽

10.1109/jsyst.2018.2800292 ◽

2019 ◽

Vol 13 (1) ◽

pp. 289-300 ◽

Cited By ~ 2

Author(s):

Subrata Dutta ◽

Mohammad S. Obaidat ◽

Keshav Dahal ◽

Debasis Giri ◽

Sarmistha Neogy

Keyword(s):

Energy Dissipation ◽

Comparative Study ◽

Cost Functions

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Estimating energy dissipation in internal solitary waves breaking on slopes

10.5194/egusphere-egu21-408 ◽

2021 ◽

Author(s):

Kateryna Terletska ◽

Vladіmir Maderich ◽

Tatiana Talipova

Keyword(s):

Energy Dissipation ◽

Solitary Waves ◽

Wave Breaking ◽

Wave Amplitude ◽

Hot Spot ◽

Slope Angle ◽

Bottom Layer ◽

Internal Solitary Waves ◽

Coastal Zones ◽

Waves Interaction

The shoaling mechanisms of internal solitary waves that propagate horizontally are an important source of mixing and transport in the coastal zones. Numerical modelling, llaboratory experiments and observations are needed for understanding wave energetics, especially energy transformation during waves interaction with the slopes. Two shoaling mechanisms are important during interaction with the slope: (i) wave breaking that results in mixing and dissipation, (ii) changing of the polarity of the initial wave of depression on the slope. Classification based on regimes of interaction with the slope was presented in [1]. Four zones were separated in &#945;&#946;&#947; (&#947; - is slope angle, &#945;-&#160; is the non-dimensional wave amplitude (wave amplitude normalized on the thermocline thickness) and &#946; &#8211; is the blocking parameter that is the ratio of the height of the bottom layer on the shelf to the incident wave amplitude) classification diagram: (I) without changing polarity and wave breaking, (II) changing polarity without breaking; (III) wave breaking without changing polarity; (IV) wave breaking with changing polarity. It was shown that results of field, laboratory and numerical experiments are in good agreement with proposed classification.&#160; In the present study we estimate energy dissipation for all the types of interaction and present the algorithm for building a zone map with a &#8216;hot spot&#8217; of energy dissipation for real slopes in the ocean.&#160;[1] K Terletska, BH Choi, V Maderich, T Talipova&#160; Classification of internal waves shoaling over slope-shelf topography RUSSIAN JOURNAL OF EARTH SCIENCES vol. 20, 4, 2020, doi: 10.2205/2020ES000730

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

Water ◽

10.3390/w11112282 ◽

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.

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Observations of Breaking Waves and Energy Dissipation in Modulated Wave Groups

Journal of Physical Oceanography ◽

10.1175/jpo-d-17-0224.1 ◽

2018 ◽

Vol 48 (12) ◽

pp. 2937-2948 ◽

Cited By ~ 6

Author(s):

David W. Wang ◽

Hemantha W. Wijesekera

Keyword(s):

Energy Dissipation ◽

Wave Height ◽

Wave Breaking ◽

Dissipation Rate ◽

Breaking Waves ◽

Wave Groups ◽

Dissipation Rates ◽

Local Wave ◽

Tke Dissipation Rate ◽

The Impact

AbstractIt has been recognized that modulated wave groups trigger wave breaking and generate energy dissipation events on the ocean surface. Quantitative examination of wave-breaking events and associated turbulent kinetic energy (TKE) dissipation rates within a modulated wave group in the open ocean is not a trivial task. To address this challenging topic, a set of laboratory experiments was carried out in an outdoor facility, the Oil and Hazardous Material Simulated Environment Test Tank (203 m long, 20 m wide, 3.5 m deep). TKE dissipation rates at multiple depths were estimated directly while moving the sensor platform at a speed of about 0.53 m s−1 toward incoming wave groups generated by the wave maker. The largest TKE dissipation rates and significant whitecaps were found at or near the center of wave groups where steepening waves approached the geometric limit of waves. The TKE dissipation rate was O(10−2) W kg−1 during wave breaking, which is two to three orders of magnitude larger than before and after wave breaking. The enhanced TKE dissipation rate was limited to a layer of half the wave height in depth. Observations indicate that the impact of wave breaking was not significant at depths deeper than one wave height from the surface. The TKE dissipation rate of breaking waves within wave groups can be parameterized by local wave phase speed with a proportionality breaking strength coefficient dependent on local steepness. The characterization of energy dissipation in wave groups from local wave properties will enable a better determination of near-surface TKE dissipation of breaking waves.

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Wave breaking and bubble formation associate energy dissipation and wave setup

Ocean Dynamics ◽

10.1007/s10236-019-01279-x ◽

2019 ◽

Vol 69 (8) ◽

pp. 913-923

Author(s):

Ashabul Hoque ◽

Nur Hossain ◽

Shuzon Ali ◽

Masudar Rahman

Keyword(s):

Energy Dissipation ◽

Wave Breaking ◽

Bubble Formation ◽

Wave Setup

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Modified Extended Hyperbolic Mild-Slope Equations

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.522-524.995 ◽

2014 ◽

Vol 522-524 ◽

pp. 995-999

Author(s):

Hua Chen Pan ◽

Zhi Guang Zhang

Keyword(s):

Wave Propagation ◽

Energy Dissipation ◽

Wave Breaking ◽

Nonlinear Dispersion ◽

Modifying Factors ◽

Nonlinear Dispersion Relation ◽

Mild Slope Equation ◽

Breaking Mechanism ◽

Wind Input ◽

Rapidly Varying Topography

A form of hyperbolic mild-slope equations extended to account for rapidly varying topography, nonlinear dispersion relation, wind input and energy dissipation during the process of wave propagation, has been derived from the mild-slope equation modified first in this paper. With the inclusion of the input of wind energy, the resultant model can be applied in some areas where the effect of wind could not be neglected. The wave-breaking mechanism which will cause energy dissipation remarkably, as well as the bottom friction, is introduced and discussed during this derivation. Since the modifying factors have taken plenty of aspects into consideration, the extended equations hold enlarged application and increased accuracy.

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Wave breaking in Boussinesq models for undular bores

Physics Letters A ◽

10.1016/j.physleta.2011.02.060 ◽

2011 ◽

Vol 375 (14) ◽

pp. 1570-1578 ◽

Cited By ~ 40

Author(s):

Magnar Bjørkavåg ◽

Henrik Kalisch

Keyword(s):

Wave Breaking ◽

Boussinesq Models

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Solitary waves perturbed by a broad sill. Part 1. Propagation across the sill

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.712 ◽

2019 ◽

Vol 880 ◽

pp. 916-934 ◽

Cited By ~ 1

Author(s):

Harrison T.-S. Ko ◽

Harry Yeh

Keyword(s):

Energy Dissipation ◽

Solitary Wave ◽

Solitary Waves ◽

Wave Breaking ◽

Wave Amplitude ◽

The State ◽

Transmitted Wave ◽

Wave State ◽

Transmitted Waves

Stability of a solitary wave disturbed by a submerged flat sill is investigated experimentally. For sills narrow compared with the solitary wave, the transmitted waves are found to be unaffected in waveform and amplitude. A wider sill disturbs the solitary wave resulting in the formation of a dispersive wavetrain following the transmitted wave. In some cases, the wave amplitude recovers, despite being perturbed, to the state of an unobstructed solitary-wave state at a certain distance beyond the sill. Wider sills cause wave breaking that occurs over the sill or, in some cases, after the wave passes through the sill. Details of waveform transformation leading toward the breaking and subsequent energy dissipation are discussed.

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