Wind generated surface waves Miles and Jeffreys theories in finite depth Modelisation & Forecast

Transcription

1 Wind generated surface waves Miles and Jeffreys theories in finite depth Modelisation & Forecast F. Bouchette, M. Manna and P. Montalvo Laboratoire Charles Coulomb (L2C), UMR 5221 UM-CNRS Geosciences Montpellier (GM), UMR 5221 UM-CNRS 12 juillet 2017 F. Bouchette, M. Manna and P. Montalvo (LaboratoireWind Charles generated Coulomb surface (L2C), waves UMR 5221 Miles UM-CNRS and Jeffreys Geosciences theoriesmontpellier in finite depth (GM), Modelisation UMR 12 juillet UM-CNRS) & Forecast 1 / 1

2 ACKNOWLEDGEMENTS MIPS Philippe COMBETTE (IES) Pascale FABRE (L2C) Estelle PITARD (L2C). Bouchette, M. Manna and P. Montalvo (LaboratoireWind Charles generated Coulomb surface (L2C), waves UMR 5221 Miles UM-CNRS and Jeffreys Geosciences theoriesmontpellier in finite depth (GM), Modelisation UMR 12 juillet UM-CNRS) & Forecast 2 / 1

3 PLAN Introduction The linear growth rate Γ Main parameters controling wave growth Lake George experiments. Modelisation & forecast with the Miles theory Γ-Miles versus Γ-Jeffreys. Forecast What was done and what remains to be done? Projects F. Bouchette, M. Manna and P. Montalvo (LaboratoireWind Charles generated Coulomb surface (L2C), waves UMR 5221 Miles UM-CNRS and Jeffreys Geosciences theoriesmontpellier in finite depth (GM), Modelisation UMR 12 juillet UM-CNRS) & Forecast 3 / 1

4 Littoral processes F. Bouchette, M. Manna and P. Montalvo (LaboratoireWind Charles generated Coulomb surface (L2C),waves UMR 5221 Miles UM-CNRS and Jeffreys Geosciences theoriesmontpellier in finite depth (GM),Modelisation UMR 12 juillet UM-CNRS) & Forecast 4/1

5 Introduction When wind blows over the free ocean surface energy and momentum flow continuously from the air to the water Surface ocean waves are generated and propagate (in deep or finite depth) Two main theories (deep water) : The Jeffreys theory and the The Miles theory Main goal : to study the Miles and the Jeffreys theories in finite depth. Bouchette, M. Manna and P. Montalvo (LaboratoireWind Charles generated Coulomb surface (L2C), waves UMR 5221 Miles UM-CNRS and Jeffreys Geosciences theoriesmontpellier in finite depth (GM), Modelisation UMR 12 juillet UM-CNRS) & Forecast 5 / 1

6 The linear growth rate Γ (no wind) η(x, t) = a cos 2π λ (x ct), a, λ, c constants (wind) η(x, t) = aexp Γt cos 2π λ (x ct), λ c Γ = Γ Miles = Γ M Resonance mechanism Γ = Γ Jeffreys = Γ J Sheltering mechanism The main results of our work : we have obtained Γ M and Γ J in finite depth Γ = Γ(U 10, δ, θ fd,... ). Bouchette, M. Manna and P. Montalvo (LaboratoireWind Charles generated Coulomb surface (L2C), waves UMR 5221 Miles UM-CNRS and Jeffreys Geosciences theoriesmontpellier in finite depth (GM), Modelisation UMR 12 juillet UM-CNRS) & Forecast 6 / 1

7 Main parameters controling wave growth U 10 wind at a height of z = 10m δ = gh U 10, finite deep wave age θ fd = κ gλ u 2π λ 0 tanh 2πh λ θ fd 0 (young wave or young sea) λ θ fd κ u gh (old wave or old sea). Bouchette, M. Manna and P. Montalvo (LaboratoireWind Charles generated Coulomb surface (L2C), waves UMR 5221 Miles UM-CNRS and Jeffreys Geosciences theoriesmontpellier in finite depth (GM), Modelisation UMR 12 juillet UM-CNRS) & Forecast 7 / 1

8 Lake George experiments. Modelisation & forecast with the Miles theory t t. Bouchette, M. Manna and P. Montalvo (LaboratoireWind Charles generated Coulomb surface (L2C), waves UMR 5221 Miles UM-CNRS and Jeffreys Geosciences theoriesmontpellier in finite depth (GM), Modelisation UMR 12 juillet UM-CNRS) & Forecast 8 / 1

9 Γ-Miles versus Γ-Jeffreys. Forecast Depending on wave age and wind velocity, the Miles and Jeffreys wave growths are compared in order to determine which of them dominates R = Γ J Γ M FIGURE : R < 1 the Miles Γ M is dominant, R > 1 the Jeffreys Γ J is dominant. Bouchette, M. Manna and P. Montalvo (LaboratoireWind Charles generated Coulomb surface (L2C), waves UMR 5221 Miles UM-CNRS and Jeffreys Geosciences theoriesmontpellier in finite depth (GM), Modelisation UMR 12 juillet UM-CNRS) & Forecast 9 / 1

10 What was done and what remains to be done? (x, z, t) (x, y, z, t) z = h, z = h(x, y) no vorticity with vorticity no bottom friction bottom friction U 10 < 30ms 1 ( 110kmh 1 ) U 10 > 30ms 1 only temporal growth spatial growth (fetch) linear non linear. Bouchette, M. Manna and P. Montalvo (LaboratoireWind Charles generated Coulomb surface (L2C), waves UMR 5221 Miles UM-CNRS and Jeffreys Geosciences theoriesmontpellier in finite depth (GM), Modelisation UMR 12 juillet UM-CNRS) & Forecast 10 / 1

11 Collaborations Laboratoire Charles Coulomb (L2C UMR 5221 CNRS-UM) Géosciences Montpellier (GM UMR 5243 UM) Institut de Recherches sur des Phénomènes Hors Équilibre (IRPHE, UMR 7342, CNRS Université de Marseille) Institut Méditerranéen d Oceanographie (MIO, UMR 7294 CNRS Université de Toulon) Universidade de São Paulo (Instituto de Fisica Teorica, São Paulo, Brasil) Qom University of Technology (Department of Physics, Qom, Iran). Bouchette, M. Manna and P. Montalvo (LaboratoireWind Charles generated Coulomb surface (L2C), waves UMR 5221 Miles UM-CNRS and Jeffreys Geosciences theoriesmontpellier in finite depth (GM), Modelisation UMR 12 juillet UM-CNRS) & Forecast 11 / 1

12 Publications P. Montalvo et al. Journal of Coastal Engineering, 77, (2013). P. Montalvo et al. Nat. Hazards Earth Syst. Sci., 13, (2013). M. Manna et al. Phys. Rev. E 90, (2014). M. Manna et al.wind generated surface waves : linear and nonlinear theories, submmited to Journal of Applied Fluid Mechanics (2016). M. Manna et al Green-Nagdhi dynamics of surface wind waves in finite depth, submmited to Wave Motion (2017). M. Manna et al.green-naghdi type equations with vorticity, submmited to JFM (2017).. Bouchette, M. Manna and P. Montalvo (LaboratoireWind Charles generated Coulomb surface (L2C), waves UMR 5221 Miles UM-CNRS and Jeffreys Geosciences theoriesmontpellier in finite depth (GM), Modelisation UMR 12 juillet UM-CNRS) & Forecast 12 / 1