Wave turbulence in shallow water models
We study wave turbulence in shallow water flows in numerical simulations using two different approximations: the shallow water model and the Boussinesq model with weak dispersion. The equations for both models were solved using periodic grids with up to 20482 points. In all simulations, the Froude n...
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todo:paper_15393755_v89_n6_p_ClarkDiLeoni2023-10-03T16:22:49Z Wave turbulence in shallow water models Clark Di Leoni, P. Cobelli, P.J. Mininni, P.D. Coastal engineering Dispersions Normal distribution Potential energy Probability density function Reynolds number Turbulence Water waves Boussinesq model Frequency spectra Nonlinear dispersion relation Nonlinear waves Shallow water flow Shallow water model Wave turbulence Weak turbulence Dispersion (waves) water chemical model chemistry computer simulation flow kinetics hydrodynamics nonlinear system procedures statistical model water flow Computer Simulation Hydrodynamics Models, Chemical Models, Statistical Nonlinear Dynamics Rheology Water Water Movements We study wave turbulence in shallow water flows in numerical simulations using two different approximations: the shallow water model and the Boussinesq model with weak dispersion. The equations for both models were solved using periodic grids with up to 20482 points. In all simulations, the Froude number varies between 0.015 and 0.05, while the Reynolds number and level of dispersion are varied in a broader range to span different regimes. In all cases, most of the energy in the system remains in the waves, even after integrating the system for very long times. For shallow flows, nonlinear waves are nondispersive and the spectrum of potential energy is compatible with ∼k-2 scaling. For deeper (Boussinesq) flows, the nonlinear dispersion relation as directly measured from the wave and frequency spectrum (calculated independently) shows signatures of dispersion, and the spectrum of potential energy is compatible with predictions of weak turbulence theory, ∼k-4/3. In this latter case, the nonlinear dispersion relation differs from the linear one and has two branches, which we explain with a simple qualitative argument. Finally, we study probability density functions of the surface height and find that in all cases the distributions are asymmetric. The probability density function can be approximated by a skewed normal distribution as well as by a Tayfun distribution. © 2014 American Physical Society. Fil:Mininni, P.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_15393755_v89_n6_p_ClarkDiLeoni |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
topic |
Coastal engineering Dispersions Normal distribution Potential energy Probability density function Reynolds number Turbulence Water waves Boussinesq model Frequency spectra Nonlinear dispersion relation Nonlinear waves Shallow water flow Shallow water model Wave turbulence Weak turbulence Dispersion (waves) water chemical model chemistry computer simulation flow kinetics hydrodynamics nonlinear system procedures statistical model water flow Computer Simulation Hydrodynamics Models, Chemical Models, Statistical Nonlinear Dynamics Rheology Water Water Movements |
spellingShingle |
Coastal engineering Dispersions Normal distribution Potential energy Probability density function Reynolds number Turbulence Water waves Boussinesq model Frequency spectra Nonlinear dispersion relation Nonlinear waves Shallow water flow Shallow water model Wave turbulence Weak turbulence Dispersion (waves) water chemical model chemistry computer simulation flow kinetics hydrodynamics nonlinear system procedures statistical model water flow Computer Simulation Hydrodynamics Models, Chemical Models, Statistical Nonlinear Dynamics Rheology Water Water Movements Clark Di Leoni, P. Cobelli, P.J. Mininni, P.D. Wave turbulence in shallow water models |
topic_facet |
Coastal engineering Dispersions Normal distribution Potential energy Probability density function Reynolds number Turbulence Water waves Boussinesq model Frequency spectra Nonlinear dispersion relation Nonlinear waves Shallow water flow Shallow water model Wave turbulence Weak turbulence Dispersion (waves) water chemical model chemistry computer simulation flow kinetics hydrodynamics nonlinear system procedures statistical model water flow Computer Simulation Hydrodynamics Models, Chemical Models, Statistical Nonlinear Dynamics Rheology Water Water Movements |
description |
We study wave turbulence in shallow water flows in numerical simulations using two different approximations: the shallow water model and the Boussinesq model with weak dispersion. The equations for both models were solved using periodic grids with up to 20482 points. In all simulations, the Froude number varies between 0.015 and 0.05, while the Reynolds number and level of dispersion are varied in a broader range to span different regimes. In all cases, most of the energy in the system remains in the waves, even after integrating the system for very long times. For shallow flows, nonlinear waves are nondispersive and the spectrum of potential energy is compatible with ∼k-2 scaling. For deeper (Boussinesq) flows, the nonlinear dispersion relation as directly measured from the wave and frequency spectrum (calculated independently) shows signatures of dispersion, and the spectrum of potential energy is compatible with predictions of weak turbulence theory, ∼k-4/3. In this latter case, the nonlinear dispersion relation differs from the linear one and has two branches, which we explain with a simple qualitative argument. Finally, we study probability density functions of the surface height and find that in all cases the distributions are asymmetric. The probability density function can be approximated by a skewed normal distribution as well as by a Tayfun distribution. © 2014 American Physical Society. |
format |
JOUR |
author |
Clark Di Leoni, P. Cobelli, P.J. Mininni, P.D. |
author_facet |
Clark Di Leoni, P. Cobelli, P.J. Mininni, P.D. |
author_sort |
Clark Di Leoni, P. |
title |
Wave turbulence in shallow water models |
title_short |
Wave turbulence in shallow water models |
title_full |
Wave turbulence in shallow water models |
title_fullStr |
Wave turbulence in shallow water models |
title_full_unstemmed |
Wave turbulence in shallow water models |
title_sort |
wave turbulence in shallow water models |
url |
http://hdl.handle.net/20.500.12110/paper_15393755_v89_n6_p_ClarkDiLeoni |
work_keys_str_mv |
AT clarkdileonip waveturbulenceinshallowwatermodels AT cobellipj waveturbulenceinshallowwatermodels AT mininnipd waveturbulenceinshallowwatermodels |
_version_ |
1807318839328768000 |