Development and Validation of Quasi-Eulerian Mean Three-Dimensional Equations of Motion Using the Generalized Lagrangian Mean Method
Abstract
:1. Introduction
2. Derivation of the Quasi-Eulerian Mean Equations of Motion
2.1. Derivation of Quasi-Eulerian Mean Equations of Motion
2.1.1. Derivation of Quasi-Eulerian Mean Momentum Equation
2.1.2. Mass Conservation Equation
3. Validation of Quasi-Eulerian Mean Equations of Motion
3.1. Model Implementation
3.1.1. DV Governing Equations
3.1.2. Depth-Dependent Wave Radiation Stress in the 2DV Model
3.1.3. Bottom Boundary Layer Thickness in the Wave–Current Interaction Condition
3.2. Numerical Approximation
3.3. Adiabatic Test
3.3.1. Bathymetry
3.3.2. Boundary Conditions
3.3.3. Numerical Results
3.4. Mean Current in the Presence of Non-Breaking Waves
3.4.1. Input Parameters
3.4.2. Boundary Conditions
3.4.3. The Numerical Results
3.5. Breaking Waves Propagating in a Wave Flume
3.5.1. Bathymetry and the Wave Properties at the Boundary
3.5.2. Boundary Conditions
3.5.3. Model Validation
3.6. Breaking Waves Propagating in a Large-Scale Facility
3.6.1. Laboratory Setup and Boundary Conditions
3.6.2. Numerical Results and Discussion
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Derivation of the GLM Momentum Equation
Appendix B. Derivation of the Radiation Stress Tensor in the GLM Framework
References
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Wave Type | Tp (s) | Hrms (m) | h (m) |
---|---|---|---|
Random | 1.7 | 0.1 | 0.5 |
Conditions | Formula (62) | Van Rijn [35] |
---|---|---|
CO | 0.1 | 0.1 |
WO | 1.3 | 1.3 |
WFC | 5.3 | 3.6 |
WOC | 4.9 | 3.6 |
Conditions | |||
---|---|---|---|
CO | 8.16 | 5.4 | 0.74 |
WO | 0.9 | 0.21 | 0.13 |
WFC | 8.10 | 37.67 | 1.94 |
WOC | 5.86 | 24.6 | 1.56 |
Experiment | Hs (m) | Tp (s) |
---|---|---|
Test 1B | 0.206 | 2.03 |
Test 1C | 0.103 | 3.3.3 |
Wave Type | Tp (s) | Hs (m) | h (m) | |
---|---|---|---|---|
Irregular | 2.5 | 0.225 | 10 | 0.667 |
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Nguyen, D.T.; Jacobsen, N.G.; Roelvink, D. Development and Validation of Quasi-Eulerian Mean Three-Dimensional Equations of Motion Using the Generalized Lagrangian Mean Method. J. Mar. Sci. Eng. 2021, 9, 76. https://doi.org/10.3390/jmse9010076
Nguyen DT, Jacobsen NG, Roelvink D. Development and Validation of Quasi-Eulerian Mean Three-Dimensional Equations of Motion Using the Generalized Lagrangian Mean Method. Journal of Marine Science and Engineering. 2021; 9(1):76. https://doi.org/10.3390/jmse9010076
Chicago/Turabian StyleNguyen, Duoc Tan, Niels G. Jacobsen, and Dano Roelvink. 2021. "Development and Validation of Quasi-Eulerian Mean Three-Dimensional Equations of Motion Using the Generalized Lagrangian Mean Method" Journal of Marine Science and Engineering 9, no. 1: 76. https://doi.org/10.3390/jmse9010076