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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Autor principal:	Mininni, Pablo Daniel
Publicado:	2014
Materias:	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
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v89_n6_p_ClarkDiLeoni http://hdl.handle.net/20.500.12110/paper_15393755_v89_n6_p_ClarkDiLeoni
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_15393755_v89_n6_p_ClarkDiLeoni
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spelling	paper:paper_15393755_v89_n6_p_ClarkDiLeoni2023-06-08T16:21:01Z Wave turbulence in shallow water models Mininni, Pablo Daniel 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. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v89_n6_p_ClarkDiLeoni 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 Mininni, Pablo Daniel 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.
author	Mininni, Pablo Daniel
author_facet	Mininni, Pablo Daniel
author_sort	Mininni, Pablo Daniel
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
publishDate	2014
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v89_n6_p_ClarkDiLeoni http://hdl.handle.net/20.500.12110/paper_15393755_v89_n6_p_ClarkDiLeoni
work_keys_str_mv	AT mininnipablodaniel waveturbulenceinshallowwatermodels
_version_	1768545617929306112

Wave turbulence in shallow water models

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