Wave turbulence in shallow water models

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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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Detalles Bibliográficos
Autores principales: Clark Di Leoni, P., Cobelli, P.J., Mininni, P.D.
Formato: JOUR
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: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 todo:paper_15393755_v89_n6_p_ClarkDiLeoni
record_format dspace
spelling 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
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