e1df0719-823e-4f91-916e-1900f987303820220913083450011wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS2224-34291991-874710.37394/232011http://wseas.org/wseas/cms.action?id=40061520221520221710.37394/232011.2022.17https://wseas.com/journals/mechanics/2022.phpBreaking Wave Simulations by a New k−l Turbulence ModelFrancescoGalleranoDepartment of Civil, Constructional and Environmental Engineering Sapienza University of Rome Rome, ITALYBenedettaIeleDepartment of Civil, Constructional and Environmental Engineering Sapienza University of Rome Rome, ITALYFedericaPalleschiDepartment of Civil, Constructional and Environmental Engineering Sapienza University of Rome Rome, ITALYGiovanniCannataDepartment of Civil, Constructional and Environmental Engineering Sapienza University of Rome Rome, ITALYThe three-dimensional motion equations are used to simulate the wave and velocity fields. These equations are written in integral contravariant form on a time-dependent curvilinear coordinate system. In this paper a new ?−? turbulence model in contravariant form is proposed for three-dimensional simulation of breaking waves. In this model the mixing length is defined as a function of the first and second spatial derivatives of the maximum water surface elevation.9132022913202211311715https://wseas.com/journals/mechanics/2022/a305111-011(2022).pdf10.37394/232011.2022.17.15https://wseas.com/journals/mechanics/2022/a305111-011(2022).pdf10.1016/j.ocemod.2011.12.002G. Ma, F. Shi, J.Y. Kirby, “Shock-capturing non-hydrostatic model for fully dispersive surface wave processes”, Ocean Model, vol. 43-44, pp. 22-35, 2012. 10.1007/s00161-018-0703-1G. Cannata, C. Petrelli, L. Barsi, F. Gallerano, “Numerical integration of the contravariant integral form of the Navier–Stokes equations in time-dependent curvilinear coordinate systems for three-dimensional free surface flows”, Contin. Mech. Thermodyn. vol. 31, pp. 491–519, 2019. 10.37394/232013.2020.15.4B. Iele, F. Palleschi, “Boundary conditions for the simulation of wave breaking”, WSEAS Transac. Fluid Mech., vol. 15, pp. 41-53, 2020. K.Z. Fang, Z.B Liu, “Modeling breaking waves and wave-induced currents with fully nonlinear Boussinesq equations”, WSEAS Transac. Fluid Mech., vol. 9, pp. 131-143, 2014. F. Palleschi, B. Iele, F. Gallerano, “Integral contravariant form of the Navier-Stokes equations”, WSEAS Transac. Fluid Mech., vol. 14, pp. 101-113, 2019. 10.1061/(asce)0733-950x(2000)126:1(1)S. F. Bradford, “Numerical simulation of surf zone dynamics”, J. Waterw. Port, Coast. Ocean Eng., vol. 126, pp. 1-13, 2000. 10.37394/232013.2020.15.4F. Gallerano, G. Cannata, L. Barsi, F. Palleschi, B. Iele, “Simulation of wave motion and wave breaking induced energy dissipation”, WSEAS Transac. Fluid Mech., vol. 14, pp. 62-69, 20191. 10.1006/jcph.1996.0130G.Jiang, C. Shu, “Efficient Implementation of Weighted ENO Schemes”, J. Comput. Phys., vol. 126, pp. 202-228, 1996. 10.1016/j.jcp.2020.109902J. Peng, S. Liu, S. Li, K. Zhang, Y. Shen, “An efficient targeted ENO scheme with local adaptive dissipation for compressible flow simulation”, J. Comput. Phys., vol. 425, pp. 1-25, 2021. 10.37394/232013.2020.15.8F. Gallerano, G. Cannata, “Noll’s axioms and formulation of the closure relations for the subgrid turbulent tensor in Large Eddy Simulation”, WSEAS Transac. Fluid Mech., vol. 15, pp. 85-90, 2020. P.L.F. Liu, P. Lin, “A numerical model for breaking waves: the volume of fluid method”, Res Report No. CACR-97-02, pp. 1-54, 1997. F.C.K. Ting, J.T. Kirby, “Observation undertow and turbulence in a wave period”, Coast. Eng., vol. 24, pp. 177–204, 1995.